1. Design Tools for Architectured Bio-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

2. Design Tools for Architectured Bio-inspired Actuators/Sensors
convert a stimulus into a measured signal
STIMULUS
mechanical, thermal, electromagnetic, acoustic, chemical…
MEASURED SIGNAL
typically electrical, optical, sometimes pneumatic, hydraulic…
Actuators
controllable work-producing devices
CONTROL SIGNAL
typically electrical, optical, mechanical, chemical, thermal…
MECHANICAL ACTION
displacement 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 , (1997).
M. Zupan, M.F. Ashby, and N.A. Fleck, “Actuator classification and selection—the development of a database,” Advanced Engineering Materials 4(12) , (2002).
J. Shieh, J.E. Huber, N.A. Fleck, M.F. Ashby “The selection of sensors” Progress in Materials Science 46 (2001)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
2/30

3. Design Tools for Architectured Bio-inspired Actuators/Sensors
Y. Forterre, J.M. Skothelm, J. Dumals, L. Mahadevan, “How the Venus Flytrap Snaps”, Nature Vol. 433, No. 27, pp , 2005.
Sensors
convert a stimulus into a measured signal
STIMULUS
mechanical, thermal, electromagnetic, acoustic, chemical…
MEASURED SIGNAL
typically electrical, optical, sometimes pneumatic, hydraulic…
Actuators
controllable work-producing devices
CONTROL SIGNAL
typically electrical, optical, mechanical, chemical, thermal…
MECHANICAL ACTION
displacement 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 , (1997).
M. Zupan, M.F. Ashby, and N.A. Fleck, “Actuator classification and selection—the development of a database,” Advanced Engineering Materials 4(12) , (2002).
J. Shieh, J.E. Huber, N.A. Fleck, M.F. Ashby “The selection of sensors” Progress in Materials Science 46 (2001)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
3/30

4. Design Tools for Architectured Bio-inspired Actuators/Sensors
Thermal expansion actuators
Actuation strain: Δl l0 Tf
eth = Δl = α(Tf – T0) = αΔT l0
Actuation stress: Δl l0 Tf
ecomp = - eth
sth = Eecomp = -EαΔT
March 15, 2013
Natasha Vermaak & Georgios Michailidis
4/30

5. Natasha Vermaak & Georgios Michailidis
Design Tools for Architectured Bio-inspired Actuators/Sensors
From CES (Mike Ashby)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
5/30

6. Design Tools for Architectured Bio-inspired Actuators/Sensors
Combinations 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 alone
Mike Ashby, “Designing architectured materials” Scripta Materialia 68 (2013) 4–7
Man-made bi-material strip example
March 15, 2013
Natasha Vermaak & Georgios Michailidis
6/30

7. Design Tools for Architectured Bio-inspired Actuators/Sensors
Combinations 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 alone
Mike 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: /icb/icq122
March 15, 2013
Natasha Vermaak & Georgios Michailidis
7/30

8. Natasha Vermaak & Georgios Michailidis
Bi-material strip Thermal actuation
To maximize force
or displacement:
large material differences required
choose appropriate materials
model the interface
3. find the optimal distribution of materials (and space):
Shape/Topology optimization via level-set method
March 15, 2013
Natasha Vermaak & Georgios Michailidis
8/30

9. Natasha Vermaak & Georgios Michailidis
Bi-material strip Thermal actuation
To maximize force
or displacement:
large material differences required
choose appropriate materials
model the interface
3. find the optimal distribution of materials (and space):
Shape/Topology optimization via level-set method
March 15, 2013
Natasha Vermaak & Georgios Michailidis
9/30

10. Natasha Vermaak & Georgios Michailidis
Design Tools for Architectured Bio-inspired Actuators/Sensors
From CES (Mike Ashby)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
10/30

11. Young’s Modulus (E) Usually, stronger bonds ~
steeper potential energy wells ~ stiffer materials ~ ↑E
March 15, 2013
Natasha Vermaak&GeorgiosMichailidis
11/30

12. Coefficient of Thermal Expansion (CTE or a)
Potential Energy
Typical interatomic potentials are asymmetric (anharmonic)
Normal Lattice positions for atoms
Positions displaced because of vibrations
Interatomic distance r
Increase of avg. interatomic separation
↑ T  ↑ atomic vibrations, energy
anharmonic potential 
avg interatomic separation ↑
(thermal expansion)
harmonic potential  no change in avg. interatomic separation
(no thermal expansion)
Symmetric (harmonic) potential
No change in avg. interatomic separation
March 15, 2013
Natasha Vermaak & Georgios Michailidis
12/30

13. Coefficient of Thermal Expansion (CTE or a)
Potential Energy
Typical interatomic potentials are asymmetric (anharmonic)
↑ interatomic bond strength (↑E)
(deeper the potential energy curve)
 thermal expansion a↓
Interatomic distance r
Increase of avg. interatomic separation
Symmetric (harmonic) potential
No change in avg. interatomic separation
March 15, 2013
Natasha Vermaak & Georgios Michailidis
13/30

14. Natasha Vermaak & Georgios Michailidis
Bi-material strip Thermal actuation
To maximize force
or displacement:
large material differences required
choose appropriate materials
model the interface
3. find the optimal distribution of materials (and space):
Shape/Topology optimization via level-set method
March 15, 2013
Natasha Vermaak & Georgios Michailidis
14/30

15. Design challenge due to the interface: efficiency vs. lifetime
large stresses or strain gradients
across bi-material interface
promotes/accelerates
damage, limits the
lifetime of actuators
To maximize force
or displacement:
large material differences (efficiency)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
15/30

16. Design solution inspired by biological actuators
Design Tools for Architectured Bio-inspired Actuators/Sensors
Design solution inspired by biological actuators
Nature uses architectured and graded or smooth interfaces (not sharp) to achieve efficiency without sacrificing lifetime
March 15, 2013
Natasha Vermaak & Georgios Michailidis
16/30

17. Natasha Vermaak & Georgios Michailidis
Interface Modelling
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 on
Temperature, 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
Energy concerns limit the size of the interface transition zone
Physics and Chemistry of Interfaces, Hans-Jürgen Butt, Karlheinz Graf, Michael Kappl, Wiley, 2003
Understanding Solids: The Science of Materials, R. J. D. Tilley, Wiley, 2004
March 15, 2013
Natasha Vermaak & Georgios Michailidis
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18. Interface Modelling MATERIAL 1 MATERIAL 2 Interface Transition ZONE
March 15, 2013
Natasha Vermaak & Georgios Michailidis
18/30

19. Design Tools for Architectured Bio-inspired Actuators/Sensors
Uniform thermal loading, DT
Maximize
vertical end-displacement
To maximize
displacement:
large material differences required
choose appropriate materials
model the interface
3. find the optimal distribution of materials (and space):
Shape/Topology optimization via level-set method
March 15, 2013
Natasha Vermaak & Georgios Michailidis
19/30

20. Maximize Vertical End-Displacement
m = a1/a2 ; n = E1/E2
Analytic optimum when the only free variable is top thickness, a1
S. Timoshenko, “Analysis of bi-metal thermostats”, JOSA, Vol. 11 (3), pp , 1925.
March 15, 2013
Natasha Vermaak & Georgios Michailidis
20/30

21. Maximize Vertical End-Displacement
Shape/Topology optimization
via the
level-set method
E1 = 1.0
E2 = 0.5
a1 = 1.0
a2 = 0.5
SOME PROBLEM &
OPTIMIZATION PARAMETERS
DT = 1 ; 100 x 50 elements; L = 1; h = 0.5
Interface zone width = 16 * element size
Element size = 1 / 100; Total iter. = 200
Material 1 volume constraint 50%
Young’s Modulus (E)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
21/30

22. Natasha Vermaak & Georgios Michailidis
2222
level set method for numerical shape optimization of elastic structures.
Our approach combines the level set algorithm of Osher and Sethian with the classical shape gradient.
Although this method is not specifically designed for topology optimization, it can easily handle topology changes
for a very large class of objective functions. Its cost is moderate since the shape is captured on a fixed Eulerian mesh.
Algorithm optimizes 2d shape under area constraint
Shape transformation results from transport of the level set eqn with hamilton jacobi eqn
Shape/Topology optimization
via the level set method
“The art of structure is
where to put the holes.”
~Robert Le Ricolais ( )
March 15, 2013
Natasha Vermaak & Georgios Michailidis
22/30

23. Natasha Vermaak & Georgios Michailidis
2323
level set method for numerical shape optimization of elastic structures.
Our approach combines the level set algorithm of Osher and Sethian with the classical shape gradient.
Although this method is not specifically designed for topology optimization, it can easily handle topology changes
for a very large class of objective functions. Its cost is moderate since the shape is captured on a fixed Eulerian mesh.
Algorithm optimizes 2d shape under area constraint
Shape transformation results from transport of the level set eqn with hamilton jacobi eqn
Shape/Topology optimization
via the level set method
Numerical Algorithm
Gregoire Alliaire, Shape and Topology Optimization, Ecole Polytechnique,
March 15, 2013
Natasha Vermaak & Georgios Michailidis
23/30

24. Natasha Vermaak & Georgios Michailidis
2424
level set method for numerical shape optimization of elastic structures.
Our approach combines the level set algorithm of Osher and Sethian with the classical shape gradient.
Although this method is not specifically designed for topology optimization, it can easily handle topology changes
for a very large class of objective functions. Its cost is moderate since the shape is captured on a fixed Eulerian mesh.
Algorithm optimizes 2d shape under area constraint
Shape transformation results from transport of the level set eqn with hamilton jacobi eqn
The level set method
Method for tracking evolving interfaces
S. Osher, UCLA,
J.A. Sethian, Berkeley,
March 15, 2013
Natasha Vermaak & Georgios Michailidis
24/30

25. Natasha Vermaak & Georgios Michailidis
2525
level set method for numerical shape optimization of elastic structures.
Our approach combines the level set algorithm of Osher and Sethian with the classical shape gradient.
Although this method is not specifically designed for topology optimization, it can easily handle topology changes
for a very large class of objective functions. Its cost is moderate since the shape is captured on a fixed Eulerian mesh.
Algorithm optimizes 2d shape under area constraint
Shape transformation results from transport of the level set eqn with hamilton jacobi eqn
The level set method
Multi-phase description
Using m level-set functions, we can describe up to n=2m different phases.
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).
March 15, 2013
Natasha Vermaak & Georgios Michailidis
25/30

26. Maximize Vertical End-Displacement
Initialization
using one
material + holes: v = 2.15
SOME PROBLEM &
OPTIMIZATION PARAMETERS
DT = 1 ; 100 x 50 elements
Element size = 1 / 100;
Total iter. = 200; ks = 0
L = 1; h = 0.5; No volume constraint
Young’s Modulus (E)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
26/30

27. Maximize Vertical End-Displacement
Initialization
E1 = 1.0
E2 = 0.5
a2 = 1.0
a1 = 0.5
using two
materials (no holes): v = 0.97
SOME PROBLEM &
OPTIMIZATION PARAMETERS
DT = 1 ; ks =0; 100 x 50 elements; L = 1; h = 0.5
Interface zone width = 16 * element size
Element size = 1 / 100; Total iter. = 200
Material 1 volume constraint 50%
Young’s Modulus (E)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
27/30

28. Maximize Vertical End-Displacement
Initialization
E1 = 1.0
E2 = 0.5
a1 = 1.0
a2 = 0.5
using two
materials (no holes): v = 1.03
SOME PROBLEM &
OPTIMIZATION PARAMETERS
DT = 1 ; ks =0; 100 x 50 elements; L = 1; h = 0.5
Interface zone width = 16 * element size
Element size = 1 / 100; Total iter. = 200
Material 1 volume constraint 50%
Young’s Modulus (E)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
28/30

29. Maximize Vertical End-Displacement
Initialization
a* = 2.0
E1 = 1.0
E2 = 0.5
a2 = 1.0
a1 = 0.5
E* = 0.25
using two
materials (no holes): v = 2.24
SOME PROBLEM &
OPTIMIZATION PARAMETERS
DT = 1 ; ks =0; 100 x 50 elements; L = 1; h = 0.5
Interface zone width = 16 * element size
Element size = 1 / 100; Total iter. = 200
Material 1 volume constraint 50%
Young’s Modulus (E)
March 15, 2013
Natasha Vermaak & Georgios Michailidis
29/30

30. Design Tools for Architectured Bio-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