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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 hiérarchisées : les leçons du vivant

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Design Tools for Architectured Bio-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 , (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) convert a stimulus into a measured signal controllable work-producing devices Actuators Sensors Natasha Vermaak & Georgios MichailidisMarch 15, /30 STIMULUS mechanical, thermal, electromagnetic, acoustic, chemical… MEASURED SIGNAL typically electrical, optical, sometimes pneumatic, hydraulic… CONTROL SIGNAL typically electrical, optical, mechanical, chemical, thermal… MECHANICAL ACTION displacement or force

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Design Tools for Architectured Bio-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 , (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) convert a stimulus into a measured signal controllable work-producing devices Actuators Sensors Natasha Vermaak & Georgios MichailidisMarch 15, /30 STIMULUS mechanical, thermal, electromagnetic, acoustic, chemical… MEASURED SIGNAL typically electrical, optical, sometimes pneumatic, hydraulic… CONTROL SIGNAL typically electrical, optical, mechanical, chemical, thermal… MECHANICAL ACTION displacement or force Y. Forterre, J.M. Skothelm, J. Dumals, L. Mahadevan, “How the Venus Flytrap Snaps”, Nature Vol. 433, No. 27, pp , 2005.

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Design Tools for Architectured Bio-inspired Actuators/Sensors Thermal expansion actuators Natasha Vermaak & Georgios MichailidisMarch 15, /30 Actuation strain: Actuation stress: th = Δ l = α(T f – T 0 ) = αΔT l0l0 ΔlΔl l0l0 TfTf l0l0 T0T0 ΔlΔl l0l0 TfTf th = E comp = -EαΔT comp = - th

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Design Tools for Architectured Bio-inspired Actuators/Sensors Natasha Vermaak & Georgios MichailidisMarch 15, /30 From CES (Mike Ashby)

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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 Natasha Vermaak & Georgios MichailidisMarch 15, /30 Man-made bi-material strip example

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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 Natasha Vermaak & Georgios MichailidisMarch 15, /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 , Mechanics Without Muscle:Biomechanical Inspiration from the Plant World, MARTONE et al, Integrative and Comparative Biology, pp. 1–20; doi: /icb/icq122

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To maximize force or displacement: Bi-material strip Thermal actuation 1. choose appropriate materials 2. model the interface 3.find the optimal distribution of materials (and space): Shape/Topology optimization via level-set method Natasha Vermaak & Georgios MichailidisMarch 15, /30 large material differences required

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To maximize force or displacement: Bi-material strip Thermal actuation 1. choose appropriate materials 2. model the interface 3.find the optimal distribution of materials (and space): Shape/Topology optimization via level-set method Natasha Vermaak & Georgios MichailidisMarch 15, /30 large material differences required

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Design Tools for Architectured Bio-inspired Actuators/Sensors Natasha Vermaak & Georgios MichailidisMarch 15, /30 From CES (Mike Ashby)

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

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Natasha Vermaak & Georgios MichailidisMarch 15, /30 Coefficient of Thermal Expansion (CTE or ) Normal Lattice positions for atoms Positions 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

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Natasha Vermaak & Georgios MichailidisMarch 15, /30 Coefficient of Thermal Expansion (CTE or ) 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 ↓

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To maximize force or displacement: Bi-material strip Thermal actuation 1. choose appropriate materials 2. model the interface 3.find the optimal distribution of materials (and space): Shape/Topology optimization via level-set method Natasha Vermaak & Georgios MichailidisMarch 15, /30 large material differences required

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Design challenge due to the interface: efficiency vs. lifetime Natasha Vermaak & Georgios MichailidisMarch 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

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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 Architectured Bio-inspired Actuators/Sensors Natasha Vermaak & Georgios MichailidisMarch 15, /30

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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 Interface Modelling Energy concerns limit the size of the interface transition zone Natasha Vermaak & Georgios MichailidisMarch 15, /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 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

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Interface Transition ZONE MATERIAL 1 MATERIAL 2 Natasha Vermaak & Georgios MichailidisMarch 15, /30 Interface Modelling

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Uniform thermal loading, T Design Tools for Architectured Bio-inspired Actuators/Sensors To maximize displacement: 1. choose appropriate materials 2. model the interface 3.find the optimal distribution of materials (and space): Shape/Topology optimization via level-set method Natasha Vermaak & Georgios MichailidisMarch 15, /30 large material differences required Maximize vertical end- displacement

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

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Maximize Vertical End-Displacement Natasha Vermaak & Georgios MichailidisMarch 15, /30 SOME PROBLEM & OPTIMIZATION PARAMETERS T = 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% Shape/Topology optimization via the level-set method E1 = 1.0 E2 = 0.5 1 = 1.0 2 = 0.5 Young’s Modulus (E)

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Natasha Vermaak & Georgios MichailidisMarch 15, /30 Shape/Topology optimization via the level set method “The art of structure is where to put the holes.” ~Robert Le Ricolais ( )

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Gregoire Alliaire, Shape and Topology Optimization, Ecole Polytechnique, Natasha Vermaak & Georgios MichailidisMarch 15, /30 Shape/Topology optimization via the level set method Numerical Algorithm

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S. Osher, UCLA, Natasha Vermaak & Georgios MichailidisMarch 15, /30 J.A. Sethian, Berkeley,http://math.berkeley.edu/~sethian/level_set.html The level set method Method for tracking evolving interfaces

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Natasha Vermaak & Georgios MichailidisMarch 15, /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=2 m different phases. The level set method Multi-phase description

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Maximize Vertical End-Displacement Natasha Vermaak & Georgios MichailidisMarch 15, /30 using one material + holes: v = 2.15 Initialization SOME PROBLEM & OPTIMIZATION PARAMETERS T = 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)

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Maximize Vertical End-Displacement Natasha Vermaak & Georgios MichailidisMarch 15, /30 E1 = 1.0 E2 = 0.5 2 = 1.0 1 = 0.5 SOME PROBLEM & OPTIMIZATION PARAMETERS T = 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% using two materials (no holes): v = 0.97 Initialization Young’s Modulus (E)

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Maximize Vertical End-Displacement Natasha Vermaak & Georgios MichailidisMarch 15, /30 using two materials (no holes): v = 1.03 E1 = 1.0 E2 = 0.5 1 = 1.0 2 = 0.5 Initialization SOME PROBLEM & OPTIMIZATION PARAMETERS T = 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)

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Maximize Vertical End-Displacement Natasha Vermaak & Georgios MichailidisMarch 15, /30 SOME PROBLEM & OPTIMIZATION PARAMETERS T = 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% using two materials (no holes): v = 2.24 Initialization Young’s Modulus (E) 2 = 1.0 1 = 0.5 E1 = 1.0 E2 = 0.5 E* = 0.25 * = 2.0

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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 hiérarchisées : les leçons du vivant

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