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Design Tools for Architectured Bio-inspired Actuators/Sensors

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

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Design Tools for Architectured Bio-inspired Actuators/Sensors

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  1. 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

  2. Sensors • convert a stimulus into a measured signal Design Tools for ArchitecturedBio-inspired Actuators/Sensors MEASURED SIGNAL typically electrical, optical, sometimes pneumatic, hydraulic… CONTROL SIGNAL typically electrical, optical, mechanical, chemical, thermal… STIMULUS mechanical, thermal, electromagnetic, acoustic, chemical… MECHANICAL ACTION displacement or force Actuators controllable work-producing devices 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 March 15, 2013 Natasha Vermaak & GeorgiosMichailidis 2/30

  3. Sensors • convert a stimulus into a measured signal Design Tools for ArchitecturedBio-inspired Actuators/Sensors MEASURED SIGNAL typically electrical, optical, sometimes pneumatic, hydraulic… CONTROL SIGNAL typically electrical, optical, mechanical, chemical, thermal… STIMULUS mechanical, thermal, electromagnetic, acoustic, chemical… MECHANICAL ACTION displacement or force Y. Forterre, J.M. Skothelm, J. Dumals, L. Mahadevan, “How the Venus FlytrapSnaps”, Nature Vol. 433, No. 27, pp. 421-425, 2005. • http://en.wikipedia.org/wiki/Bimetallic_strip Actuators controllable work-producing devices 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 March 15, 2013 Natasha Vermaak & GeorgiosMichailidis 3/30

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

  5. Design Tools for ArchitecturedBio-inspired Actuators/Sensors From CES (Mike Ashby) March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 5/30

  6. 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 Design Tools for ArchitecturedBio-inspired Actuators/Sensors Mike Ashby, “Designing architectured materials” Scripta Materialia 68 (2013) 4–7 Man-made bi-material strip example • http://en.wikipedia.org/wiki/Bimetallic_strip March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 6/30

  7. 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 Design Tools for ArchitecturedBio-inspired Actuators/Sensors Mike Ashby, “Designing architectured materials” Scripta Materialia 68 (2013) 4–7 Biological bi-material strip example Mechanics Without Muscle:Biomechanical Inspiration from the Plant World, MARTONE et al, Integrative and Comparative Biology, pp. 1–20; doi:10.1093/icb/icq122 J.W.C. Dunlop, R. Weinkamer, and P. Fratzl, “Artful interfaces within biological materials”, Materials Today Vol. 14, No. 3, pp.70-78, 2011. March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 7/30

  8. 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 & GeorgiosMichailidis 8/30

  9. 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 & GeorgiosMichailidis 9/30

  10. Design Tools for ArchitecturedBio-inspired Actuators/Sensors From CES (Mike Ashby) March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 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 Interatomic distance r Increase of avg. interatomic separation No change in avg. interatomic separation Normal Lattice positions for atoms Positions displaced because of vibrations Symmetric (harmonic) potential Typical interatomic potentials are asymmetric (anharmonic) ↑ T ↑ atomic vibrations, energy anharmonic potential  avginteratomic separation ↑ (thermal expansion) harmonic potential  no change in avg. interatomic separation (no thermal expansion) March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 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 No change in avg. interatomic separation Symmetric (harmonic) potential March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 13/30

  14. 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 & GeorgiosMichailidis 14/30

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

  16. Design Tools for ArchitecturedBio-inspired Actuators/Sensors Design solution inspired by biological actuators Nature uses architecturedand graded or smoothinterfaces (not sharp) to achieve efficiency without sacrificing lifetime March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 16/30

  17. 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 & GeorgiosMichailidis 17/30

  18. Interface Modelling Interface Transition ZONE MATERIAL 2 MATERIAL 1 March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 18/30

  19. Design Tools for ArchitecturedBio-inspired Actuators/Sensors Maximize vertical end-displacement Uniform thermal loading, DT 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 & GeorgiosMichailidis 19/30

  20. Maximize Vertical End-Displacement Analytic optimum when the only free variable is top thickness, a1 m = a1/a2 ; n = E1/E2 S. Timoshenko, “Analysis of bi-metal thermostats”, JOSA, Vol. 11 (3), pp. 233-255, 1925. March 15, 2013 • Natasha Vermaak & GeorgiosMichailidis 20/30

  21. Maximize Vertical End-Displacement E1 = 1.0 Shape/Topology optimization via the level-set method a1 = 1.0 E2 = 0.5 • 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 & GeorgiosMichailidis 21/30

  22. Shape/Topology optimization via the level set method “The art of structure is where to put the holes.” ~Robert Le Ricolais (1894-1977) March 15, 2013 Natasha Vermaak & Georgios Michailidis 22/30

  23. Shape/Topology optimization via the level set method Numerical Algorithm GregoireAlliaire, Shape and Topology Optimization, EcolePolytechnique, http://www.cmap.polytechnique.fr/~optopo/level_en.html March 15, 2013 Natasha Vermaak & Georgios Michailidis 23/30

  24. The level set method Method for tracking evolving interfaces S. Osher, UCLA, http://www.math.ucla.edu/~sjo/ J.A. Sethian, Berkeley,http://math.berkeley.edu/~sethian/level_set.html March 15, 2013 Natasha Vermaak & Georgios Michailidis 24/30

  25. 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 & GeorgiosMichailidis 26/30

  27. Maximize Vertical End-Displacement Initialization E1 = 1.0 using two materials (no holes): v = 0.97 a2 = 1.0 E2 = 0.5 • a1 = 0.5 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 & GeorgiosMichailidis 27/30

  28. Maximize Vertical End-Displacement Initialization E1 = 1.0 using two materials (no holes): v = 1.03 a1 = 1.0 E2 = 0.5 • a2 = 0.5 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 & GeorgiosMichailidis 28/30

  29. Maximize Vertical End-Displacement Initialization a* = 2.0 E1 = 1.0 using two materials (no holes): v = 2.24 E* = 0.25 a2 = 1.0 E2 = 0.5 • a1 = 0.5 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 & GeorgiosMichailidis 29/30

  30. 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

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