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Design Tools for Architectured Bio-inspired Actuators/Sensors. N. Vermaak 1 , G. Michailidis 2 , G. Parry 1 , R. Estevez 1 , G. Allaire 2 , Y. Bréchet 1 1 Univ. Grenoble SIMAP; 2 Ecole Polytechnique CMAP. March 15, 2013 Workshop for the Cours Architectures - PowerPoint PPT Presentation
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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
Design Tools for ArchitecturedBio-inspired Actuators/Sensors
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
Design Tools for ArchitecturedBio-inspired Actuators/Sensors
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 3/30
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.
Design Tools for ArchitecturedBio-inspired Actuators/Sensors
Thermal expansion actuators
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 4/30
Actuation strain:
Actuation stress:
eth = Δl = α(Tf – T0) = αΔT l0
Δll0Tf
l0T0
Δll0Tf
sth = Eecomp = -EαΔT ecomp = - eth
Design Tools for ArchitecturedBio-inspired Actuators/Sensors
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 5/30
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
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 6/30
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
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 7/30
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
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 8/30
large material differences required
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
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 9/30
large material differences required
Design Tools for ArchitecturedBio-inspired Actuators/Sensors
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 10/30
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)
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 12/30
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
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 13/30
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↓
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
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 14/30
large material differences required
Design challenge due to the interface:efficiency vs. lifetime
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 15/30
To maximize force or displacement:
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
Design Tools for ArchitecturedBio-inspired Actuators/Sensors
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 16/30
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
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 17/30
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
Design Tools for ArchitecturedBio-inspired Actuators/Sensors
To maximizedisplacement:1. choose appropriate materials2. model the interface3. find the optimal distribution of materials (and space):
Shape/Topology optimization via level-set method
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 19/30
large material differences required
Maximize vertical end-displacement
Maximize Vertical End-Displacement
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 20/30
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
Maximize Vertical End-Displacement
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 21/30
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
Natasha Vermaak & Georgios Michailidis March 15, 2013 23/30
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
Natasha Vermaak & Georgios Michailidis March 15, 2013 25/30
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
Maximize Vertical End-Displacement
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 26/30
using one material + holes: v = 2.15
Initialization
SOME PROBLEM & OPTIMIZATION PARAMETERS
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
)
Maximize Vertical End-Displacement
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 27/30
E1 = 1.0
E2 = 0.5
a2 = 1.0
a1 = 0.5
SOME PROBLEM & OPTIMIZATION PARAMETERS
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
)
Maximize Vertical End-Displacement
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 28/30
using two materials (no holes): v = 1.03
E1 = 1.0
E2 = 0.5
a1 = 1.0
a2 = 0.5
Initialization
SOME PROBLEM & OPTIMIZATION PARAMETERS
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%
Youn
g’s M
odul
us (E
)
Maximize Vertical End-Displacement
Natasha Vermaak & Georgios MichailidisMarch 15, 2013 29/30
SOME PROBLEM & OPTIMIZATION PARAMETERS
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 = 2.24
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
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