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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Young’s Modulus (E) Usually, stronger bonds ~**

steeper potential energy wells ~ stiffer materials ~ ↑E March 15, 2013 Natasha Vermaak&GeorgiosMichailidis 11/30

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**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

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**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

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**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

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**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

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**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

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**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 17/30

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**Interface Modelling MATERIAL 1 MATERIAL 2 Interface Transition ZONE**

March 15, 2013 Natasha Vermaak & Georgios Michailidis 18/30

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**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

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**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

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**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

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**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

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**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

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

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**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

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**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

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**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

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**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

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**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

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**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

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