Design Tools for Architectured Bio-inspired Actuators/Sensors

Design Tools for ArchitecturedBio-inspired Actuators/Sensors

N. Vermaak1, G. Michailidis2, G. Parry1, R. Estevez1,G. Allaire2, Y. Bréchet1 1Univ. Grenoble SIMAP;2Ecole Polytechnique CMAP

March 15, 2013

Workshop for the Cours Architectures hiérarchisées : les leçons du vivant


J.E. Huber, N.A. Fleck, and M.F. Ashby, “The selection of mechanical actuators based on performance indices,” Proc. R. Soc. London A, Vol 453(1965) pp. 2185-2205, (1997).M. Zupan, M.F. Ashby, and N.A. Fleck, “Actuator classification and selection—the development of a database,” Advanced Engineering Materials 4(12) 933-940, (2002).J. Shieh, J.E. Huber, N.A. Fleck, M.F. Ashby “The selection of sensors” Progress in Materials Science 46 (2001) 461-504

convert a stimulus into a measured signal

controllable work-producing devicesActuators

Sensors

Natasha Vermaak & Georgios MichailidisMarch 15, 2013 2/30

STIMULUSmechanical, thermal,

electromagnetic, acoustic, chemical…

MEASURED SIGNALtypically electrical, optical, sometimes

pneumatic, hydraulic…

CONTROL SIGNALtypically electrical,

optical, mechanical, chemical, thermal…

MECHANICAL ACTIONdisplacement

or force


J.E. Huber, N.A. Fleck, and M.F. Ashby, “The selection of mechanical actuators based on performance indices,” Proc. R. Soc. London A, Vol 453(1965) pp. 2185-2205, (1997).M. Zupan, M.F. Ashby, and N.A. Fleck, “Actuator classification and selection—the development of a database,” Advanced Engineering Materials 4(12) 933-940, (2002).J. Shieh, J.E. Huber, N.A. Fleck, M.F. Ashby “The selection of sensors” Progress in Materials Science 46 (2001) 461-504

convert a stimulus into a measured signal

controllable work-producing devicesActuators

Sensors


STIMULUSmechanical, thermal,

electromagnetic, acoustic, chemical…

MEASURED SIGNALtypically electrical, optical, sometimes

pneumatic, hydraulic…

CONTROL SIGNALtypically electrical,

optical, mechanical, chemical, thermal…

MECHANICAL ACTIONdisplacement

or force

http://en.wikipedia.org/wiki/Bimetallic_strip Y. Forterre, J.M. Skothelm, J. Dumals, L. Mahadevan, “How the Venus Flytrap Snaps”, Nature Vol. 433, No. 27, pp. 421-425, 2005.


Thermal expansion actuators


Actuation strain:

Actuation stress:

eth = Δl = α(Tf – T0) = αΔT l0

Δll0Tf

l0T0

Δll0Tf

sth = Eecomp = -EαΔT ecomp = - eth



From CES (Mike Ashby)

Design Tools for ArchitecturedBio-inspired Actuators/SensorsCombinations of two or more materials or of materials and space, configured in such a way as to have attributes not offered by any one material aloneMike Ashby, “Designing architectured materials” Scripta Materialia 68 (2013) 4–7


Man-made bi-material strip example

http://en.wikipedia.org/wiki/Bimetallic_strip

Design Tools for ArchitecturedBio-inspired Actuators/SensorsCombinations of two or more materials or of materials and space, configured in such a way as to have attributes not offered by any one material aloneMike Ashby, “Designing architectured materials” Scripta Materialia 68 (2013) 4–7


Biological bi-material strip example

J.W.C. Dunlop, R. Weinkamer, and P. Fratzl, “Artful interfaces within biological materials”, Materials Today Vol. 14, No. 3, pp.70-78, 2011.

Mechanics Without Muscle:Biomechanical Inspiration from the Plant World, MARTONE et al, Integrative and Comparative Biology, pp. 1–20; doi:10.1093/icb/icq122

To maximize force or displacement:

Bi-material strip Thermal actuation

1. choose appropriate materials2. model the interface3. find the optimal distribution of materials (and space):

Shape/Topology optimization via level-set method


large material differences required









From CES (Mike Ashby)

Natasha Vermaak&GeorgiosMichailidisMarch 15, 2013 11/30

Usually, stronger bonds ~

steeper potential energy wells ~ stiffer materials ~ ↑E

Young’s Modulus (E)


Coefficient of Thermal Expansion (CTE or a)

Normal Lattice positions for atomsPositions displaced because of vibrations

↑ T ↑ atomic vibrations, energy

anharmonic potential avg interatomic separation ↑(thermal expansion)

harmonic potential no change in avg. interatomic separation (no thermal expansion)

Increase of avg. interatomic separation

Typical interatomic potentials are asymmetric

(anharmonic)

Interatomic distance r

Potential Energy

Symmetric (harmonic) potential

No change in avg. interatomic separation


Coefficient of Thermal Expansion (CTE or a)

Increase of avg. interatomic separation

Typical interatomic potentials are asymmetric

(anharmonic)

Interatomic distance r

Potential Energy

Symmetric (harmonic) potential

No change in avg. interatomic separation

↑ interatomic bond strength (↑E)(deeper the potential energy curve) thermal expansion a↓







Design challenge due to the interface:efficiency vs. lifetime



large material differences (efficiency)large stresses or strain gradients across bi-material interface

promotes/accelerates damage, limits the

lifetime of actuators

Design solution inspired by biological actuators

Nature uses architectured and graded or smooth interfaces (not sharp) to achieve efficiency without sacrificing lifetime



Physics and Chemistry of Interfaces, Hans-Jürgen Butt, Karlheinz Graf, Michael Kappl, Wiley, 2003Understanding Solids: The Science of Materials, R. J. D. Tilley, Wiley, 2004

Interface Modelling

Energy concerns limit the size of the interface transition zone


atom species 1 species 2

Sharp interface boundary on atomic scale (semiconductors by MBE)

Smooth or graded (broad) transitions (or thin layers of new compounds) by interdiffusion or surface reactions that depend onTemperature, diffusion coefficient, defect density, reactivity of the components…

Energy concerns and (minimizing interfacial energy) means maximizing atomic matching to reduce the number or broken bonds / lattice mis-match

Interface Transition

ZONE

MATERIAL 1 MATERIAL 2Natasha Vermaak & Georgios MichailidisMarch 15, 2013 18/30

Interface Modelling

Uniform thermal

loading, DT


To maximizedisplacement:1. choose appropriate materials2. model the interface3. find the optimal distribution of materials (and space):




Maximize vertical end-displacement

Maximize Vertical End-Displacement


S. Timoshenko, “Analysis of bi-metal thermostats”, JOSA, Vol. 11 (3), pp. 233-255, 1925.

m = a1/a2 ; n = E1/E2

Analytic optimum when the only free variable is top thickness, a1



SOME PROBLEM & OPTIMIZATION PARAMETERS

DT = 1 ; 100 x 50 elements; L = 1; h = 0.5Interface zone width = 16 * element sizeElement size = 1 / 100; Total iter. = 200Material 1 volume constraint 50%

Shape/Topology optimization

via the level-set method

E1 = 1.0

E2 = 0.5

a1 = 1.0

a2 = 0.5

Youn

g’s M

odul

us (E

)

Natasha Vermaak & Georgios Michailidis March 15, 2013 22/30

Shape/Topology optimizationvia the level set method

“The art of structure is where to put the holes.”

~Robert Le Ricolais (1894-1977)

Gregoire Alliaire, Shape and Topology Optimization, Ecole Polytechnique, http://www.cmap.polytechnique.fr/~optopo/level_en.html


Shape/Topology optimizationvia the level set method

Numerical Algorithm

S. Osher, UCLA, http://www.math.ucla.edu/~sjo/

Natasha Vermaak & Georgios Michailidis March 15, 2013 24/30J.A. Sethian, Berkeley,http://math.berkeley.edu/~sethian/level_set.html

The level set methodMethod for tracking evolving interfaces


M. Wang and X. Wang, Color level sets: a multi-phase method for structural topology optimization with multiple materials, Comput. Methods Appl. Mech. Engrg. 193 (2004).G. Allaire, C. Dapogny, G. Delgado, G. Michailidis, Multi-phase structural optimization via a level-set method, (in preparation).

Using m level-set functions, we can describe up to n=2m different phases.

The level set methodMulti-phase description



using one material + holes: v = 2.15

Initialization


DT = 1 ; 100 x 50 elementsElement size = 1 / 100; Total iter. = 200; ks = 0L = 1; h = 0.5; No volume constraint

Youn

g’s M

odul

us (E

)



E1 = 1.0

E2 = 0.5

a2 = 1.0

a1 = 0.5


DT = 1 ; ks =0; 100 x 50 elements; L = 1; h = 0.5Interface zone width = 16 * element sizeElement size = 1 / 100; Total iter. = 200Material 1 volume constraint 50%

using two materials (no holes): v = 0.97

Initialization

Youn

g’s M

odul

us (E

)




E1 = 1.0

E2 = 0.5

a1 = 1.0

a2 = 0.5

Initialization



Youn

g’s M

odul

us (E

)






Initialization

Youn

g’s M

odul

us (E

)

a2 = 1.0

a1 = 0.5

E1 = 1.0

E2 = 0.5E* = 0.25

a* = 2.0


N. Vermaak1, G. Michailidis2, G. Parry1, R. Estevez1,G. Allaire2, Y. Bréchet1 1Univ. Grenoble SIMAP;2Ecole Polytechnique CMAP

March 15, 2013

Workshop for the Cours Architectures hiérarchisées : les leçons du vivant

Design Tools for Architectured Bio-inspired Actuators/Sensors

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