Implementation of Nano-mechanics in Geotechnical Engineering Hyungrae Cho And Chung R. Song Department of Civil Engineering The University of Mississippi University, MS 38677
Dec 18, 2015
Implementation of Nano-mechanics in Geotechnical
Engineering
Hyungrae ChoAnd
Chung R. Song
Department of Civil EngineeringThe University of Mississippi
University, MS 38677
Introduction Background Nano-mechanics Tentative Results Conclusions
Contents
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Introduction
The macro-scale material behavior is a representation of the average micro-scale material behavior.
The micro-scale material behavior is a representation of the average molecular-scale (Nano- scale) material behavior.
By obtaining molecular-scale material properties, the macro-scale material behavior is obtained, with limited input parameters and with great accuracy and details.
With the blooming Nano-technology, molecular-scale material properties have more importance than ever.
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Theoretical Background(Traditional MM, MD, NM)
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TorsionBend AngleStretch BondVDWCoulTotal EEEEEE
21 )( oStretch Bond rrkE
ji ij
ji
oCoul r
qqeE
4
2
ji ij
o
ijoVDW r
R
r
RoDE
612
2
Well developed.
Theoretical Background (Traditional Continuum Mechanics)
n
n
nt
n
nn
W
U
t
K
Where,
nK is the stiffness matrix, n is the coupling matrix,
n is the flow matrix, U is the incremental nodal displacement,
W is the incremental pore water pressure, t is the incremental time,
n is the equilibrium force, and n is the flow vector
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Well developed.
Most things are smeared into the equilibrium equation.
-Elasticity, Plasticity, grain rotation, grain interaction, damage, …..
Theoretical Background (Advantages/Disadvantages)
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Items Advantages Disadvantages
Nano-mechanics
Capture detailed Information
Need minimal input data
Paramount amount of computation.
Unfamiliar theory to common engineers
Conti-nuum mechanics
Capture averaged real scale behavior.
Familiar theory
Difficult to capture detailed information Need to bridge Nano-
Mechanics and Continuum Mechanics
Theoretical Background Bridging Nano- and Continuum-
(Equivalent frame element method)
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fKu
Li and Chou (2003)
Odegard et al. (2001)
Ostoja-Starzewski, (2002)
2
21
)(2
1
)(
LL
EAE
rrkE
stretchaxial
oStretch Bond
Ansys
Theoretical Background Bridging Nano- and Continuum-
(RVE method)
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v
AdVV
A1
A: Properties in molecular level
A’: Properties in continuum level
DPD: Maiti et. al. (2004)
Voyiadjis et al. (2004)
Theoretical Background Bridging Nano- and Continuum-
for soils
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•Soil grains are continuum in Nano- to micro scale (sand grains and clay minerals).
•But they are discrete media in macro scale (soil masss).
•Therefore, bridging b/t Nano-, micro, and macro scales for soils shall be done as follows;
Molecular Mechanics
(Nanoscale)
Particulate
Mechanics
(Mesoscale)
Continuum
Mechanics
(Macroscale)
Tentative Results(Surface charge of clay minerals)
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Muscovite:
-194.165 kcal/mol
Montmorillonite:
-65604 kcal/mol
Kaolinite:
-162.832 kcal/mol
Tentative Results(Properties of muscovite)
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Elastic Constants (GPa)
_______________________
397.3 341 453.2 -1.847e-010 15.78 8.953e-010
341 503.4 459.4 3.126e-010 -102.7 -8.669e-010
453.2 459.4 672 5.684e-011 -40.49 -2.558e-010
-9.419e-012 -1.377e-011 -1.421e-011 238.3 5.689e-012 -71.75
15.76 -102.7 -40.46 -2.078e-010 123.5 -7.194e-010
-7.529e-012 8.329e-012 -1.61e-011 -71.75 7.336e-012 229.5
Tentative Results(Properties of Quartz-beta)
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Elastic Constants (GPa)
_______________________
103.8 11.6 12.28 0.02317 -0.01545 -2.309
11.48 103.9 12.25 0.1154 -0.05009 2.353
12.13 12.23 95.51 0.2123 -0.07562 0.1028
0.01682 -0.03887 -0.02016 46.08 -2.373 0.01008
-0.08894 -0.0679 -0.04894 -2.455 40.21 0.09949
-2.259 2.331 0.02657 0.004098 0.1255 40.33
Tentative Results(Bridging nano- and micro using DEM)
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Particulate Mechanics
DEM: φ = 26.5o
for e=0.763
Molecular Mechanics: E=104 GPa
μ=0.1061
Continuum?
Continuum Mechanics
FEM:
What can we do?
Conclusions/Remarks
With the aid of accessible software to Nano-mechanics, material scientists can predict the detailed material properties that was never possible in the past.
Application of Nano-mechanics to obtain the property of macro-scale requires substantial computational efforts, but it is impossible.
For soils bridging nano-, micro- and macro scales is achieved by combination of molecular mechanics, particular mechanics and continuum mechanics.
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Thank you for your attention.
Questions?
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