RECENT ADVANCES IN THE MODELING AND SIMULATION OF …nanomaterials2019.usacm.org/.../files/NanoscaleMechanicsWorksho… · techniques and applications of machine learning to gain

RECENTADVANCESINTHEMODELINGANDSIMULATIONOFTHEMECHANICSOFNANOSCALEMATERIALS

OrganizingCommittee:VasilyBulatov,LawrenceLivermoreNationalLaboratory

Long-QingChen,PennsylvaniaStateUniversityCeliaReina,UniversityofPennsylvania

DavidSrolovitz,UniversityofPennsylvania

Authors:CeliaReina,UniversityofPennsylvania

AakashKumar,UniversityofPennsylvania

U ACM

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TableofCONTENTS

INTRODUCTION 5

SESSION1:FIRSTPRINCIPLECALCULATIONSANDQUANTUMPROPERTIES 6

VikramGavini:Large-scalereal-spaceelectronicstructurecalculations 6

AmartyaBanerjee.Symmetry,deformationsandthesearchforunprecedentedmaterialsfromfirstprinciples. 8

MauricioPonga:Howdefectsaffectquantummechanicalpropertiesincrystallinematerials. 9

SESSION2:PLASTICITY 10

DavidRodney:Physicalfoundationofnon-SchmidyieldcriterioninBCCmetals 10

EugenRabkin.Themicrostructuraloriginsofsizeeffectinstrengthofmetalnanoparticles. 12

JohnBassani:Non-associativeplasticflow:insightsfrommultiscalesimulations 13

SESSION3:DEFECTSI 14

DavidMcDowell.Somechallengesinlengthandtimescalingformodelingdislocations. 14

MichaelOrtiz.AtomisticsimulationofhydrogenstorageinPdnanoparticles. 16

EmmanuelClouet.Secondaryslipofscrewdislocationsinhcpzirconium. 17

SESSION4:DEFECTSII 18

JaimeMarian.Simulatingdynamicstrainaginginbody-centeredcubicmetalsondiffusivetimescales 18

AnterEl-Azab.Acontinuumtheoryfordefectsandmicrostructureevolutionunderirradiation. 20

SESSION5:GRAINBOUNDARIESANDINTERFACES 21

YashashreeKulkarni.Mechanisticinsightsintocrystallineinterfacesviathermalfluctuations 21

NikhilAdmal.Polycrystalplasticitywithanisotropicgrainboundaryevolution 22

BrandonRunnels.Unifyingmechanismsofgrainboundarymigrationthroughacontinuumthermodynamicframework. 23

SESSION6:MECHANICSOFMATERIALSI 25

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GarrittTucker.Implementinghigher-orderdescriptorstounravelcompetingdeformationeffectsatanatomicscale 25

TimothyRupert.Probingnanoscalecomplexiontransformationswithcomputationaltechniquesthatcomplementexperiments. 26

JunLou.Quantitativein-situnanomechanicalstudyoflowdimensionalmaterials. 27

MitraTaheri.Towardthetailoringofmaterialspropertiesfarfromequilibrium:convergenceofmicroscopy,dataScience,andtheory 28

SESSION7:MECHANICSOFMATERIALSII 29

RyanElliott.Aframeworkfortheinterpretationofmodulatedmartensitesinshapememoryalloys 29

PrashantPurohit.Interactionsandassemblyofinclusionsonlipidmembranes. 31

AndrejKosmrlj.Statisticalmechanicsofmicroscopicallythinthermalizedstructures. 32

SESSION8:MECHANICSOFMATERIALSIII 34

PradeepSharma.FlexoelectricityandElectrets 34

KaushikDayal.Electromechanicsandstatisticalmechanicsofdielectricelastomers 35

PedroPonte-Castaneda.Macroscopicinstabilitiesanddomainformationinelastometriccomposites 36

SESSION9:PHASEFIELDMODEL 38

PeterVoorhees.Themorphologyandtopologyofnanoporousmetals 38

PeterVoorheeswasabsentduetomedialreasonsandthepresentationwasthereforenotgiven. 38

KatsuyoThornton.Nanoscalesimulationsusingphase-fieldcrystalmodels 38

MartinDiehl.Couplingcrystalplasticityandphasefieldmethods:thefutureofintegratedcomputationalmaterialsengineering? 39

SESSION10:SCALEBRIDGINGI 40

JarekKnap.AcceleratingScaleBridgingviaSurrogateModeling 40

YuriMishin.Physcally-informedartificialneuralnetworksforatomisticmodelingofmaterials 41

XinYan.Time-scalinginatomisticandtherate-dependentmechanicalbehaviorofnanostructures 42

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SESSION11:SCALEBRIDGINGII 43

DanMordehai.Calculatingtheactivationparametersofthermallyactivateddislocationmechanisms 43

AndreaLiu.Whatwelearnfrommachinelearning 44

DISCUSSIONSANDOPENCHALLENGES 45

POSTERPRESENTATIONS 48

ADMINISTRATIVESUPPORTANDACKNOWLEDGEMENTS 50

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IntroductionThe workshop “Recent Advances in the Modeling and Simulation of the Mechanics ofNanoscaleMaterials"washeldattheSinghCenterforNanotechnologyoftheUniversityofPennsylvania in Philadelphia from August 21-23, 2019. It was a US Association ofComputational Mechanics (USACM) thematic workshop under the auspices of theNanotechnology Technical Thrust Area (TTA), which received financial support from theNationalScienceFoundation.Itbroughttogetherexpertsattheforefrontofthemodelingandsimulationofthemechanicsof nanoscale materials, to discuss recent advances in electronic structure calculations,atomistic modeling, continuum approaches for microstructure evolution, scale bridgingtechniques and applications of machine learning to gain fundamental insight in materialbehavior.Topicsofinterestalsoincludedtheapplicationofthesetechniquestogaininsightintoeffectivematerialresponse.The workshop included the participation of junior and senior faculty members via 32invitedpresentations,aswellas19PhDstudentsandpostdocs,whosharedtheirresearchvia poster presentations. The total number of attendees was 64, which enabled vividdiscussionsamongallparticipants.Thethree-daymeetingwasorganizedinelevensessions,whichincludedasessiononfirstprinciple calculations and quantum properties, a session on plasticity, two sessionsdedicated to defects, one session on grain boundaries and interfaces, three sessionsfocusingonmechanicsofmaterials,onesessiononphasefieldmodels,anditwasconcludedwith two sessions on scale bridging, which included talks on applications of machinelearningtechniquestoaidthesame.

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Each of the presentations was 30 minutes long including questions. Presenters wereencouraged to discuss open challenges in the modeling and simulation of nanoscalephenomenainadditiontotheirrecentadvancesinthefield,withtheobjectiveofpromotingdiscussionsduringtheworkshop.Thisreportprovidesadetaileddescriptionoftheworkshop.Itincludesasummaryofallthepresentations, followingtheconferenceprogram,aswellasasummaryofthediscussions,identifying important challenges and opportunities for this community. A list of posterpresentations is also included. The report concludes with an acknowledgement of alladministrativeandtechnicalstaffs,whichwereinstrumentalintheorganization,executionandsuccessofthisworkshop.

Session1:FirstPrincipleCalculationsandQuantumProperties

VikramGavini:Large-scalereal-spaceelectronicstructurecalculationsOverviewandmotivation:About 25% of high performance computing resources for scientific and technologicalpursuitarededicatedtoelectronicstructurecalculations.Thesecalculations, inparticular,DensityFunctionalTheory(DFT)haveenjoyedgreatsuccess in theaccuratepredictionofvariousphasesinmaterialsaswellasdefectenergetics.Despiteitssuccess,therearethreeimportantchallenges:

1. Simulationdomainsizerestrictions:Mostsimulationcodesarebasedonplane-wavediscretization,whichrequireperiodicboundaryconditions.

2. Pseudo-potential approximation: It has been shown that this may not betransferable for transition metals, or extreme environments like high-pressureconditions.

3. Themodelexchange-correlation(X-C)functionals(whichaccountsforallquantummechanicalinteractions)donotworkforstronglycorrelatedsystems.

Background:TheKohn–Sham(KS)equations(eigenvalueproblem)arethegoverningequationsforDFT.ThestateoftheartforsolvingthemcanbedividedbetweenFourierspaceformulationsandrealspaceformulations.Theformerarethemostpopular.Ithasspectralconvergenceanditis very efficient forperiodicproblems, although it has auniform resolution (not ideal fordefect calculations), and present scalability issues. The other approach is real spaceformulations.Withinthisclass,FEdiscretizationsofKS-DFThaveinterestingfeatures, likesystematic convergence, can handle complex geometries and boundary conditions, andresolutioncanbe increasedwhereneeded.Finally it isbasedon localbasis functionsandscalesverywellonparallelarchitectures.Themaindisadvantagesarethatitrequiresmanybasis functions and it results in a generalized eigenvalue problem. First efforts in thisdirection using linear finite elements appeared to indicate that this method was nottractable.However,higherorderfiniteelementsshowedabetterperformance,withclosetooptimalconvergence.Thoughthisdoesnotsolvetheissuesassociatedwiththegeneralizedeigenvalueproblem.

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Approachandresults:To tackle these challenges, a FE approach based on spectral finite elements is presented,which uses a Gauss-Lobatto-Legendre quadrature rule and a Chebyshev accelerationtechnique. Benchmark calculations with other open source codes such as QuantumEspresso, indicate much faster calculations for both periodic and non-periodic systems,thanks to its great scalability. These developments are available in an open source code(DFT-FE).DFT-FE can also handle all-electron calculations although it is not very efficient ascompared to using Gaussian basis. To speedup the calculation, an enriched FE basis isproposed, which utilizes results from single atom Kohn-Sham calculations, truncated tomaintainlocalsupport.Thisleadstoasignificantlyreducednumberofdegreesoffreedomandreducedspectralwidthof theHamiltonian.Thespeedupachieved isof twoordersofmagnitude for silicon nanoclusters, and it rapidly becomes faster than NWChem as thesystemsizeincreases.Finally, to address the challenge associated with X-C approximations, the followingframeworkwasproposed.Theideaistodomanybodyquantumcalculationsonsmallscalesystems,wherethesecalculationsarepossible,andthensolvetheinverseDFTproblemi.e.findtheX-Cfunctionalthatwouldgivethesamesolution.SincetheX-Cpotentialandenergyis universal,machine learning couldbeused to systematically improve thedescriptionofthe X-C potential. However, doing inverse DFT has been a long-standing challenge incomputationalchemistry.Thefacedchallengeswereprimarilyassociatedwiththefactthatthe Gaussian basis used are incomplete and have thewrong asymptotics, which leads tospuriousoscillationsinthesolution.Arecentbreakthroughonthisfronthasbeenachievedby combining 4 key elements: PDE constrained optimization, a complete higher order FEbasis for discretization, cusp correction, and using homogeneous Dirichlet boundaryconditions to take care of the far-field asymptotics. This allowed computing the X-Cpotentialtochemicalaccuracy.Conclusions:

• LargescaleKSDFTcalculationswereachievedusingarealspaceformulationwithhigherorderFEelementbasisandChebyshevfiltering.

• Efficient all electron KS-DFT where achieved using FE by using enrichmentfunctionsandadaptivequadratures.

• Successfully solved the inverse DFT problem to compute the X-C potential tochemicalaccuracy.

References:[1]P.Motamarrietal.,“DFT-FEAmassivelyparalleladaptivefinite-elementcodeforlarge-scaledensityfunctionaltheorycalculations,”ComputerPhysicsCommunications246(2020):106853. [2] B. Kanungo et al., “Exact exchange-correlation potentials from ground-state electrondensities,”NatureCommunications,10,4497,2019

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AmartyaBanerjee.Symmetry,deformationsandthesearchforunprecedentedmaterialsfromfirstprinciples. Overviewandmotivation:Symmetries in materials can be thought of as a fundamental concept to motivate thediscoveryandcharacterizationofnewmaterials.Amathematicalframeworktocharacterizematerials beyond classical periodic structures (i.e., crystals) is based on the concept ofObjective Structures. These are structures in which corresponding atoms see the sameenvironmentup toa translationandorthogonal transformation.Theyareassociatedwithnon-periodicsymmetriesandalmostallelementsintheperiodictableorganizethemselvesin the form of objective structures (e.g., crystals, helical nanotubes, fullerene). ClassicalDensityFunctionalTheory(DFT)codesaredesignedforstudyingperiodiccrystalsandarenot suitable for the general class of objective structures. Here, Objective-DFT (i.e., a DFTmethod for specifically studying Objective Structures) is presented and applied to twoclassesofobjectivestructures:(i)clustersandmolecules,and(ii)helicalstructures.Approachandresults:The formulation and implementation of Objective-DFT is presented following a structurethat is analogous to classical DFT codes based on the plane wave method (for instance,generalized harmonic analysis is used instead of Fourier transform, and objective/helicalwavesareusedasbasissetsinsteadofplanewaves).Theresultingformulationenablestheuseofsymmetriestoreducethecomputationalcostofstudyingtheelectronicpropertiesofa given structure. Additionally, it enables the electronic structure calculations ofnanostructures under non-uniform deformations such as bending and torsion, which arenot easy to model using conventional approaches (i.e., employing periodic boundaryconditions). Some examples presented include the prediction of the bendingmodulus ofgraphene,silicene,germaneneandstaneneneabinitio.ObjectiveDFTalsoproducescyclicband diagrams which allow one to see the changes in the electronic structure of ananomaterialasitisbent.Finally,thecaseofhelicalsymmetryisdiscussed.Asanexample,black phosphorus nanotubes undergoing twisting are studied using this method. ThetwistingstiffnessofthisstructureusingObjectiveDFTcanbepredicted,andtheeffectsofatomicrelaxationcanbeincluded.Inthiscase,ahelicalbanddiagramisobtained,andthisshowsatransitionfrominsulatortometalforsomenanotubes.Conclusions:

• ObjectiveDFTisdevelopedasapowerfultooltostudyobjectivestructures.• ObjectiveDFT is likely tobe instrumental in thediscoveryandcharacterizationof

novelmaterials.• Properties of cyclic and helical structures are explored using implementations of

ObjectiveDFT,andinterestingnanoscalephenomenaarediscoveredandstudied.

References:[1] A. Banerjee et al., “A spectral scheme for Kohn-Sham density functional theory ofclusters,”JournalofComputationalPhysics287(2015),226-253.[2] A. Banerjee et al., “Cyclic density functional theory: A route to the first principlessimulation of bending in nanostructures”, Journal of Mechanics and Physics of Solids 96(2016),pp605-631.

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[3] S. Ghosh et al. “Symmetry-adapted real-spacedensity functional theory for cylindricalgeometries:Application to largegroup-IVnanotubes”.PhysicalReviewB,100(12)(2019),125143.

Mauricio Ponga: How defects affect quantum mechanical properties incrystallinematerials.(JointworkwithDavidFunes,NormanMuller)Thistalkwascomposedoftwoparts:PartI:Superconductingradiofrequencycavities.PartII:Frameworktopredicttwinningin2Dmaterials.Overviewandmotivation(partI):Meissner effect in superconducting radio frequency cavities is a manifestation of exoticquantumbehavior:when the temperature is above the critical temperature themagneticfield penetrates the material. However, when the temperature is lower than the criticaltemperatureandittransitionstothesuperconductingstate,themagneticfieldisrepulsedand thematerial acts as amagnet. In the presence of defects, themagnetic field can gettrapped in the material, which can kill the superconducting state. This problem is ofrelevanceinparticleaccelerators,whereitisobservedthatthermaltreatmenthasastrongimpactinthepropertiesofcavitiesasitinfluencesthedefectpattern.Thegoalsofthestudiespresentedareto(i)understandtheeffectofannealingprocessondislocationdensity,(ii)obtainabasicunderstandingofdislocationclimb,and(iii)provideaframeworktosimulatethesephenomena.Abigchallengeisthetimescale,asthethermalprocesscantakehoursordays.Approachandresults(partI):The toolsused to tackle the timescale challengeareacceleratedmoleculardynamicsanddiscretedislocationdynamics.Experimentalresultsarealsousedforvalidation.ThefirstprocesssimulatedisdislocationclimbinNb,facilitatedviavacancies.Thevacancydiffusion ismodeled using the approach of Venturini andOrtiz to characterize the grandcanonicalfreeentropyofthematerialasafunctionoftheoccupationnumber,andaFokker-Planckequation,tomodelthetransportprocess.Thecodeisanadd-ontoLAMMPSandwasused to analyze the climb of edge and screw dislocations in Nb. The annealing ofdislocationsisthensimulatedusingdiscretedislocationdynamicsandtheresultsarebeingvalidatedagainstexperimentalresults.Overviewandmotivation(partII):Two-dimensional materials exhibit defects such as dislocations, vacancies, holes, grainboundaries, though their interplay has been less studied than in three-dimensionalmaterials.Theprecisegoalwastoexploretwinningin2dmaterialsasamechanismforachievingnewpropertiesinasystematicwayviadeformation.

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Approachandresults(partII):Twiningisaplanardefectwherebythetwosidesarerelatedtoeachotherviaarotationorshear satisfying the twinning equation. This twinning equation serves as a kinematicframework to explore all possible twin configurations. Interestingly the number of twinpossibilitiesisextremelylarge,evenin2D,andthelowdeformationoneswereanalyzedinfurtherdetail.Theenergy for theseselectedmodeswerecomputedwithatomisticandabinitiomethods.SomeoftheonescomputedforMoS2havealsobeenfoundexperimentally.Manyoftheseboundarieshavebeenobservedtoemergenumericallywhendeformingthematerialunderuniaxialloading.Next, the electronic properties of the material were analyzed. Twin boundaries did notchangethenatureofthematerialforgraphene,butthebandgapsweremodifiedforMoS2.This implies that the electronic behavior and thermal conductivity of thematerial canbemodifiedbymeansofdefects.Conclusions:

• Modelingcapabilitiestolinkdefectandquantummechanicsarestilllimited.• The interplay between twinning defects and electronic properties, provides a

mechanism for controlling electronic and thermal behavior via mechanicaldeformations.

References:[1]D.F.Rojasetal.,“Twinningintwo-dimensionalmaterialsanditsapplicationtoelectronicproperties”,ElectronicStructure96(2019)1,025001.

Session2:Plasticity

DavidRodney:Physicalfoundationofnon-SchmidyieldcriterioninBCCmetals (JointworkwithEmmanuelClouet,LisaVentelon,FrançoisWillaime,LucileDezeraldandAntoineKraych)Overviewandmotivation:ExperimentalevidenceshowsthatBCCmetalsdonotfollowSchmidlaw,inwhichplasticityiscontrolledbytheshearstressalongtheBurgersvectorofthedislocationprojectedontothe glide plane: (i) they exhibit twinning-antitwinning asymmetry, and (ii) othercomponentsoftheyieldstressareshowntoaffecttheplasticbehavior.Tocharacterizethisnon-Schmidteffect,authorshaveusedageneralizedyieldcriterion,inwhich stresses that affect dislocation glide are combined linearlywith phenomenologicalparameters (one parameter, a1, for twinning/antitwinning asymmetry, and two moreparameters for non-glide effects). These parameters are often identified using atomisticsimulations,usingafittingprocedure.However,thereisnocompleteunderstandingonthephysicaloriginsof theseparameters,and it isalsounclearwhysucha linearcombinationworks sowell.Answering thesequestions (for screwdislocations) isprecisely thegoalofthispresentation.

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Approachandresults:Detailedstudiesonthe twinning-antitwinningasymmetryreveal that therearedeviationsinthedislocationpathwithrespecttotheglideplanewhengoingfromonewelltothenext.This therefore implies that thedriving forceon thedislocationhas tobeprojectedon theactual trajectory.Approximating thepathaspiecewise linear, amodifiedSchmid lawwaswrittenthatdependsonthedeviationangle(α).ThisangleismaterialdependentandcanbecomputedfromDFT.Thissimplecorrectionqualitativelyreproducesexperimentaldataand quantitatively reproduces results from DFT calculations. Interestingly, usingtrigonometric identities, the functional form previously proposed on phenomenologicalgroundsisrecovered,withanexplicitdependenceoftheparametera1onalpha.Non-glideeffectsare thenstudiedusingDFTbyapplyingpureshearperpendicular to theBurgers vector of the dislocation. As expected the Peierls barrier depends on the shearstress. This has been qualitatively explained by Vitek, is based on the fact that thedisplacement field perpendicular to the dislocation is dilatational and that there is acoupling between the external field and the dilatational field. To understand thisquantitatively,itisproposedtomodelthedislocationcoreasanEshelbyinclusion,andusethe eigenstrain approach of Mura to model the coupling, namely, how internal stresseschangealongthePeierlsbarrier.TheresultingpredictionsfallrightontopoftheDFTdata,bothwithandwithoutresolvedshearstress.Bothoftheaboveeffectscanthenbeputtogethertohaveamodelfortheenthalpyofthedislocation that recovers twinning/antitwinning asymmetry and non-glide effects.Furthermore a generalized yield criterion can be obtained by noting that, at the Peirelsbarrier, thefirstandsecondderivativeoftheenthalpyofthedislocationmustvanish.Theresultingyieldcriteriahastheclassicalfunctionalformpreviouslyutilized,wherenowtheparameters have a quantifiedphysicalmeaning anddependonα and the eigenstrain viarelaxation volumes. It is important to note that all the parameters that characterize non-glidebehaviorcanbecomputedfromthezerostressPeierlsbarrier.Conclusions:

• Twinning/antitwinning asymmetry is related to deviations of the dislocation pathawayfromtheglideplane

• Non-glide effects are due to the deformation of the dislocation core that can bemodeledusinganEshelbyinclusionapproach.

• Future work includes non-glide effects on twinning and extension to finitetemperatures.

References:[1] L.Dezerald et al. "Plastic anisotropy anddislocation trajectory inBCCmetals."NatureCommunications7(2016):11695.

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Eugen Rabkin.The microstructural origins of size effect in strength of metalnanoparticles.(JointworkwithTylerFlanagan,OlegKovalenko,Seok-WooLee)Overviewandmotivation:Theparadigm“Smaller isstronger” isnow10yearsold,and ithas itsoriginsprimarily incompressionexperimentsonfocusedionbeam(FIB)machinedmicroandnanopillars.Dataformtheseexperimentsapproximately followsamastercurvewhichdescribes thepowerlaw behavior of normalized resolved shear stress on the diameter of the pillar, and theexponentisabout-2/3.However,thefabricationtechniqueforthesenanopillarsintroducesmanydefects,primarilyatthesurfacelayer,whichcanhardenthesurfacethusmakingthepillarsstrongerasthesizeisreduced.OtherexperimentalmethodsviaetchinghaveenabledtofabricatemicropillarswithoutFIBandcompressionexperimentsontheserevealnosizeeffect.Itwasthenspeculatedthattheplasticity could be nucleation controlled. However, other deficiencies have also beenpointedoutforthisfabricationmethod:thepillarsresultingfromtheetchingprocessareasolidsolution,withsoluteatomsatadistancesmallerthanpillardiameter.Thiswork aims at understanding theorigin of the size effect of goldnanoparticlesundercompressionandexplainingsomeofthediscrepanciesthatexistbetweenexperimentsandtheory.Approachandresults:Dewetting of thin films on a substrate is proposed as an alternativemethod to fabricatenanostructures, namely, faceted nanoparticles, which form driven by the decrease of thetotalsurface/interfaceenergy.Theresultingparticlesarebelievedtobedefectfree,soitissuitabletostudynucleationcontrolledplasticity.The load displacement curves for faceted Au micro-particles exhibit an elastic regionfollowed by a sudden particle collapse. This critical stress for collapse is given by thenucleation of dislocations, which then proceed in avalanches leading to the suddendeformation. The compressive stress at which the collapse occurs approaches thetheoretical strength of Au (several GPa) and a trend of “smaller is stronger” with anexponent of 0.77 is observed. These findings were also supported by MD simulations,wheretheexponentfoundtherewasverysimilartotheexperimentalexponent.The above results were very satisfying. However later experiments on faceted Nimicroparticles obtained by solid state dewetting depicted different exponents for theexperimentsandsimulations(morethandoubleinexperiments). FurtherexperimentsonMo nanoparticles showed that while rounded particles exhibited no size dependence,facetedparticlesexhibitanunusuallyhighexponentofabout1.In view of these inconsistencies, further experiments on Au were performed. For largerparticles,thepreviousresultswererecovered,whereassmallerparticlesizesshowedsometrendofsaturation.TEManalysesoftheparticlesshowedthatsmallAuparticlesaredefect-freewhilelargerparticleshavedislocations.Thisprobablydeterminesthesizeeffect.Thiswas modeled using the truncated source model using the dislocation density fromexperiments. This model gave results similar to that of the experiments with saturation

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occurring forsmallerparticles.Thismodelwasalsoable toquantitativelypredict thesizeeffectofAupillars.Experimentally, large particles are probably large because they initially have defects thatenabletheirgrowthduringthedewettingprocess,andthisalso inducessizeeffectsundercompressiontest.Conclusions:

• Smallmetalparticlesobtainedbysolidstatedewettingaredefect-freeandachievethetheoreticalstrength.

• Largeparticlesarelargebecausetheycontaindefects• Defectsareresponsiblefortheartificialsizeeffectinstrength.

References:[1] A. Sharma et al. "Nickel nanoparticles set a new record of strength."NatureCommunications9,4102(2018).[2] T.J. Flanagan et al. "The effect of defects on strength of gold microparticles."ScriptaMaterialia171(2019):83-86.

JohnBassani:Non-associativeplasticflow:insightsfrommultiscalesimulationsOverviewandmotivation:Non-associativeplastic flowisrelatedtonon-Schmideffects incrystals, thoughitnotonlyhappens in crystals, but also in granular solids and amorphous materials. In crystals,dislocation coresmay not be confined to the slip planes, leading to a dependence of thePeierls stresson the full stress state (notonly shear stresses). Indisorderedsystems, thesourcesofplasticdeformationsaretheso-calledsheartransformationzones(STZs),whichcanshearundertheapplicationofstresses.Inbothcases,thejerkyflowisobserved,whichseems to be a characteristic of non-associative flow, much like slip-stick in frictionalmaterials.Historically, Schmid law was predominantly thinking of basal slip in hexagonal closed-packedmaterials.But,asnotedbyCottrell,fortoolong,fcchasbeentakenasthemodelforplastic behavior,while it really is the exception rather than the norm (dislocations in fccmaterialshaveveryplanarcores).PragerandDruckerstartedalreadythinkingaboutnon-associativeflow,astheyrecognizedthatfrictionwasamodelforplastictypebehavior.Itishereconjecturedthatnon-associatedflowistheappropriateplasticitytheoryformostmaterials,bothcrystallineanddisordered,andthatleadstosignificanteffects.Approachandresults:Asimplemechanismdisplayingnon-associatedplastic-flowbehaviorisfriction.Inthiscase,theyieldfunction(F)dependsontheshear(S)aswellasthenormalforce(N).Becausetheslipisnotinthedirectionofthenormalforce,theflowpotential(G)isadifferentfunction.Asasimpleexample,GcanbetakentojustbeS,although,ingeneral,itcandependonbothSandN.Theresultingdissipationispositivebutthereisasecondorderwork,whichcouldbenegativeandthatcouldleadtoahighlydestabilizingbehavior.

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Mathematically, non-associated flow (i.e., F and G different) leads to incrementalequilibrium equations that are not self-adjoint, and therefore one does not have nicevariationalprinciplesasforself-adjointsystems.VitekandGrogerstudiedthecorestructureunderstressofscrewdislocationsinMousingabondorderpotentialandastrongdiscrepancywasfoundwithrespecttoSchmidlaw.Basedon theseresults,amodifiedyieldcriteriawas formulated,where theeffectiveyieldstressdepends not only on the Schmid stress, but also on the other components. The resultingyield surface exhibits tension-compression asymmetry. Furthermore, the active slipsystems can actually be different in tension and compression. Building upon this, singlecrystal plasticity calculations were done, as well as predictions of the yield and flowfunctionsforarandompolycrystalusingaTaylormodel.Interestingly,theflowpotentialisjusttheVonMisesfunction.Variousapplicationswerethenexplored:cavitation,sheetnecking,stretchingofthinsheets,which were shown to significantly depend on the non-associated behavior. Correlationswerefoundbetweenlowvaluesofthesecond-orderworkwithstrainbursts.Inconclusion,non-associatedflowhasitoriginsinnon-planarcoredislocationstructuresincrystallinematerials, and in friction in granularmaterials, and its effects are nowwidelyfound.Conclusions:

• Theexistenceofnon-planarcorestructuresofscrewdislocationsleadstosignificanteffects of non-glide stresses on plastic flow in single crystals that persist in theeffectivebehaviorofpolycrystals,leadingtonon-associatedplasticflowcontinuummodelsatalllevels.

• Effectsoffrictioningranularsolids,willleadtodependenceofthestructureofSTZsonthefullstateofstressesandthusleadtonon-associatedflow.

• ParaphrasingCottrell:associatedplasticflowconstitutivebehavioristheexceptionratherthantherule.

• Macroscopic deformation and failure modes can be significantly affected by non-associatedflow.

Session3:DefectsI

David McDowell. Some challenges in length and time scaling for modelingdislocations. Overviewandmotivation(challenge1):One of the big challenges is to model the gulf that exists between atomistic scale andmesoscales of crystal plasticity. Multiple methods currently exist for bridging theintermediate scales, such as coarse-grained atomistics, microscopic phase field models,discrete dislocation dynamics or statistical dislocationmodels. Further strategies includeCoupledAtomisticsandDiscreteDislocation(CADD)method,quasi-continuummethodandthedomaindecompositionmethod.

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Approachandresults(challenge1):A method with attractive features for predictive mesoscale modeling is the ConcurrentAtomistic-Continuum method (CAC). It has fully resolved atomistics and uses the samegoverning equations and interatomic potentials in both atomistic and coarse-graineddomains.Inthismodelingstrategy,dislocationscantravelseeminglybetweenfullyresolvedatomisticregionsandcoarse-grainedregions.CACenablestostudysystemswithoutperiodicboundaryconditionsandreachtimescalesand loading conditions which are much more realistic than classical periodic moleculardynamicsimulations.Examplesofinterestincludeinteractionsofdislocationswithmultiplesurfacesanddefectssuchasdislocationpile-ups,grainboundaries,voids,andimpenetrableobstacles.Itisworthnotingthatthesesortsofinteractionswouldbehardtosimulatewithdiscretedislocationdynamicswhereassumptionswouldhavetobemaderegardingtheseinteractions.Overviewandmotivation(challenge2):A second, but related challenge in themodeling of dislocations, is the thermally assistedobstacle bypass of dislocations.Most simulations have beenperformed in the overdrivenregime,whereuniversalscalingrelationsapply.Approachandresults(challenge2):AstrategyfollowedhereistouseNudgedElasticBand(NEB)(CACcanactuallyalsobeusedforNEBcalculations)andanattempt frequency thatgoes inverselywith the lengthof thedislocationsegment.Itturnsoutthatthelong-rangedislocationinteractionsarecriticaltomodelthisprocess,andthatrandomarrayofobstaclesofferlessresistancethanaperiodicarrayofobstacles.Itisimportanttonotethatmanybodydislocationproblemslieawayfromequilibriumandare entropically stabilized. This implies that the entropic prefactor is important tocharacterizeinTST.Overviewandmotivation(challenge3):Finally,athirdchallengeorgapinthemodelingofdislocationsistheuncertaintyinbridgingatomistics and experiments to the mesoscale and reconciling information coming fromdifferentsources.AnapplicationconsideredisthecoordinatedkinkpairformationinBCCalpha ironwiththeobjectiveof informingtheparametersof theKocks-Ashby-ArgonFlowRule.Theresultingparametersofabottom-upapproacharehowevernotwithin the95%confidenceintervaloftheexperiments.Approachandresults(challenge3):The approach considered to overcome this initial disagreement is that of constrainedlikelihood,wherethebottom-upinformationisusedtopenalizeparametersestimationthatare based on top-down modeling, based on surrogate models. This results in a goodcompromisebetweentheinherentapproximationsthatexist ininteratomicpotentialsandtheuncertaintiesthatexistinexperimentalobservations.Amorerecentapproachconsistsonaugmentingthepreviouslyusedtop-downandbottom-up likelihood functions with an inter-scale discrepancy layer. This achieved a lowercalibrationvariance.

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Conclusions:

• CACisapowerfulmethodformesoscalemodeling,althoughthetimescalechallengestillremainslargelyunsolved.

• Reconcilinginformationfromsimulationsandexperimentsisimportant,forwhichacoupleofstrategieshavebeenproposed.

References:[1]S.Xuetal."Aquasistaticimplementationoftheconcurrentatomistic-continuummethodforFCCcrystals."InternationalJournalofPlasticity72(2015):91-126.[2]C.Sobieetal."Scaletransitionusingdislocationdynamicsandthenudgedelasticbandmethod."JournaloftheMechanicsandPhysicsofSolids105(2017):161-178.[3] S. Foiles et al. "Preface for focus issue on uncertainty quantification in materialsmodeling."ModellingandSimulationinMaterialsScienceandEngineering27(2019).

MichaelOrtiz.AtomisticsimulationofhydrogenstorageinPdnanoparticles. (JointworkwithM.PAriza,J.P.Mendez,X.Sun,M.Ponga,K.G.Wang)Overviewandmotivation:Therearemanyexamplesforwhichonerequiresatomisticanddiffusetimescalessuchaslithiationofsilicon,theevolutionofthemicrostructureforalloysorcorrosion.Alloftheseareoutofthescopeofmoleculardynamicsinviewsofthelargegapinspaceandtime,evenwith theadventof exascale computing. Coarse-graining strategiesare thus required.Thestrategy presented is diffusive molecular dynamics (DMD), which combines a statisticaldescription of atomistic fluctuations, Onsager type empirical kinetic relations, and quasi-continuumforthespatialcoarse-graining(althoughthislastpartisnotdescribedhere).Approachandresults:Theapproachpresentedadoptsagrandcanonical representationof sites (note that theseare not atoms, but sites), where the state of each site is characterized by its position,momenta and occupancy. The axiom of maximum entropy is then applied to obtain thegrand canonical probability distribution as a function of the mean field of the atoms(expected position, momenta, energy and occupancy). The resulting grand canonicalpartition function provides the grand canonical free entropy and the local equilibriumrelations, which reduce to conventional statistical mechanics for the case uniformtemperatureandchemicalpotential.Calculations of the partition function are however complicated. Here, a convenient trialHamiltonian(harmonic)isusedinsteadoftheexactonetoobtainanapproximationoftheentropyfunctionandthemesoscopicdynamics.Thevariablesof thetrialHamiltoniancanactuallybeoptimized,leadingtoanadditionalequation.Closurerelationsareneededtocharacterizetheevolutionofthetemperatureandchemicalpotential.Here, these aremodeled usingOnsager theory, that is, using a discrete Fourierlaw and a discrete Fick’s law. There is currently work in progress to derive the kineticrelationsconsistently fromLiouvilleequationandaGalerkinreduction(thoughthis isnotpossible to do yet for the grand-canonical ensemble, as the Liouville type equation isunknownforthiscase).

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The approach is applied to the process of hydrogen absorption and desorption in Pdnanostructures, which exhibit two phases. Interestingly, applying DMD to nanowiresdeliversasharpphaseboundarythatpropagates,andthevelocitypropagationcomesfromthe model. For Pd nanoparticles, the misfit strains between the two phases leads to theappearance of misfit dislocations. These defects relax the energy, but also pin down theinterface,andthusslowdowntheabsorptionofH.Thisinterplaybetweenmorphologyandkineticsmaythusbestudiedasafunctionofparticleshapes.Conclusions:

• DMDisausefulparadigmfortransportphenomenawithatomisticfidelity.• Usefulinunderstandinghydrogenabsorptioninnanoparticles.

References:[1]G.Venturinietal."Atomisticlong-termsimulationofheatandmasstransport."JournaloftheMechanicsandPhysicsofSolids73(2014):242-268.[2] X. Sun et al. "Atomistic modeling and analysis of hydride phase transformation inpalladium nanoparticles."Journal of theMechanics and Physics of Solids125 (2019): 360-383.

EmmanuelClouet.Secondaryslipofscrewdislocationsinhcpzirconium. (JointworkwithEmileMaras)Overviewandmotivation:Zrisatransitionmetalwithhcpstructure,whereplasticityiscontrolledatlowtemperaturebythemobilityofscrewdislocations,wheretheprincipalglideplanesoccurintheprismaticplanes.However,atsufficientlyhightemperaturesitcanalsocross-sliptoglideonbasalandpyramidalplanes.Thecorestructureofscrewdislocationscanbeobtainedusingab-initiocalculations,whichshow that themost stable configuration is dissociated into two partials in the prismaticplane,althoughotherstructuresalsoexistinthepyramidalplane,andinbothprismaticandpyramidal.Theenergybarrierscanalsobecomputedversusthereactioncoordinate.Fromit,itcanbeinferredthatthereiseasyglideintheprismaticplaneandenergybarriersinthepyramidalplanes.Glideinthebasalslipisexaminedhere.Approachandresults:Ab initio calculationswere used to testwhether screwdislocations can glide in the basalplane. Specifically, NEB calculations were performed which indicated the presence of anintermediateconfiguration.Thetrajectoryevolvesthroughacombinationofprismaticandpyramidalglides,whichleadstoanaveragebasalglide.Accordingtotheseresults,thebasalslipisacompositeglideratherthanelementaryone.However,thisisincontradictionwithexperiments,whichshowevidenceofelementarybasalslip.Theabovesimulationsassumedthatdislocationswerestraight.Toovercomethislimitation,moleculardynamicsimulationswereperformedtostudytheglideofscrewdislocationsinthebasalplaneasa functionof temperatureandstress. It isobservedthatthedislocationmoves via the nucleation and propagation of kinks, and the average velocity is strongly

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dependent on stress and temperature, as expected. A detailed analysis of the position inspace and time shows jumps in the pyramidal planes leading again to basal slip only onaverage, incontradictionwithexperimentalobservations.However, thiscanbearesultoftheMDsetup,asthebasalplaneisthemaximumresolvedshearstressinthesimulation.Inaddition,thestressratesinmoleculardynamicsaremuchlargerthaninexperimentsduetothetimescalelimitations.FurtherNEBcalculationswerethenperformed,takingnowintoaccountthenucleationandpropagationofkinks.Tworegimeswereidentifiedcorrespondingtolowandhighstresses.TheshapeofcriticalkinkpairwasthenextractedfromMDasa functionofappliedstressanditwasobservedthatitslightlywidenswithincreasingstressintheslowstressregime,whileitwidensatamuchhigherratewithadecreaseintheheightinthehighstressregime.This information can then be used to get the activation volume (first derivative of theactivationenthalpyasafunctionoftheappliedstress),whichexhibitsadiscontinuitywithstress. Reasonable fits can be obtainedwith analytical expressions. The trajectory can beextracted from the NEB calculations, showing a pure basal slip for low stresses, and acombined prismatic and pyramidal slip for high stresses. The results from NEB andmolecular dynamics are in good agreement for the high stress regime, which is the oneaccessibletoMD.Conclusions:

• Basal and pyramidal glide are competing mechanisms with the first one beingfavoredat lowstresses(in theexperimentalrange),andthe latterathighstresses(inagreementwithMDsimulations).

References:[1]E.Clouetetal"Dislocationlockingversuseasyglideintitaniumandzirconium."NatureMaterials14(2015):931-936.[2]P.Kwasniaketal, “Basal slipof<a>screwdislocations inhexagonal titanium”,ScriptaMaterialia162(2019)296-299.

Session4:DefectsII

JaimeMarian.Simulating dynamic strain aging in body-centered cubicmetalsondiffusivetimescales (Jointworkwith:YueZhao,LucileDezerald)Overviewandmotivation:Plasticity inBCCmaterials,suchasW, isgovernedbystraightscrewdislocationsegmentsthatmoveinajerkyorcontinuousfashion.TypicalofBCCmaterials,theflowstressofhighpurity single crystal W exhibits a very strong temperature dependence, which can beunderstoodwith theaidof variousmodels for thedifferent regimespresent (line tensionmodel, elastic interaction model, kink-diffusion model). If solutes are added (e.g. Re assubstitutional solute), the thermal dependence of the flow stress can lead to combinedsofteningandhardeningeffects.Thequestionaddressedishowtoaddsoluteatoms(bothsubstitutionaland interstitional) to thestandardplasticitypictureofBCCmetals.Someofthechallengesare(i)elementaryscrewdislocationmotionandsolutejumpsareatomisticin size, yet dislocationmotion and solute diffusion occurs atmesoscopic time scales. (ii)

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bothmotionsarestronglythermallyactivatedand(iii)BCCplasticitydisplaysanumberofanomalies(ascomparedtofcc).Approachandresults:A mesoscopic approach is presented to model BCC alloys, building up on a previousframeworkforpureW.Insuchframework,kineticMonteCarloisusedfortheevolutionofdislocations, (as it is strongly thermally activated), kink-pair nucleations aremodeled asrareeventswhoseratedependontemperatureandstresses(thisfollowsoriginalideasbySrolovitz and Bulatov) and non-Schmid effects (twinning/anti-twinning asymmetry andnon-glide effects) follow the framework of Vitek, Groger and Bassani. The variousparameters involvedare computedusingquantumsimulations andatomistic simulations.Theresultingvelocityofthedislocationasafunctionoflengthfollowsalinearrelationshipatlowstressandtemperature.Underextremeconditionsthough,alotofdebrisisproducedthat is induced fromself-pinning, aphenomena thathasbeenobservedexperimentally insomesystems.Theadditionofsolutes,suchasRe(substitutionalsolute)inW(itisacommercialalloy),canincreasetheductility(thisisthecaseforW).Tomodelthis,theKMCmodelisaugmentedbyaddinginteractionwithsolutesintwoways:(i)effectofstressfieldofdislocationsonsolutediffusion(thiscanbecharacterizedbytheactivationvolumetensorusingDFT)(ii)andtheeffect of solute atoms on dislocation structure (the long range effect is simply an elasticdilatationeffect,whiletheshortrangeeffectsareinelasticandneedtobecomputedusing,forinstance,DFT).ThisinteractionismorecomplexinBCCmetalsthanFCCones,assolutescan interactwithbothedgeandscrewsegmentsandthenatureof the interaction isquitedifferent.There are three key processes in the motion of dislocations in these alloys: kink-pairnucleation,kinkde-trappingandsolutediffusion.Quantifyingtheratesoftheseeventsasafunctionoftemperatureandstress,deliversthatdiffusiondoesnotplayanimportantroleascouldbeexpected.The resulting dislocation velocities can be equated to an equivalent flow stress, and it isobserved that the flow stresses slightly decreaseswith concentration for low values, andthen increases at higher concentrations, with a square root type of hardening that isconsistentwithexperimentalobservations.Physically,atlowconcentrations,kink-pairsareeasilynucleated,whiletheblockingduetosolutesisminimal.Astheconcentrationgoesupthough,kinkblockingdominates.Amapmaythenbedrawnthatseparatessolutesofteningfromsolutehardeningasafunctionoftemperatureandconcentration.Moving next to BCC interstitial solid solutions, the existence of unstable flow is welldocumented. Here, diffusion of solute is going to be prevalent. In particular O in W isstudiedand it is found that tetrahedral sitesare lowerenergyas compared tooctahedralinterstitial sites. Tetrahedral-tetrahedral diffusion is then studied by means of NEB DFTcalculationsasa functionofstresses.Short-range inelastic interactionsarealsostudied indetail, and two stable configurations are found (easy core and hard core). A stresstemperaturemapwas developed for this case for a given concentration (0.2%O)wherethreedifferentregimesareidentified:1. At high temperatures, intermediate stress conditions, solute diffusion/trappingdominatesoverkink-pairnucleation(calledsolutedecorationofthedislocation).

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2. At intermediate temperatures and intermediate stress conditions, both solute anddislocationinteractonsimilartimescales,leadingtojerkyflow.3.Atlowtemperaturesandintermediatestresses,thesoluteeffectivelydoesnotmoveandkinknucleationdominates,whichleadstosolutehardening.Thisinformationcanbemappedtoastrainrate,temperaturemap,wherethethreeregimesarealsoclearlyvisualized.Conclusions:

• KMCallowstosimulatediffusivetimescalesfordislocationmotion.• Proposedasolutechemo-mechanicalcouplingviaDFTcalculation.• Developedasubstitutionalsolidsolutioninteractionmodelthatpredictssoftening-

to-hardeninginW-Re.• Developed an interstitial solid solution interactionmodel that predicts jerky flow

regimeinW-O.References:[1]Y.ZhaoandJ.Marian."Directpredictionofthesolutesoftening-to-hardeningtransitionin W–Re alloys using stochastic simulations of screw dislocation motion."Modelling andSimulationinMaterialsScienceandEngineering26(2018):045002.[2]Y.Zhaoetal. "Electronicstructurecalculationsofoxygenatomtransportenergetics inthepresenceofscrewdislocationsintungsten."Metals9(2019):252.

Anter El-Azab.A continuum theory for defects and microstructure evolutionunderirradiation.Overviewandmotivation:Nuclearmaterials are often subjected to extreme environments of temperature, pressureand irradiation. These adverse environments lead to a wide range of defects andmicrostructures depending on irradiation temperature, such as atomic disorder, stackingfault tetrahedral, dislocation loops, dislocation networks, voids and bubbles. The variousresponsescanbecategorizedasmicrostructureevolution,compositionevolution,orphasechange,which leadat theengineeringscale toswellingandgrowth,creep,hardening,andcorrosion.Foreachofthesethreecategories, there isawiderangeof individualmodelingstrategies. There is currently a lack of a grand theory of irradiation effects in materials,particularly for alloys. Here, this science gap is being addressed through the use ofcontinuummechanicsandnon-equilibriumthermodynamics.Approachandresults:Theproposedframeworkintegratestheusualcontinuummechanicswithkineticsofsolutesand defects and thermodynamics, with the latter providing constitutive closures. Defects(e.g.dislocations,pointdefects)areincorporatedintothecontinuummechanicsframeworkviaincompatibleinelasticdeformations.(Thetotaldeformationisoftendecomposedintoanelastic and an inelastic part, bothofwhich are generally incompatible.)The stressesmaythen be related to the elastic deformation via Hooke’s law, for instance, and the totaldeformation directly links to the displacement field. The mechanics problem is thengoverned by the equilibrium equationwhile additional equations are required for defectand microstructure evolution. These are obtained by invoking a linear constitutive

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postulate compatible with energy conservation and the second law of thermodynamics.This frameworkhasbeenappliedtostudyvoidnucleationandgrowthunderFrenkelpairproduction,aswellasswelling,usingadiffuseinterfaceapproach.Conclusions:

• A field theoretic framework for irradiation effects can be established using theframeworkofcontinuummechanicsandthermodynamics.

Session5:Grainboundariesandinterfaces

Yashashree Kulkarni. Mechanistic insights into crystalline interfaces viathermalfluctuations Overviewandmotivation:Membranesevenifappearflatorsmooth,microscopically,duetothermalvibrations,theywill exhibit fluctuations. These fluctuations have important implications in biologicalmembranes (physiological processes) and 2D materials, like graphene (morphology,mechanical and electronic properties). The question raised here is: what are thereimplicationsofthermalfluctuationsoncrystallineinterfaces,suchasgrainboundariesandtwinboundaries?Crystalline interfaces may be considered as interfaces separating two phases. The alsoexhibitfluctuations,althoughoftheorderof1or2latticespacings(andafewpicoseconds),in contrast with lipid membranes where fluctuations are of tens of nanometers. Theadvantage of these small fluctuations is that they are amenable to study via moleculardynamicssimulations.Thermal fluctuations are here used to study the stiffness andmobility of grain and twinboundaries,i.e.bothequilibriumandnon-equilibriumproperties.Approachandresults:Thetalkisdividedintothreeparts:1.Kineticsoftwinboundariesviathermalfluctuations.Energetic parameters such as stiffnessmay be obtained form interface fluctuations usingstatisticalmechanics.Specifically,assumingforsimplicitythatfluctuationsonlyexistinonedirection, the interfacialheight canbeexpanded inFourier space.Onecan thenwrite theenergyof themembraneand invokeequipartitionofenergy towriteanexpressionof thevarianceoftheFouriercoefficientsasafunctionofthewavenumber.Thisdependencewilldepend on the energy expression. These expressions can be used to derive stiffness (orotherparametersappearing intheenergyexpression)after the fluctuationsareevaluatedvia MD simulations. For twin boundary a slope of -1 is observed in the variance versuswavenumber in logarithmic scale. Karma et al. obtained a -1 slope aswell for low anglegrain boundaries, and attributed this slope to shear-coupled GB motion. Similarmechanisms exist for twin boundaries. Other grain boundaries exhibit -2 slope due tosurfacestretching,i.e.,adifferentmechanism.

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2.Entropicinteractionsbetweenfluctuatingtwinboundaries.There have been numerous studies of entropic interactions in lipidmembranes,where itwas observed that there are repulsive forces between nearby interfaces resulting insuppressionof fluctuationsofsmallwavelengths.Foragrainboundarywith -2slope, lowwavelength fluctuationsalsogotreduced,while for twinboundaries, theywereenhanced.Analytical studies using elasticity theory confirmed that indeed there was an attractiveforce.However,theamplitudeisquitesmall,anditisunclearwhatitsimplicationsare.3.MobilityofgrainboundariesviathermalfluctuationsMigration of grain boundaries is governed by the grain boundary mobility.Karmaandothers cameupwith the idea that thenormalmotionof themeanpositionoffluctuating grain boundary can be treated as a 1D Brownian motion, which enables toobtain the mobility coefficient via mean square displacement. Many previous studiesfocused on high temperature where a linear dependence with time is clearly observed.However,studiesongrainboundariesatlowertemperaturesshowedadifferentbehavior,which is expected, as the linear dependence in time is only valid for time scales that arelarger, and not accessible frommolecular dynamics simulations. Taking into account theadditional analytical terms that are often neglected for long time scales, themobility canstill be extracted usingGreen-Kubo type of relations,where the velocity autocorrelationscanbeobtainedfromMD.Conclusions:

• Fluctuations can be used to study equilibrium and non-equilibrium properties ofinterfaces.

References:[1] D. Chen and Y. Kulkarni. "Thermal fluctuations as a computational microscope forstudyingcrystallineinterfaces:Amechanisticperspective."JournalofAppliedMechanics84(2017):121001.[2] D. Chen and Y. Kulkarni. "Atomisticmodeling of grain boundarymotion as a randomwalk."PhysicalReviewMaterials2(2018):093605.

NikhilAdmal.Polycrystalplasticitywithanisotropicgrainboundaryevolution (JointworkwithJaimeMarian,JavierSegurado,GiacomoPo,MattJacobs,StanleyOsher)OverviewandmotivationPolycrystallineplasticitytograinboundaryevolutionisimportant,forinstance,fordynamicrecrystallization (DRX). It occurs in a wide variety of processes, such as welding. Theoverarching goal of the work presented is to predict microstructure evolution duringdynamic loading, in particular, to capture deformation, microstructure evolution andpredict nucleation of defect-free grains. It should also take into account grain boundarymigration mechanisms into account, and it should be computationally scalable to largepolycrystals.Approachandresults:Shearingofbycrystalsleadstonormalmotionofgrainboundaries,andthisischaracterizedby the so-called coupling factor. This factor was long thought to be a geometric factor,thoughrecentresultsclearlyshowthatitdependsontheboundaryconditionsandtheneed

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toensurecompatibility.Consequently,thecouplingfactorisnotagrainboundarypropertythatcanbeusedasafundamentalquantityincontinuummodels,butrather,itshouldbeanoutcomeofthesimulation.Thismotivatestheneedtocouplegrainmicrostructuremodelsandcrystalplasticity.Existinggrainmicrostructuremodels(theydonotaccountfordeformation)includediffuseandsharpinterfacemodels.Amongthediffusemodels,theKobayashi-Warren-Cartermodelservesasaninspirationforthepresentwork,anditisexplainedinfurtherdetail.TheKWCenergyfunctionalisbasedontwoparameters,phi(indicatesdisorder)andtheta(indicatesmisorientation), and theassociatedEulerLagrangeequationallows themodelingofgrainshrinkageandrotation.However KWC model is phenomenological in nature. Yet, it lends itself very nicely toincludecrystalplasticityinit.Acrystalplasticityfreeenergyisthusproposedasafunctionof phi (similar to KWC), the elastic deformation and the dislocation density tensor. It iscomposedofanelasticenergyandagrainboundaryenergyinspiredbyKWC,wherethetaisreplacedbythedislocationdensity.Theresultingmodelallowssimulatinggrainshrinkage,rotationandsliding.Here,thecouplingfactorisanoutcomeofthemodeldependingonslipsystemsallowedinthemodel.Themodelalsohasthecapabilitytopredictgrainnucleationviaagglomerationofdislocations.The model has some limitations: (i) it is specialized to only misorientation angledependence (a generalization to 3D is needed), (ii) the KWC functional form placesrestrictions on the dependence of the GB energy on misorientation, (iii), there is noconsideration of symmetry, (iv) it is numerically inefficient, and (v) the sign of couplingfactor ispre-decided.Thefirst four limitationscanbeovercome.Ageneralizationto3Disproposed.Asforthenumerics,inspirationisdrawnfromthresholdingmethods,whichareextremely fast compared to phase fieldmodels. Preliminary results indeed indicate greatcomputationaladvantages.

Conclusions:

• IntegratedKWCmodelformicrostructureevolutiontocrystalplasticity.• Generalizedto3Dandimprovednumericalefficiencywiththresholdingmethods.

References:[1] N.C. Admal et al. "A unified framework for polycrystal plasticitywith grain boundaryevolution."InternationalJournalofPlasticity106(2018):1-30.[2] N.C. Admal et al. "A three-dimensional misorientation axis-and inclination-dependentKobayashi–Warren–Carter grain boundarymodel."Journalof theMechanicsandPhysicsofSolids128(2019):32-53.

BrandonRunnels.Unifyingmechanismsofgrainboundarymigrationthroughacontinuumthermodynamicframework. Overviewandmotivation:It is commonly believed that disconnections are carriers of shear coupling in grainboundarymobility.Disconnectionsaredefectswithbothaburgersvectorandastepheight(they can be interpreted as dislocations of dislocations). In contrast to grain boundary

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energetics,dataforgrainboundarymobilitydoesnotexhibitsuchclearpatternswithgrainboundary character. Coupling factors can be positive and negative and can act verydifferentlydependingonloadingconditions.Animportantquestionthusemerges:whataretheintrinsicpropertiesgoverninggrainboundarymobility?Approachandresults:Here, grain boundary motion is interpreted as crystal plasticity with a clear map interminology (e.g., mobility -> yield, thermal motion -> thermal softening, disconnectionmodes->slipsystems,shearcoupling->normalityflowrule,etc.).Grain boundary motion can be understood at the continuum setting as a permanentdeformation FGB. From an atomistic perspective, there are infinite numbers oftransformation modes, each with an associated disconnection mode. From a continuumperspective though,FGBhas tobe isochoric andhas to satisfyHadamard condition,whichthus limits it to pure shear. In addition, the energy landscape is non-convex, which willlikely result in strain localization and fine phase mixtures. It is suggested that grainboundarystructures,disconnectionandmodeswitchingareactuallymanifestationsofthisnon-convexity.ThemodelusedtodescribeGBmotionisavariationalmodelbasedonminimumdissipation(itincludesafreeenergyandadissipationenergy),whereinterfacepositionisaninternalvariable.Asanansatzformodeselection,aminimizationisperformedovergrainboundarymodes.Itissuggestedthatthedissipationenergyisthesoughtafterintrinsicpropertyandthreemethodsaresuggestedforitscalculation.Method1:Upperboundfordissipationenergyusingoptimaltransport.The energy versus reaction coordinate is smoother than expected, but the dissipationenergy versus tilt angles displays some interesting results, namely mode switching.Howeverthereisasystematicoverestimationofthedissipationenergy.Method2:Dissipationenergyextractedformareaunderthestress-straincurve.Dissipation energy is proportional to plastic work, and it is here computed for twoconditions(displacementdrivenshearandsyntheticdrivingforce)givingconsistentresults.Additionallytherearecuspslikestructures.Theobtaineddissipationisonlyasgoodasthesimulatedboundaries,andresultsarecurrentlylimitedto0K.Method3:ContinuumgrainboundarymigrationmodelThe continuum model is based on energy minimization for the elastic response and anevolution equation for FGB. Its application to various examples show some interestingfluctuationsthatlooklikedisconnections.Conclusions:

• Minimum dissipation potential formalism is useful for the modeling of grainboundarymigration.

• Dissipationforeachmodearesuggestedtobeintrinsicproperties.• Modeswitchingisduetonon-convexityofthestrainenergydensity.

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References:[1] I. Chesser et al. "A continuum thermodynamic framework for grain boundarymotion."JournaloftheMechanicsandPhysicsofSolids(2019):103827.

Session6:MechanicsofMaterialsI

Garritt Tucker.Implementing higher-order descriptors to unravel competingdeformationeffectsatanatomicscaleOverviewandmotivation:Innanocrystallinematerials,bothexperimentsandcomputationalstudiesshowatransitionpointwheretheflowstresspeaksversusgraindiameter.Someoftheobservationsfromtheliterature note that: (i) there is a transition from dislocation to grain boundary drivendeformation as grain size is reduced, (ii) the maximum strength grain size has beenqualitatively observed to occur near this transition. The goal here is to quantify theseobservationsbyquantifyingtheroleofdefects(grainboundariesanddislocations)duringstrainaccommodation,andhowthesecorrelatewiththemacroscopicmaterialbehavior.Inaddition, grain boundary structure and behavior will be analyzed using higher-orderdescriptors(atomisticshapemoment).Approachandresults:Nanocrystallineatomisticsimulationboxesaregeneratedforvariousgrainsizesfromphasefield generatedmicrostructures.Mechanical deformation is thenperformedon these, andthe results are post-processed to understand deformation mechanisms. As previouslydiscussed,theflowstresspeakswithgrainsize.Toquantifytheindividualmechanismsandtheirroleinstrainaccommodation,theatomicdeformation gradient tensor, atomic micro-rotation vector and atomic strain vector arecomputedandcombinedwithclassicalmetricssuchascommonneighboranalysisandslipvectors. These enable to distinguish dislocations, grain boundaries and twinning, and toquantifythestrainandstrainfractionsduetothesemechanismsasafunctionofgrainsize.Theresultsmatchverywellwiththedifferentregimeshighlightedbytheflowstressversusgrain size. Lowgrain size is grainboundarydominated (inverseHall-Petch regime), largegrain size is grain dominant (Hall-Petch regime), and the peak corresponds to an equalcompetition.Thehypothesisregardingtheflowstresspeakwasthusquantifiedtobetrue.Aninterestingquestionthenemergesastowhethertheflowstresspeakcanbemovedtoadifferentgrainsizebyaffectingthesemechanisms.Astudyofnanocrystallinealloys,namelyNi-P using a hybrid Monte Carlo/MD approach, reveals that indeed the solute affectspositionof thatpeak.Amoredetailed studyof thedistributionof the solutewithin grainboundariesindicatesthatit isveryinhomogeneous,withmoresoluteinhigh-energygrainboundaries,thoughdatashowslargescattering.Tothis,itisnotedthatmicroscopicdegreesof freedom (even for the same macroscopic degrees of freedom) vastly influence themechanical properties. A question is therefore whether there are better grain boundarydescriptors. They considered shape descriptors based on spherical harmonics tocharacterize local atomic environment. These are tested over various grain boundarystructures as well as to analyze grain boundary migration. The goal is to connect thesedescriptorstomaterialbehavior.

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Conclusions:

• TransitionfromdislocationtoGBdrivenplasticityinnanocrystallinematerialswasquantifiedusingmetricsforstraincontributionsfromthedifferentmechanisms.

• New grain boundary descriptors are proposed to characterize grain boundarystructureandbehavior.

Timothy Rupert.Probing nanoscale complexion transformations withcomputationaltechniquesthatcomplementexperiments. (JointworkwithZhiliangPanandVladTurlo)Overviewandmotivation:Anoverarching goal is to tailordefects to controlmaterial properties.A goodexampleofthis is the stabilization of grain boundaries in nanocrystallinematerials, which has beenwidely studied. Here, changes in grain boundary structure are targeted. In particular,amorphousintergranularfilms(AIF)areaddedtograinboundaries,toleadananolayerGBcomplexion.Approachandresults:ExperimentalresultsshowthatAIFcantoughennanocrystallinematerialsandmakethemmore ductile. It also increases the stability of the nanostructural material at hightemperaturesandspeedsuptheconsolidationofpowderduringsintering.AIFs are formed experimentally by pre-melting the grain boundaries and quickly coolingthesystemdown.However,thedistributionisheterogeneousinthicknessoverthesample.Atomistic simulations canbeused tounderstandandcharacterize the structure, topologyandstatisticsofthesecomplexions.HybridMonteCarlo/molecular dynamicsmodeling is used to analyze the grainboundarystructure at a resolution that is inaccessible to experiments. Looking at the radialdistribution functions, the interiors of these layers look like a bulk phase, and smalldifferencesarefoundneartheamorphous-crystallineinterfaces.Thereisactuallyafurthertransition region that differs from bulk amorphous phases, which is independent of filmthicknessathightemperatures.Alsoathightemperatures,thenearbycrystalshavelessofaneffectonhowthetransitionregionslooklike.Thedistributionofthethicknessishardtoquantifyexperimentally,asitisverysensitiveonhow thoseboundaries are imaged, and there is abias towards thickermorevisible films.Atomistic simulations with varied doping show that there are huge variations in GBcomposition,whichexplainsthevariationinGBthickness.Finally,atomisticmodelsarealsoimportantforalloydesign. Theycanguideexperiments,byidentifyingthecorrecttemperatureandcompositions.Conclusions:

• Short-range order can be used to identify local structural variations withinamorphouscomplexions.Atransitionregionisidentified.

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• Localgrainboundarycompositioncanvarywidelyinapolycrystal.ThisvariationisresponsibleforthethicknessvariationofAIFs.

• Alloychoicesareimportantforcomplexionstructures.References:[1]ZPanandTJRupert,“Spatialvariationofshort-rangeorderinamorphousintergranularcomplexions”,ComputationalMaterialsScience131(2017):62-68[2] V Turlo and TJ Rupert, “Prediction of a wide variety of linear complexions in facecenteredcubicalloys”,ActaMaterialia185(2020):129-141

Jun Lou.Quantitative in-situ nanomechanical study of low dimensionalmaterials. ThistalkiscomposedoftwopartsPartI.Metalplasticityatsmalllengthscales(Aunanowires).PartII.Fracturetoughnessandtougheningof2Dmaterials,suchasGraphene.Overviewandmotivation(PartI):Mechanical properties arewell known to be size-dependent. For nanocrystals, one has apseudo Hall-Petch relationship, where the relevant scale is the diameter of the metallicnanowire. For sizes below ~10 nm, there is a transition of deformation mechanism,whereby surface dominates the plastic behavior,with dislocations being nucleated at thesurface.Approachandresults(PartI):Lou’sgroupiscapableofsynthesizingnanowireswithdiametersfromafewnanometerstoa fewhundredofnanometers, all single crystals, to focuson surfaceeffects.Observationsandmeasurementsof thedeformationof thesenanowires are thenanalyzedusing in situTEM,wheretheclampingisdoneviacold-welding(automaticfusingofnanowires,whenincontact, to formasingledefect-freenanowire).Uniaxial testsofAunanowires reveal thatplasticdeformationoccursbynucleationofpartialdislocationsat thesurface thatquicklyslip through the crystal, ultimately leading tonecking till a single atomic chain.However,repeated experiments on Au nanowires, reveal that some of them exhibit a brittle-likefracture. In this case, twin structuresdevelopperpendicular to the tensile axis, becomingweakpointwherefracturecaninitiateandquicklypropagatethroughthecrosssection.Thecauseofthisverydistinctbehaviorwassolvedincollaborationwithatheoreticalgroup,andit was discovered that the cause was a misalignment issue when performing the tensiletests. For largermisalignments (>~10degrees), twins activate firstwhich leads to brittlefailure, whereas partial dislocation nucleation at the surface dominates for smallorientations.Overviewandmotivation(PartII):Graphene has very interesting properties like extremely high mobility and mechanicalproperties, and holds promise for applications such as flexible electronics and functionalnanocomposites.

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The mechanical properties of graphene have been previously investigated viananoindentation. However, considering the small area probed for such experiments, it ispossiblethatsuchareaisdefectfreeleadingtoresultsclosetothetheoreticalstrength.Approachandresults(PartII):Themechanicalpropertiesofgraphenedrasticallychangeinthepresenceofdefects.Thisisimportant, as applications will have to deal with large surfaces of graphene, whichnecessarilycontaindefects.Animportantpropertyisthenfracturetoughness.Experimentalmeasurementsofthefracturetoughnessrevealaverysmallvalue(likeaceramic).Anaturalquestion is then whether the grain structure allows changing such value. However,numerical simulations indicated that little gain could be achieved in this manner (about10%).Wethenconsideredrebargraphene,whichconsistsofagraphemesheetreinforcedwithnanonwires,whichresultedinanincreaseofabout50%ofthefracturetoughness.Conclusions:

• Theoryneedstocomplementexperiments.• Therearealotofopportunitiesfortwodimensionalmaterials.

References:[1] Y Liu et al, “Cold welding of ultrathin gold nanowires”, Nature Nanotechnology, 5(2010):218-224.[2]EFHacopianetal, “Tougheninggrapheneby integratingcarbonnanotubes”,ACSNano12(2018):7901-7910.

MitraTaheri.Towardthetailoringofmaterialspropertiesfarfromequilibrium:convergenceofmicroscopy,dataScience,andtheory Overviewandmotivation:Microscopyhasa longhistoryofsuccessesandfailuresgoingthroughthedevelopmentofoptical microscopy, transmission electron microscopy (TEM), aberration correction TEM(ACTEM). Upcoming developments include on the fly studies to look at non-equilibriumevents, and intelligent microscopy that combines theory, machine learning andexperimentaltechniques.Approachandresults:Agrandchallengeistheunderstandingofmaterialsfarfromequilibrium,suchasstronglycorrelated systems or extreme thermal events, which requires high spatio-temporal andenergyresolution.Also,chemicalorderisbecomingincreasinglyimportant,forinstance,intheanalysisofgrainboundariesorhighentropyalloys.Newtoolstopushtheboundaryofelectronmicroscopyinseveralofthesefrontswerepresented,leadingtoaparadigmshiftinmicroscopy and spectroscopy. Some specific advances include improved DQE (detectivequantumefficiency)tohighlyincreasethesignaltonoiseratio.Asaresultofthelargespatio-temporalresolution,dataiscollectedatamassiverate,whichtherefore requires on-the-fly processing. Here, machine learning tools can enable theidentificationofdefects,forinstance,fromverynoisydata.

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Someoftheapplicationsstudiedwiththesetoolsinclude-Theunderstandingofnon-equilibriumgeometriesingrainboundariesduringirradiation,with the goal of building radiation tolerant materials. Aspects studied include grain sizeeffects,effectsoflocalstrains,grainboundariesdegreesoffreedom,andtheircorrelationswithdefectabsorption.- Grain boundary dislocation densities and geometrically necessary dislocations. Theapproach taken combines precision electron diffraction with automated crystallographicorientation mapping to look at the Nye tensor, which subsequently can give thegeometricallynecessarydislocation(GND)density.-Newtechniquesthatprovidesynchrotronleveldata inTEMtospatiallyresolvethe localorderatGBsarealsopresented.Thesetechniquescombinedwithcharacterizationsof theGNDsshowthatsinkefficiencydependsonthemicroscopicdegreesoffreedomoftheGBs(evenbetweenboundarieswithidenticalmacroscopicdegreesoffreedom).SimulationsbyDavidSrolovitzfurthersupportedthis.-Theaboveresultsraise thequestionofwhetherGBequilibriumis justamicrostate.Theanswer is yes. Experiments and simulations on equilibrium GBs and disordered or non-equilibriumGBsshowthattheyhavedifferentsinkefficiency.Overall, the toolsdevelopedenableahighresolution inspace, timeandenergy.However,interactions with theory and simulation are crucial to answer fundamental questionsregardingtheroleofpreexistingdislocations,theroleofhighlydislocatedgrainboundariesandtheirevolutiontounderstandsinkefficiencyandradiationtolerance.Open questions include dislocation and point defect interaction, absorption at grainboundaries,dislocationdefectdrag,anddislocationdefecthighways.Conclusions

• New high-resolution techniques enable to visualize and quantify GB dislocationcontentandlocalorder.

• A lot more is needed on the theory side to understand GB structure and itsevolution.

References[1] G.A. Vetterick et al. "Achieving radiation tolerance through non-equilibrium grainboundarystructures."Scientificreports7(2017):12275.[2] J.L.Hartetal. "ASynchrotron intheTEM:SpatiallyResolvedFineStructureSpectraatHighEnergies."arXivpreprintarXiv:1909.06323(2019).

Session7:MechanicsofMaterialsII

Ryan Elliott.A framework for the interpretation ofmodulatedmartensites inshapememoryalloys (JointworkwithVincentJusuf)Overviewandmotivation:Shape memory alloys are materials that undergo reversible martensitic phasetransformations (they are first-order diffusionless, solid-to-solid phase transformations)underthermalormechanicalloading.Theyarerelatedtochangesinthecrystalstructureof

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thealloy.Fromacontinuumperspective thesetransformationscorrespondstochanges inthe free energy landscape and its (single or multiple) minima as a function of load ortemperature.Akeyfeaturediscoveredinthelastdecadeisthatthestrainoftransformationbetweenthemartensiteandaustenitephasesmeasuredbyadeformationgradientcantellalotaboutthemacroscopic properties of these structures. In particular, theminimum eigenvalue of thestresstensorhasbeenshowntorelatetothelevelofhysteresis,andthusreversibilityanddamage.In addition, some shape memory alloys have modulated microstructures (MMs), whichoften require a much larger unit cell to describe the martensite phase. However, firstprinciplecalculationsshowthatthesmallunitcellmartensiteisthelowestenergyphase.Itthus remains an open question why modulated microstructures are observedexperimentally.TherearebasicallytwoexistenttheoriesfortheexperimentalobservationofMMs,bothofwhicharebasedonkinematicargumentswithoutlookingattheenergy:(i)adaptivemartensitehypothesis:MMsasnano-twinningofgroundstate(ii)periodiczig-zagofclosed-packedplanesandthinkingofdifferentstackingsequencestobuilddifferentMMs.Understandingthesestructuresfromanenergeticperspectiveispreciselythefocusofthiswork.Approachandresults:In 2011 Elliott developed a model for base martensite (non-modulated martensite). Inparticular,hedevelopedaneffectiveinteratomicpotentialthatallowedhimtodoatomisticstaticsand lookat thebifurcationproblemtoexploreallpossiblephasespredictedbythemodel. The model was able to predict the existence of various structures and phasetransitions.There ishope that it canalsopredictmodulatedstructures,asbifurcationscorrespond todifferentwavevectorsbecomingunstable. Indeed itwaspossible to find thesestructures,andtheythusarenatural featuresof theenergy landscape.TheresultingMMsphasesarequite stable and close to the basemartensite phase, and they aremuchmore compatiblethanthebasemartensite.Actually,whenkinematiccompatibilityisenforcedasaconstraint,MMsbecometheenergyminimizingphases.Itwasobservedthatallthemodulatedstructuresfoundwiththeatomisticmodelconsistedof stacking of four different types of planes associatedwith two basemartensite phases.Based on this observation, aModulatedMartensiteMixtureModel (M^4)was developed,wherea simple ruleofmixturewasused for thedeformationof theMMs.This gaveverygood prediction for the properties of the real MMs (better than predictions based onpreviousmodels). Then, the rule of mixtures was used to try to find amore compatiblestructurethanthosefoundviapreviousatomisticcalculations.SuchaMMwasindeedfoundand this was confirmed by atomistic model that it was more compatible than what waspreviouslyfoundbefore.Themodelthushadapredictivecapability.Conclusions

• MMsareenergyminimizingphaseswhenenforcingkinematiccompatibility.• MMscanbeinterpretedasmixturesoftwophases.

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• A simplemixture rule allows predicting a new structure that ismore compatiblethanpreviouslyidentifiedones.

References[1]D.B.Ghoshetal."Structuralphasetransitionpath-followingandstablephasescoutingthroughacoupledDFT–BFBalgorithm."ModellingandSimulationinMaterialsScienceandEngineering19(2011):085007.

PrashantPurohit.Interactionsandassemblyofinclusionsonlipidmembranes. (JointworkwithXinyuLiao)Overviewandmotivation:Cellmembranes are lipid bilayers that,mechanically speaking, act as a fluid in the plane.These lipidmembranes can have embedded proteinmolecules that can diffuse around, aprocess that is important for viral infections. Most of the studies of these processes aremadeusingcoarse-grainedmolecularsimulations,althoughsomeexperimentsalsoexist.Inthis diffusion process, thermal fluctuations are an important component, and are heremodeled using a continuum mechanics approach combined with statistical mechanicsanalysis.Approachandresults:Lipid membranes are modeled as a flat membrane using the Helfrich model, where theenergy accounts for themean curvature and hydrostatic tension (Gauss curvature is notimportant). A triangular finite element discretization is then used,where each triangle isassumedtoremain flatduring thedeformation.Theenergy thenadoptsaquadratic form,whichiseasilyamenabletostatisticalmechanicalanalysistocomputethepartitionfunctionand the free energy. Simple thermodynamic relations can then be used to compute thechangeofprojectedareawithtension,andtheentropy,resultingingoodapproximationsoftheanalyticalsolutionofHelfrichasthenumberoffiniteelementsincreases.Inclusions are then modeled as rigid inclusions within the finite element discretization.Additionally,theanglebetweentheinclusionsandthemembranesatthepointofcontactisimposedusingapenaltymethod.Thefreeenergymaythenbecomputedasafunctionofthedistancebetween two inclusions tounderstandwhether there isan interaction force.Theenergetic and entropic contributions are computed separately and recover the functionalformpreviously proposed. The energetic and entropic terms are competing terms,whichlead to amaximum free energy at an optimal separationdistance. Inclusion clustersmaythenbeanalyzed,forwhichthereisnoanalyticalsolution,andagaininthiscase,thereisanoptimaldistance.Next,thediffusionoftheseinclusionsismodeledusingoverdampedLangevindynamicsandassociated Fokker-Plank equation, where the drag comes from the fluid nature of themembrane and is modeled using the Saffman-Delbruck formula, and the potential is thepreviouslycomputedonebymeansofstatisticalmechanics. First thediffusionofasingleproteinisanalyzedunderthepresenceofasecondinclusionthatisconsideredfixed.Underreflecting boundary conditions, the Fokker-Plank equation delivers the Boltzmanndistribution at equilibrium. The first passage time can also be computed for variousboundary conditions. For self-assembly conditions, the passage time is an order of

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magnitude smaller than what was seen in experiments but the membrane that can besimulatedismuchsmallerinthemodelandhencetheresultsarenotunreasonable.Foramoredetailedanalysis,thehydrodynamicsinteractionsbetweeninclusionshavetobeconsidered.AwaytoaccounttheseinteractionsisthroughtheOseentensor.Itisobservedthathydrodynamicinteractionsspeeduptheself-assemblyprocess.Conclusions

• Proposeda time-efficientapproach fromstatisticalmechanics tocompute the freeenergyofathermallyfluctuatingmembranewithinclusions.

• Thisallowsstudyingtheself-assemblyprocessofinclusions.References[1]X.LiaoandP.K.Purohit."Self-assemblyonalipidmembraneviewedasafirstpassagetimeproblem."JournaloftheMechanicsandPhysicsofSolids135(2020):103787.

Andrej Kosmrlj.Statistical mechanics of microscopically thin thermalizedstructures. Overviewandmotivation:Thinsolidshellsandstructurescannowbe fabricatedatverysmallscaleswherethermalfluctuations become important. The main question here discussed is how do thermalfluctuations affect their mechanical properties? This is discussed in the context of flatsheets, spherical shells and cylindrical shells, using tools from renormalization groupcalculationsandmoleculardynamicsimulations.Approachandresults(freestandingflatsheets):The material is assumed linear elastic, though deformations can be considerable (i.e.nonlinear kinematics). Actually, these nonlinearities are responsible for many of theinterestingresultshereshown.A useful analogy to understand the behavior of thermally fluctuating flat sheets can befound in themechanics of crumpled sheets.When the amplitude of the quenched ripples(inducedbycrumpling)islargerthanthethicknessofthesheets,thebendingofcrumpledsheets becomes harder, while stretch/shear becomes easier. Qualitatively, similarmechanical behavior is induced by thermal fluctuations when the magnitude of heightfluctuationbecomes larger than the thicknessof thesheet,which isdefinedas thesquarerootoftheratioofthebendingmodulusandtheYoung’smodulusin2Dmaterials.Sincethemagnitudeofheightfluctuationsincreaseswithtemperatureandwiththesizeofthesheet,we can introduce a characteristic length scale lthermal at which the magnitude of heightfluctuationsbecomes comparable to the sheet thickness. For a regular sheet of paper thethermal lengthscale isgiganticand thus thermal fluctuationsare irrelevant.However, for2Dmaterialssuchasgraphene,thethermallengthscaleatroomtemperatureisoftheorderof nanometers, and thus the effect of thermal fluctuationsbecome important.Beyond thecharacteristic thermal length scale, thermal fluctuations effectively renormalize bendingrigidity and Young’smodulus andmake them scale dependentwith universal power lawexponents. These different exponents are related to each other due to the rotational

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invariance,andtheycanbeestimatedwiththerenormalizationgrouptheoryandatomisticorMonteCarlosimulations.The projected area of the sheets is also temperature dependent. The thermal expansioncoefficienthastwocontributions:onethatispositiveisinducedfromthethermalexpansionofatomicbonds,andasecondentropiccontribution,whichisnegative,isinducedbyheightfluctuations. As a consequence, fluctuating membranes can have negative thermalexpansioncoefficients.External tensile stress suppresses the height of the fluctuations. This effect dominates atscales larger thana lengthscale lstress,which is inverselyproportional to themagnitudeofappliedtensilestress.TherelativevalueofthevariouslengthscalesandthesystemsizeLdefinesthreedomains:(i)forL<lstress,theprojectedareaincreaseslinearlywiththeappliedstresseswith the slope corresponding to the renormalizedbulkmodulus; (ii) for lthermal <lstress<L,nonlinearstress-strainbehaviorisobservedwithauniversalpowerlawexponent,and(iii)forlstress<lthermal,thermaleffectsarecompletelysuppressedandclassicalmechanicsisrecovered.Under compression, the sheet may buckle. Interestingly, analyses reveal that thermalfluctuations increase the critical buckling load for sheets that are larger than the thermallengthscale.Theincreasedcriticalbucklingloadisdirectlyrelatedtothethermalstiffeningofthebendingrigidity,whichisalsoverifiedwithMDsimulations.The analyses above all pertain to isotropic sheets. For anisotropic sheets, the thermalfluctuationsdependonthefulltensorofelasticconstants.However,atlargelengthsscales,duetothermalfluctuations,theanisotropicsheetsbehavelikeisotropicsheets.Approachandresults(sphericalshells):Due to the shell curvature, the strain tensor contains an additional term, which couplesbending and stretching deformations. As a consequence, the magnitude of radialfluctuations is suppressed at large length scales. In this case, the magnitude of thefluctuationsdoesn’tincreasewiththesystemsize,butratherwithanewelasticlengthscale,thatisgivenbythesquarerootoftheradiusandthethicknessoftheshell.Whenthiselasticlength scale is larger than the thermal length scale, then thermal fluctuations becomeimportant. Similarly, to the flat sheet case, thermal fluctuations lead to an increase in therenormalized bending rigidity and a decrease of the normalized Young’s modulus. Inaddition,thermalfluctuationsgenerateaneffectiveentropiccompressivestress(analogousto some external pressure) that reduces the critical buckling pressure of the shell. Atsufficientlylargetemperaturestheeffectivecompressivestresscaninducethespontaneouscollapseofthesphericalshellevenintheabsenceofexternalpressure.Approachandresults(cylindricalshells):Cylindrical shells also contain additional terms in the kinematics induced by curvature.Similartosphericalshells, thermalfluctuationsbecomerelevantbeyondthecharacteristicelastic length scale, and the renormalized Young’s modulus (bending rigidity) decreases(increases) with the same power law exponents as that of flat sheets. Different fromsphericalshells, thecriticalbuckling load isnon-monotonicwithtemperature.Thecriticalbucklingloadisinitiallyreducedduetothermalkicksovertheactivationbarrier,butathightemperatures the critical buckling load increases due to the renormalization of elasticconstants.

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Conclusions• Thermalfluctuationcanbecomeimportantatsmallscales.• Thermalfluctuationscanleadtounusualandsurprisingmechanicalbehavior.

References[1] A. Košmrlj and D.R. Nelson. "Statistical mechanics of thin spherical shells."PhysicalReviewX7(2017):011002.[2]A.KošmrljandD.R.Nelson.“Responseofthermalizedribbonstopullingandbending”,PhysicalReviewB93(2016):125431.

Session8:MechanicsofMaterialsIII

PradeepSharma.FlexoelectricityandElectrets Overviewandmotivation:Piezolectricitydealswiththecouplingofelectricalsignalsandmechanicaldeformation,sothat one can induce the other and vice versa. Applications are very varied (e.g. tennisrackets,wireless sensors, robotic arms)with energyharvestingbeingofmarked interest.Howevertheenergyscaleislowwhichreducesapplicationstosmalldevices,andtherearecurrentlymanyeffortstoengineerhighpiezoelectricity.Approachandresults:Incentrosymmetriccrystalsthecenterofpositiveandnegativechargescoincide(evenafteruniformdeformation)andthereisconsequently,nopolarization. Innon-centrosymmetriccrystals though, charge separation can be achieved with deformation, and can thus bepiezoelectric.Thenumberofpiezoelectricmaterialsisthereforegivenbytheirstructureforuniformdeformations,andtherearea limitednumberofthem.However, fornon-uniformstrains, it is possible to develop an asymmetry, even for centrosymmetric crystals (nonpiezoelectric).Thisphenomenonisdenotedasflexoelectricityandithasbeendemonstratedexperimentally.It is possible toobtain an apparentpiezoelectricbehavior at thenanoscalewithoutusingpiezoelectric materials, by incorporating an inclusion. The inclusion will lead to localdeformations, which by flexoelectricty, will generate a polarization. If, on average, thesepolarizationsdon’taverageouttozero,anetpiezoelectriceffectwillbeachieved.Therecipethus consists on having high elastic and dielectric constants, small size (to induce largestrain-gradients),non-centrosymmetricshapeandoptimumvolumefraction.Numerical calculations on BTO and graphene sheets with triangular holes show that apolarizationcanbeachieved forsmallholes foranoptimalvolume fraction.Theseresultshavealsobeenverifiedexperimentallyonothersystems.Animportantopenissueinthisfieldisthelackofarigoroushomogenizationtheory.Also,determiningflexoelectricpropertiesnumericallyandexperimentallyischallenging,thoughDFT efforts by Vikram Gavini and Amartya Banerjee will certainly greatly help in thisendeavor.

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Since strain and strain gradients scalewith the inverse of the elasticmoduli, large straingradients are easier to achieve in soft materials. Also, soft materials are of interest forapplicationsinsoftrobotics,biologicalapplicationsandstretchableelectronics.Althoughmany softmaterials are not piezoelectric, they can become electromechanicallyactive via the so-calledMaxwell stress,which is present in all dielectricmaterials. Morespecifically,anelectricfieldcandeformthematerial(thesedeformationsmaybelarge),butthereisnoconverseeffect(cannotbeusedforenergyharvesting).AlsotheMaxwellstresseffectisnonlinear,itrequiresaveryhighvoltageanditisnotreversible.An idea is to embedmassless charges in a softmaterial to create piezoelectricmaterials.Thistypeofmaterialsexistsandiscalledelectrets.Theirmeasuredpiezoelectricityismuchhigherthanthatofoneofthebestpiezoelectricmaterials.Workinprogressincludesflexoelectricityinsoftmaterials,wherecurrentresultsareveryencouraging,andcomparisonswithexperimentalinvestigationsarepending.Also, using two-scale asymptotics, Liu and Sharma homogenized electrets and found thatthere is a true effective piezoelectric property and an emergent piezoelectricity.Interestingly,severalexactrelationswereobtained,whichisrareinhomogenizationtheory.Finally, it was noted that fleoxelectricity plays an important role in biology, and isresponsible,forinstance,forourhearingcapabilities.ConclusionsOpen issues in electrets include (i) the combination of electrets with flexoelectricity toexploit size effects, (ii) charge stability at high temperatures (they leak after some time),(iii)makingelectretsoutofreallysoftmaterials.References[1] S. Krichen and P. Sharma. "Flexoelectricity: A perspective on an unusualelectromechanicalcoupling."JournalofAppliedMechanics83.3(2016):030801.[2] Q. Deng et al. "Electrets in soft materials: Nonlinearity, size effects, and giantelectromechanicalcoupling."PhysicalReviewE90(2014):012603.

Kaushik Dayal.Electromechanics and statistical mechanics of dielectricelastomers Overviewandmotivation:Dielectric elastomers show promise for many applications (e.g. soft robotics, biomedicaldevices), but they are not so used in real settings, as very high fieldswould be required(evenclosetoelectricalbreakdown).Itisalsoworthmentioningthatdielectricelastomersmaynotnecessarilybeseenaspassiveelements thatdeformunder theapplicationof theelectricfield,buttheirmicrostructureandelectromechanicalcouplingcanbeoptimized.Approachandresults:Sequences of models (monomer, single chain and polymer network) are proposed tounderstandthebehaviorofdielectricelastomers.

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Themonomermodel followsstandard literaturewithenergeticcontributions that include(strainenergy,bondenergy–small-,dipolestrain,electrostatic term,andexternalelectricfield energy). Simplifying assumptions are made for the various terms. In particular,interactionenergiesbetweenmonomersareneglected(usingatwoscaleapproach).Toconstructthechainmodel,monomersareassumedtonotstretch,andtheirorientationcan thus be characterized via a probability distribution over the sphere. Statisticalmechanicsisthenusedtocomputethepartitionfunctionandfreeenergy.Resultsinclosedform are obtained in two limits (small strain case, and very large strain) and these arecomparedwith numerical experiments at various values of the electric field, exhibiting agoodagreement.Arruda and Boyce approach is then used to get to the networkmodel. It is assumed forsimplicitythatthechainsareuniformlyorientedonthesphere,andtheintegrationoverthesphere is approximated by integrating over eight specific chains, which are the onesresultingfromconnectingthecenterofacubewithitseightcorners.Thissortofprocedureworksverywellascanbeobservedforinstancebycomparingtomoreaccuratequadraturerules.Theresultingbehaviorisanalyzedfortwothoughtexperiments.Thefirstonceconsistsonsimultaneously applying a voltage (that induces a compression) and a traction thatpreciselybalancesoutthedeformation.Thisallowsobservingthenon-naïvebehaviorofthematerial.Asignificantdeformationisobservedasaresultoftheelectricfield,evenwithouthavingoptimizedthemicrostructureinanyway.Thesecondthoughtexperimentconsistsofasimultaneousshearandavoltage.Itisobservedthattheelectricfieldcanfurtherinduceashear, thus breaking the symmetry in material behavior. Both of these results can beinterpretedatthecontinuumlevel.Conclusions

• ThereareadditionalcontributionstotheMaxwellstresses(estimated~15%).• Overallincompressibilityimpliesthatchainsmuststretchiftheyrotate.Also,chains

rotate to alignwith the field. These give rise to an unexpected coupling betweenelectricfieldanddeformations.

References[1] N. Cohen et al. "Electroelasticity of polymer networks."Journal of the Mechanics andPhysicsofSolids92(2016):105-126.

Pedro Ponte-Castaneda.Macroscopic instabilities and domain formation inelastometriccomposites Overviewandmotivation:Elastomeric composites with periodic microstructure may develop microscopic ormacroscopic instabilities. An example of microscopic instability is given by a porouselastomer consisting of 2D periodic systems with circular holes, when subjected tocompression or tension. Another more interesting example which develops microscopicinstabilities is that of periodic rigidly reinforced composites, where depending on the

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loadingconditions,differentpatterns(wavelengthoftheinstability)develop,includinglongwavelengthinstabilities.Inthecontextofrandomcomposites,elastomericcompositescanonlydevelopmacroscopicinstabilities(theconceptofmicroscopicinstabilitiesdoesnotreallymakesense).ExamplesofthesehavebeenshownbyPonteCastañeda.Whathappensafteramacroscopicinstability(whichcorrespondstolossofellipticity)?Lossofellipticityinmetalsisassociatedwithshearlocalization,whicheventuallyleadstocracksandfailure.Intheseelastomersthebehaviorisdifferentandresultsindomainformation,torelaxthestresses.Thereisamathematicalprocedureforcomputingthesemicrostructures,which is calledquasi-convexification.Thismethodologyhasbeenpreviouslyapplied foraclass of reinforced elastomers leading first to a microscopic or a macroscopic instabilitydepending on the concentration of the reinforcing phase. Experimental investigations onsimilarsystemsexhibitchevron(doublelaminar)microstructures.Approachandresults:Foraperiodicmicrostructure,thehomogenizedbehaviorisgivenbyconsideringtheenergyunderaffineboundaryconditionsassociatedwithallpossiblecombinationsoftheunitcells(could be over one or several unit cells depending on thewavelength of the instability).Before the onset of any instability the composite is described by the so-called principalsolution,which is theone-cellperiodicsolution.Theresultingenergy isquasi-convex,andthereforerank-oneconvexbutnotnecessarilystrictlyrank-oneconvex.Tocharacterizethebehaviorbeyondtheinstabilitypointthefollowingstrategyisused.Theidea is that thehomogenizedenergy is,byconstruction lower than theprincipal solution,andconsequently,bytakingthequasi-convexenvelopeonbothsides,lowerthanthequasi-convexificationoftheprincipalsolution(insomecasesitmaybeequal).Althoughthequasi-convexenvelopeisingeneralhardtocompute,thereareothernotionsofconvexification,andrelationsoftheseviainequalitiesthatallowgeneratingestimates.Inparticular,iftherankoneenvelopeisquasi-convex,itmustcorrespondtothequasi-convexenvelope. Thankfully the rank-one envelope is easy to compute (using Kohn-Strangformula).Theresultsindicatethattherearethreeregimesorphasesdependingonthedeformation.Oneoftheseistheprincipalsolution,whichisobservedfor largedeformations.Theothertwocorrespondtoonelaminationand2laminations.Aninterestingoutcomeofthisexampleisthatlossofglobalrank-oneconvexityandlossofellipticitydonotalwayscoincide. Ingeneral, lossofglobalrank-oneconvexitytakesplacebeforelossofellipticity(lossoflocalrank-1convexity).Conclusions

• Macroscopicinstabilitiesarefollowedbydomainformation.• Lossofrank-oneconvexitygenerallytakesplacebeforelossofellipticity.• Doesrelaxationviaprincipalsolutionalwayswork?

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References[1] R. Avazmohammadi, and P. Ponte Castañeda "Macroscopic constitutive relations forelastomers reinforced with short aligned fibers: Instabilities and post-bifurcationresponse."JournaloftheMechanicsandPhysicsofSolids97(2016):37-67.[2]J.FurerandP.PonteCastañeda."Reinforcedelastomers:Homogenization,macroscopicstabilityandrelaxation."JournaloftheMechanicsandPhysicsofSolids(2019):103689.

Session9:PhaseFieldModel

PeterVoorhees.Themorphologyandtopologyofnanoporousmetals

PeterVoorheeswasabsentduetomedialreasonsandthepresentationwasthereforenotgiven.

KatsuyoThornton.Nanoscalesimulationsusingphase-fieldcrystalmodels Overviewandmotivation:Continuummodels including phase fieldmodels are useful in predictingmany aspects ofmaterial behavior. However, in some cases, neglecting the description of atoms leads tocruciallossofinformation,forinstance,whendefectsareconsidered.Phase field crystal (PFC) is a promisingmethod to simulate atomistic details at diffusivescales, and has been applied to many systems, such as formation of strain inducedcompositionaldomains,epitaxyordefectstructureandenergetics.Here,themethodretainsdynamicinformationviatheprobabilitydistribution.PFCfreeenergycaninfactbederivedfrom classical density functional theory, under suitable assumptions, and it thus hasphysicalfoundationswithapproximations.Abigquestioninthecommunityiswhetherthemethodcanbeparameterizedtospecificmaterialstoprovidequantitativepredictions.This talk focusedon two topics: (i) identifying lowenergygrainboundary structuresandmetastableones,and(ii)modelingof2Dmaterials.Approachandresults(applicationstograinboundaries):Identificationofgrainboundarystructuresisoftendoneinmolecularstaticsbyslidingonecrystalwithrespecttotheother.Thisishoweveratediousprocessandsometimesitdoesnot find the lowest energy state. The approach taken here to identify grain boundarystructureanditsenergeticsisbyhavingtwocrystalsthatareinitiallyseparated,andtheseare allowed to grow. This can be done for different orientations and shifts in order toidentifythelowest-energygrainboundarystructure.Theseareoftencharacterizedbylessdiffusive peaks which are indicative of lower atommobilities, as could be expected. Theresults obtained are compared with grain boundary structures predicted by geneticalgorithm,showingaremarkableagreement.SuchcomparisonsweredoneforvariousGB,evensomeexhibitingnanofaceting.Consequently,PFCcanbeusedasurrogatemodelthatcouldbeusedforinstance,toinforminitialconditionsforatomisticmodels.Approachandresults(applications2Dmaterials):2D materials are a promising application for PFC. Most previous studies are howeverconfinedtotwodimensions.Here,thegoalistodevelopathree-dimensionalmodelofthese

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2Dmaterialstoexaminebucklingundercompressionfortriangularandhoneycomblattice.Simulationresultswerepresentedtodemonstratethenewmodel.Conclusions

• PFC provides atomistic description over diffusive time scales and naturallyincorporateselasticity.

• PFCcanidentifygrainboundarystructures.Itcanbeausefulcoarse-grainedmodel.• Developeda3Dmodelfor2Dmaterials.

MartinDiehl.Couplingcrystalplasticityandphasefieldmethods:thefutureofintegratedcomputationalmaterialsengineering? (JointworkwithP.Shanthraj,P.Eisenlohr,F.Roters,D.Raabe)Overviewandmotivation:IntegratedComputationalMaterialsEngineering(ICME)“entailsintegrationofinformationacross lengthandtimescalesforallrelevantmaterialphenomenaandenablesconcurrentanalysisofmanufacturing,designandmaterialswithinaholisticsystem”[1].Thegoalistoconnectprocessing,microstructureandproperties,whichistheholygrailofcomputationalmaterialscienceandengineering.Theabovegoalishoweverfarfromreach.Thistalkisthusmuchnarrowerandfocusesonthecontinuummodelingofpolycrystallinematerials(physicsbasedmodels)atengineeringtime and length scales, integrating all relevant phenomena. Phenomena besides plasticitythatarediscussedincludedfracture,twinningandchemomechanics.Approachandresults:Continuummodelingofcrystalplasticityistypicallybasedonthekinematicdecompositionofthedeformationgradientbetweentheelasticandplasticpart,wheretheplasticvelocitygradient iswrittenas functionof theshearratealong thevariousslipsystems.Theshearrates depend on the critical resolved shear stress, which evolve during the deformation(hardening). The constitutivemodels for the shear rates are either phenomenological orphysicsbased.Here,aphysics-basedapproachdevelopedand implemented togetherwithJaime Marian and David Cereceda is presented. This model integrates DFT, atomisticsimulationsandkMCresultsandaccountsfornon-Schmideffects.Thisleadstoacontinuummodels that is fully parameterized with by results from atomistic simulations and thatresultsinyieldstressesthatcompareverywelltoexperiments,whichisquiteremarkable.Forhardening,onecanuseageneralizedTaylorlaw,wheretheparameterscanbeobtainedfromdiscretedislocationdynamics(DDD).Fracturemaybemodeledusingthephasefieldmethod,wherethephasefieldparameterisadamageparameter.ThisapproachisusedtounderstandfractureincastAlalloys,whosemicrostructure in the form of voids has been characterized experimentally, although thecrystallographicorientation isunknown.Thebehavior is showntobestronglydependentonthegeometryofthevoidsaswellascrystalorientation.Twining can also be modeled using a phase field approach, which allows to simulatetwinning evolution and its couplingwith dislocationdensity. Various examples simulatedshowedmicrostructures,whichstronglyresembleexperimentalimages.

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Regarding chemomechanics, precipitation is modeled as a spherical inclusion with aneigenstrain(Eshelbyproblem),andthematrixisconsideredtohavecompositiondependentelastic constants. Simulations are carried out on the codes DAMASK and OpenPhase andcompared to each other. Chemomechanical coupling strongly affects the precipitationkinetics.Conclusions:

• Recrystallizationisaveryimportantproblemforsteelmanufacturing,whichwouldbe great to model in combination with crystal plasticity. Possible approachesinclude(i)cellularautomataapproach,(ii)KWCapproach(e.g.AdmalandMarian),(iii)multi-phasefield.

References:[1]J.Allisonetal."Integratedcomputationalmaterialsengineering:anewparadigmfortheglobalmaterialsprofession."JOM58.11(2006):25-27.

Session10:ScaleBridgingI

JarekKnap.AcceleratingScaleBridgingviaSurrogateModeling (JointworkwithTingWang,KennethW.Leiter,PetrPlechac)Overviewandmotivation:Multiscalemodelingisasystematicapproachforconstructinghigh-fidelitymaterialmodelsby combining physics of relevant scales. Scale bridging is however computationallychallenging. This is the case, for instance, of themodeling of energeticmaterials, such asRDX, where the coupling between chemical composition andmechanical deformations isnotoriously complicated: a multiscale strategy that combines FEM and DPD-E LAMMPS,withoutincludingchemistryisalreadycomputationallyintractable.Consequentlythereisaneedtoreducethecomputationalcostofthelowerscalemodel,whichisherepursuedviasurrogatemodels.Approachandresults:Gaussian process regression is a common approach for surrogate modeling. It providespredictionsanduncertaintiesonnon-simulateddata.However,itrequiresinvertingalargematrix (the covariance matrix), which can also lead to large computational costs. Theapproach suggested here is to do adaptive online Gaussian process regression (localsurrogatemodels). This approach highly reduces the computational cost, however globalcontinuity and smoothness is lost. A global approach can be obtained with hierarchicalCholesky decomposition. It is a multiresolution approach, it gives smoothness andcontinuity,anditsignificantlyreducesthecomputationalcost.Thegoalistoapplythesestrategiestothesimulationofenergeticmaterials,incorporatingchemistry. Simulations of scaled thermal explosion experiments are currently work inprogress.

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Conclusions:• Multiscalemodeling canproducehigh-fidelitymodels, but canbe computationally

impractical.• Surrogatemodelingcanreducecomputationalcost.Examplesare,Gaussianprocess

regressionandhierarchicalCholeskydecomposition.

Yuri Mishin.Physcally-informed artificial neural networks for atomisticmodelingofmaterials (JointwithJ.Hickman,G..PurjaPun,V.I.Yamakov)Overviewandmotivation:Atomistic simulations of materials rely on interatomic potential to characterize forcesbetween atoms, and consequently, potentials are the most critical ingredient. Classicalpotentials express energy and forces as a function of atomic coordinates. The functionalformisoftenmotivatedbyphysical/chemicalintuition,andparametersareoptimizedwithexperimentalorDFTdata.Theresultingpotentialscanbesimpleorcomplex,theyareveryfast and can be used formultiple purposes (e.g., mechanical behavior, diffusion kinetics,thermodynamic properties). An important drawback though is that they are specific tocertainclassesofmaterials(e.g.metalswithEAMpotentials,covalentwithTersofforSW),whichposesdifficulties forsimulatingmixedmaterials. Inaddition, since thereareonlyafewparameters, they tend to be inaccurate, and they cannot be improved systematically.Thedevelopmentisalsodifficultandslowprocess.Overthepast10-15yearsanewapproachappearedwherebyinteratomicpotentialsweredeveloped using machine learning approaches. Here, instead of atomic positions, itconsiderslocalstructurefingerprintsthatcapturetheenvironmentofeveryatom,andthisis mapped to energetics with nonlinear regression strategies that use a wide range ofparameters.Theresultingmodelsareextremelyaccurate(DFTlevel),muchfasterthanDFT,applicabletoanytypeofbonding,andcanbeimprovedsystematicallywithmoreDFTdata.However, they are a pure mathematical interpolation with no guidance from physics orchemistry,and,asaresult,theycanonlyinterpolate,andnotextrapolate.Inaddition,theyrequiremassiveDFTcalculationsfortheirparameterizationandtheyaremuchslowerthantraditionalinteratomicpotentials.Approachandresults:Physically-informedNN (PINN) potentials are proposed,with the goal of getting the bestfrombothworlds.Theideahereistousetraditionalpotentialswithparametersthatcanbeadjustedonthefly(everyatominthesimulationhasitsownsetofparameters)bymeansofstructural fingerprints and a neural network. Extrapolation and transferability outside ofthetrainingdomainisthenimproved.Inordertonotfocusonaspecificclassofmaterials,amoregeneralinteratomicpotentialisconsidered,namelyan (empirical)analyticalbondorderpotential. It includesshort-rangerepulsion, bondorder, bondangledependenceandbond screeningbyneighbors, it has8parameters,anditisapplicabletometallicandcovalentmaterials.Theresult,asdemonstratedforinstanceforAlandSi,isaphysicallymeaningfulinteratomicpotential, even under extrapolation, while having the same accuracy as NN potentials.

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Regarding its computational performance, it is about 20 to 170 times slower thantraditionalpotentials,butmuchfasterthanDFT.Itenableslarge-scaleMDsimulationswithDFTaccuracy,asshown,forinstance,forcracknucleationonagrainboundary.Conclusions:

• MLpotentialemergeasnext-generationmodels,thoughtheyareseverelylimitedbythelackoftransferabilityduetothelackofphysics.

• PINNisoneexampleofphysicsguidedMLmodels.• ThedirectionofthefieldgoesintotheintegrationofMLandphysics.• WorkinprocessincludesmulticomponentPINN.

References:[1] G.P. Purja Pun et al, “Physically informed artificial neural networks for atomisticmodelingofmaterials”NatureCommunications,10(2019)2339.

XinYan.Time-scalinginatomisticandtherate-dependentmechanicalbehaviorofnanostructures(JointworkwithPradeepSharma)Overviewandmotivation:Atomistic simulations provide a unique window to look at the microscopic behavior ofmaterials. It has been extremely useful to study 2D materials, alloys, biomaterials ornanoindentationexperimentsforinstance.However,thetimescaleaccessibletomoleculardynamic simulations is highly limited and often below the time scales of interest, whichoftenleadstotheuseofunreasonablyhighstrainrates.Processessuchascreep,corrosionor protein folding are thus very hard to model. Many methods have been developed toovercomethisdifficulty,thoughthetimescaleproblemisyetunsolved.Approachandresults:The proposed approach combines four techniques: autonomous Basin Climbing (ABC),nudgedelasticband(NEB),kineticMonteCarlo(kMC)andtransitionstatetheory(TST),tostudylowstrainratephenomena.Inparticular,ABCisusedtoidentifytheenergyminimaandsaddlepoints,NEBisusedforthecalculationoftheenergybarriers,andkMCandTSTareusedtoselectthetransitionpathwayandadvancetime.Thistechniqueisdemonstratedoverthreematerialsandprocessesathighandlowstrainrates,tohighlightthestrongsensitivityofmechanicaldeformationstostrainrates.Thehighstrainratesimulationscanbebenchmarkedagainstmoleculardynamicssimulations,whiletheapproachdescribedabovewillenabletoperformtheslowstrainratesimulations.

- Nano-pillar compression of Ni. At high strain rates, the nanopillars deform to abarrelshape,asitmayalsobeseeninmoleculardynamicsimulations.Atlowstrainrates though, the behavior is very different: there is amorphization and surfacereconstruction. This behavior is inaccessible to MD simulations, but similarexperimentalobservationshavebeenmade.

- Plasticity in amorphous Li-Si nanostructures. This is an important material forenergy storage applications and it exhibits largemechanical deformations duringloading-unloading. Here, the stress-strain curve exhibits a strong strain ratesensitivity.At lowstrainrates, theonsetofyield is lower, thecurvedisplaysmore

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fluctuations and the residual stresses are larger upon unloading. The underlyingdeformationmechanismsleadingtothisbehaviorcanbeunderstoodusingatomisticvisualization.Theseindicatethatwhenthematerialhasmoretimetodeform(lowstrainrates),thestrainisdistributedthroughoutthesampleandmanymoreatomsexhibitnon-affinedisplacements(sheartransformationzones).

- Void nucleation in Li-Si alloys for various concentrations of Li. Here again, thebehavior is also strongly affected by the strain rate, and voids nucleate at lowerstrainsforslowerloadingconditions.

Conclusions:

• Time-scalebottleneckinatomisticsimulationsisstillfarfromcompletelysolved.• MethodssuchasthosebasedonABCcanprovidenewinsightfortheseproblems.

References:[1]XYanetal,“Timescalinginatomisticsandtherate-dependentmechanicalbehaviorofnanostructures”,NanoLetters16(2016):3487-3492.[2] X Yan et al, “Elucidating the atomistic mechanisms underpinning plasticity in Li-Sinanostructures”,Physical.ReviewMaterials1(2017)055401.

Session11:ScaleBridgingII

Dan Mordehai.Calculating the activation parameters of thermally activateddislocationmechanisms(JointworkwithStavNisany,TomerGur-Apter)Overviewandmotivation:Plasticity in defect free materials are controlled by nucleation of dislocations, and thisprocess is here examined usingmolecular dynamic simulations, with the caveat that thestrainratesarealwaysmuchlargerthaninexperiments.Approachandresults:Nucleation is a thermally activated process, where the energy barrier depends ontemperatureandtheexternalforce.Thepointwheretheenergybarrierdisappearscanbedenoted as spontaneous nucleation. The most common method to compute activationbarrierforthenucleationeventisthenudgedelasticband(NEB),althoughitcorrespondstozerotemperature.WeiCaiproposedastrategytocomputetheentropiccontribution,butitisverytedious.Experimentally,ChrisSchuhproposedtoextractthecumulativedistributionfunction(cdf)ofthestrengthfromnanoindentationexperiments,inordertoestimatetheenergybarrierundersomesimplifyingassumptions(duetothecomplicatedstressfield).ThisideaswerefurtherexploitedbyDanGianola,whoconsideredtensiledeformationofnanowires,wherethestressfieldismuchmoresimple.Here,approximationswerealsomadeontherelationbetween theenergetic andentropicpartof the energybarrier.Mordehaibrings this abitfurther and noted that the activation volume can be extracted form the width of thedistributionwithoutassuminganyspecificformoftheenergybarrier.

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ThisstrategywasappliedtoMDsimulationsoffacetedMonanoparticles.Whenneglectingthe entropy barrier, it was obtained that the energy barrier follows a power law withexponent near 1.5,which appears inmany thermally activated processes: STZ in glasses,stretched proteins, twin boundary motion. Entropic contributions were then considered,usingtheMeyer-Neldelcompensationrulemodel,althoughthefitwasnotcompletelyideal.ThissamestrategywasalsoappliedtoMDsimulationsof tensiletests innanowiresalongthe [110] direction. Here nucleation does not always occur at the same point, as it alsodepends on temperature. Sometimes nucleation occurs at the acute angle of the crosssectionandothersattheobtuseangle.Here,cdfareextractedforeach,wherehigherorderCDFapproximationsareused.Conclusions:

• Amethodisproposedtodirectlyextractactivationvolumesformcdf,comingfromsimulationsorexperiments.

• Appliedtonucleation-controlledplasticityinnanostructures.• Nucleationmodelsformultiplesitesarecurrentlyunderdevelopment.

References:[1]D.ChachamovitzandD.Mordehai,”TheStress-DependentActivationParametersforDislocationNucleationinMolybdenumNanoparticles”,ScientificReports8,3915(2018)

AndreaLiu.Whatwelearnfrommachinelearning (Jointworkwith S. S. Schoenholz, E.D. Cubuk,R. J. S. Ivancic, F. Landes, T. A. Sharp,D. J.Strickland, S. L. Thomas, G. Biroli, O. Dauchot, D. J. Durian, D. S. Gianola, E. Kaxiras, D.Reichman,J.Rottler,D.J.Srolovitz) Overviewandmotivation:In liquids any particle can rearrange at any time. In crystals, particles in defects likedislocations are far more likely to move than those in the crystalline environment. Inglasses,areallparticles thesame,orare theresomeparticleswithahigherpropensity torearrange?Thishasbeenanopenquestionfordecades.Identifyingsuchparticlesfromthestructures andwhether the structure can actually tell something about the dynamics hasbeena50-year-old standingproblem.Thecomplexityof thisproblem is evident from thefactthatstructurechangeslittlewhiledynamicscanchangealot.Itturnsoutthatthislong-standingproblemisextremelyeasytosolvewithmachinelearning.Approachandresults:The key is that machine learning uses many structural variables to find the linearcombination that correlates best with particle rearrangements. This in contrast totraditional methods, which are often based on a single variable. Examples of thesequantities are g(r) for various values of r. A hyperplane is then constructed that bestseparatestherearrangingfromnon-rearrangingparticles.Thedistancetothathyperplanedefinesavariablecalledthesoftness.Softnessencodestherelationbetweenstructureanddynamics.Interestingly,itonlydependsonparticlepositions(nottheinteractions),whichis good for experiments. However, the hyperplane is not universal (different for eachsystem),incontrasttodislocations.

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Acloselooktotheapparentparadoxthatinglassydynamicsstructurebarelychangeswhiledynamics changesa lot (e.g. likeWCAandLJpotentials), reveals that softness isdifferentand captures the important structural signatures. Interestingly, relaxation times as afunctionofsoftnessarealmostidenticalforthetwosystems(canusesamehyperplane).This idea has been tested formany systems (e.g., atoms, polymers, colloids, grains)withdifferentinteractions(e.g.vanderWaals,covalent,hardcorerepulsions),andwithdifferentsources of rearrangements (e.g., thermal, mechanical), spanning various orders ofmagnitude in particle size and stiffness and for all these systems thismethod to predictrearrangementsworks. Interestingly, thesesystems indicate that there isauniversalityoftheyieldstressindisorderedsolidsaswellasauniversalityintheresponseofsoftnesswithstrain.Furthermore,therearrangementprobabilityforafixedsoftnessisArrhenius,whichimpliesthat there is an energy barrier to rearrange, which depends on softness. However, sincethere is a distribution of softness in thematerial, the overall dynamics is not Arrhenius.Interestingly,thereisatemperaturewheretherearrangementprobabilityisindependentofsoftness.Thistemperaturecorrespondstotheonsetofglassybehavior.Thisseemstoworkverywellforothersystemsaswell.Applying the above analysis to polycrystals allows visualizing the softness of the variousgrainboundariesandotherdefectssuchasvacancies.Inthissystemaswell,theprobabilityofrearrangingisalsoArrhenius,whichallowsextractingfreeenergybarriers.Incontrasttoglassysystems,thecurvesdon’tcrossandsothereisnoonsettemperature.Conclusions:

• Softness is a hidden structure parameter that correlates strongly with glassydynamics.

• Theconceptofsoftnessworksacrossallspectrumsoforder/disorderedmaterials.• There is a barrier height associated to each softness, which indicates a relation

betweenstructure(softness)andenergylandscape.References:[1] E.D. Cubuk et al, “Structure-property relationships from universal signatures ofplasticityindisorderedsolids”Science,358(2017)1033.[2] T.A. Sharp et al, “Machine learning determination of atomic dynamics at grainboundaries”,ProceedingsofNationalAcademyofSciences(115)2018:10943-10947.

DiscussionsandopenchallengesThe following challenges and opportunities have been identified based on the variouspresentationsandensuingdiscussions.Calculationoftheexchange-correlationenergyfunctionalindensityfunctionaltheory.The exchange-correlation potential accounts for all quantum mechanical interactions inDFTcalculations.Althoughitisauniversalfunction,i.e.materialindependent,itispresentlyunknown,anditthereforehastobemodeled.Thisimpliesthatstronglycorrelatedsystemscannot be modeled accurately. The calculation of this exchange-correlation energy

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functional represents the Holy Grail in quantum mechanics. Important advances on thisfronthavenbeenshown,forinstance,byVikramGaviniinhistalk.Non-Schmideffectsandnon-associatedflowAs noted by Cottrell and emphasized in various talks during theworkshop (see talks byJohnBassani,DavidRodney,JaimeMarianorMartinDiehl),associatedflowhasfortoolongbeen taken as the standard plasticity formulation, despite it beingmore of an exceptionrather than the rule. Fundamental advances in the microscopic understanding of non-associative flow rules have been achieved, for instance, byDavidRodney, althoughmanyquestionsremain.Deviationsofthedislocationpathwaywithrespecttotheglideplanearestronglymaterial dependent, and it is still unclearwhat controls themagnitude of thesedeviations. Inaddition,mostof thecurrentunderstanding isbasedonscrewdislocations,while fewer studies exist formixeddislocations.At themacroscopic scale, twoadditionalchallenges have been identified. One relates the development of good homogenizationmethodsfornonself-adjointproblems,liketheequationsfornon-associatedflow;andthesecondonereferstonumericalschemesthatcanactuallyresolvetheseeffectsandeasilygetconvergence. Finally,itwasalsoquestionedwhethernon-normalityflowrulecouldresultasaconsequenceofthenon-convexenergyforgrainboundariesandtheirassociatedmodeswitching.ThetimescalechallengeinmultiscalematerialmodelingA recurrent theme in the workshop was the need to have modeling and simulationcapabilities that simultaneously have atomistic spatial resolution and can reach diffusivetime scales. Such a capability is important for the understanding of phenomena such asdefect interaction, lithiation, corrosion or protein folding. Various strategies to dealwiththis challenge have been presented, including diffusivemolecular dynamics (seeMichaelOrtiz’s talk), concurrent atomistic-continuummethod (see DavidMcDowell’s talk), phasefieldcrystal(seeKatsuyoThornton)andmethodsbasedonautonomousbasinclimbing(seeXin Yan’s talk). However, this challenge is far from being solved due to the lack of acomprehensive non-equilibrium statistical mechanics theory. Present approaches arecurrentlyproblemspecificanditisbelievedthataunifiedcoarse-grainingtheory,althoughhighlydesired,isfarfromreach.SymmetryandsymmetrybreakingMany materials have underlying symmetries. The classical example is that of crystallinelattice, which is based on translational periodicity. However, a much more generaldescription of material symmetries, which includes translations, rotations, and theircombinationwas formalizedwith the theory of objective structures. Computational toolsthat can leverage these symmetries in their simulation (see Amartya Benerjee’s talk) areopeningthedoortoanalyzeanddiscovernewmaterialproperties.Anotherinterestingandrelatedtopicdiscussedduringtheworkshopisthatofsymmetrybreaking,whichcanleadtoemergentflexoelectricandpiezoelectricbehavior(seePradeepSharma’stalk).FluctuationsatthenanoscaleFluctuations are often neglected in the description of materials, as they tend to beinsignificantatlargerscales.However,theybecomeextremelyimportantatthenanoscale.For instance, thermal fluctuations can strongly impact the mechanical behavior (seeAndrej’sKosmrljtalk),andtheyencodethesignatureofthermallyactivatedprocesses(seeDanMordehai’stalk).Furthermore,fluctuationsprovideacomputationalmicroscopetoget

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insight into non-equilibrium phenomena such as interface motion (see YashashreeKulkarni’stalk).Defectstructureandevolution.Anintegratedtheoretical-experimentalapproachMultipletalksinthisworkshophavebeendevotedtotheunderstandingofdefectstructure,interaction and evolution, via theoretical/computational techniques (e.g.,Mauricio Ponga,DavidRodney,DavidMcDowell, JaimeMarian,AnterEl-Azab,YashashreeKulkarni,NikhilAdmal, Brandon Runnels, Garritt Tucker, Timothy Rupert, Katsuyo Thornton, DanMordehai)andexperimentalapproaches(e.g.,JunLou,MitraTaheri).Manyopenquestionsstill remain though, including,without being comprehensive, dislocation and point defectinteraction, absorption at grain boundaries, grain boundary structure and evolution ordislocation defect drag. Presentations and discussions all converged to the need ofintegrated theoretical and experimental efforts to tackle these questions, to leverage thecomplexity/simplifications of real/numerical experiments and the spatial and temporalresolutionofthevariousapproaches.NovelcharacterizationtoolsinbothexperimentsandsimulationsAdvancesinhigh-resolutionexperimentaltechniquesinspace,timeandenergy,aswellasincreased computational resources are enabling a very detailed visualization of thematerials’microstructureandevolution.Yet,extractingamechanisticunderstanding fromthese massive amounts of data, either experimental or computational, require thedevelopment of characterization tools that can systematically identify the importantdegrees of freedom that correlate with a given behavior as well as quantify the variousdeformationmechanisms thatmaybe simultaneously competing.Advances in this regardwerediscussedforinstancebyGarritTucker,whointroducedshapemomentdescriptorstocharacterizetheatomicenvironmentingrainboundaries,orbyMitraTaheri,whichutilizesmachinelearningtoidentifydefectsfromverynoisydata.AtthenexusbetweenphysicsandmachinelearningMachine learning has emerged as a very powerful and highly accurate tool for datainterpolation, with applications to multiscale modeling (see Jaroslaw Knap and YuriMishin’stalk)andclassification(seeMitraTaheriandAndreaLiu’stalk).Althoughitisoftenseenas“magic”blackbox,itactuallystillrequiresagreatamountofintuition(whichdatatousefortrainingandvalidationset,whichpropertiescorrelatewitheachother,etc.),buttheoutcome tends to be much better than with traditional approaches. However, machinelearning tends to perform extremely poorly under extrapolation due to the absence ofphysics in its formulation. Strategies for integrating physics andmachine learning are animportant challenge.A great exampleof such integration canbe found in the talk of YuriMishin,butmanyopportunitiesremainatthisintersection. PlasticityincrystallineandamorphousmediaTheunderstandingofplasticbehavior in amorphousmediahasbeenproven tobehighlychallenging.Incontrasttocrystallinematerials,wheredislocationscanbeclearlyidentifiedascarriersoftheplasticbehavior,theidentificationofstructuralsignaturesinamorphousmaterialsthatcorrelatewiththedynamicshasbeena50-year-oldchallenge.Onlyrecently(seetalkbyAndreaLiu),softnesswasidentifiedthankstomachinelearningasthesoughtafterstructuralmeasure. Ithasalso led to the identificationofvariousuniversal relationsgreatly advancing the understanding of amorphous media. Interestingly, the concept ofsoftnessappliestoaverywiderangeofmaterials,includingalsoorderedmedia.Anatural

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questionthereforerisesaswhetherthiscouldprovideanewwayoflookingatplasticityincrystalsandgrainboundaryphenomena.

PosterpresentationsInadditiontotheoralpresentationspreviouslyreviewed,atotalof20posterswerepresentedduringtheworkshop.Theauthors,affiliationsandpostertitlesarelistedbelowinalphabeticalorder.• LuAn,VillanovaUniversityCharacterizationoffree-standingfilmsanditsapplications

• MohamedElHediBahri,PrincetonUniversityInfluenceofthermalfluctuationsontheelasticmoduliof2Dmaterials

• BryanChem,UniversityofPennsylvaniaUltra-broadbandresonantmetamaterialforenhancedwaveattenuation

• ShuvrangsuDas,UniversityofPennsylvaniaEffects of brine inclusions and crystallographic anisotropy on the rheological response ofseaice

• KshiteejDeshmukh,CarnegieMellonUniversityBond energies of molecules using strictly-correlated-electron (SCE) limit of Density-Functional-Theory

• MartinDiehl,Max-PlankInstituteforIronResearchBeyond crystal plasticity-multiphysics tools for integrated computational materialsengineering

• AhmedGhareeb,UniversityofIllinoisatUrbana-ChampaignAn adaptive quasi-continuum approach for modeling fracture in nonlinear networks:Applicationtopolymericmaterials

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• YejunGu,JohnsHopkingsUniversityThe effect of hydrogen on the plastic deformation of metals as predicted from discretedislocationdynamicsimulations

• JamesHickman,NISTDevelopmentofphysicallyinformedneuralnetwork(PINN)potentialswithapplicationstosiliconandgermaniumsystems

• ShenglinHuang,UniversityofPennsylvaniaDiscovery of size-dependent continuum diffusive models via fluctuation-dissipationrelations

• AakashKumar,UniversityofPennsylvaniaDiffusionattheNi/alpha-Al2O3interfacesusingreactivemoleculardynamics

• SergioLucarini,IMDEAMaterialsEfficientalgorithmsforgrainmicrostructureevolution

• SiddharthaSarkar,PrincetonUniversityBucklingofthermalizedcylindricalshells.

• JaspreetSingh,UniversityofPennsylvaniaCnoidalwavepropagationinanelasticmetamaterialAllostericinteractionsinabirodmodelofDNA

• ShohamSen,CarnegieMellonUniversityRecursive Projection Method as a means to improve convergence in Density FunctionalCalculations

• ChuanpengSun,UniversityofPennsylvaniaStick-slipkineticsinabistablebarimmersedinaheatbath

• ErikTamsen,TechnischeUniversitatDresdenAfullyconsistentmicro-macrotransitionapproachfordynamicsatfinitestrains

• HaoranWang,DukeUniversityAchieving high-fidelity molecular dynamics simulations by stochastic reduced ordermodeling

• TingWang,ArmyResearchLaboratoryAcceleratedscalebridgingwithsparselyapproximatedGaussianlearning

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AdministrativesupportandacknowledgementsTheworkshoptremendouslybenefitedfromincrediblestaffsupport,namely,RuthHengst,fromtheUSAssociationofComputationalMechanics(USACM),KatherineThompsonfromthePenn InstituteofComputational Science (PICS), andPeterLitt andSusanWaddingtonfromtheDepartmentofMechanicalEngineeringandAppliedMechanicsoftheUniversityofPennsylvania. Inaddition,wewould liketo thankFeliceMacera, for thephotography,andCETSatPenn(ComputingandEducationalTechnologyService)forthetechnicalsupport.

The organizers further acknowledge the generous financial support provided by theNational Science Foundation, through award number 1929268 from theDivision of Civil,MechanicalandManufacturingInnovation.

U ACM