Mathematical modelings of smart materials and structures

Christian Licht (1) , Thibaut Weller (1)

1 M3 - Modélisation Mathématique en Mécanique

We aim to present mathematical models of smart materials and smart structures. Smart materials are materials which present significant multiphysical couplings. They are integrated in smart structures which take technological advantages of some multiphysical effects. We establish a classification of piezoelectric crystalline materials and propose simplified but accurate models of thin plates or slender rods made of piezoelectric or electromagneto-elastic materials. In the first part algebraic tools from group theory are used, whereas in the second one some tools of variational and functional analysis are suitable to solve some convergence questions for boundary value problems depending on small parameters.

Mots clés: Group theory; singular perturbations methods; asymptotic analysis; plates and rods models

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Christian Licht, Thibaut Weller. Mathematical modelings of smart materials and structures. International Conference on Mathematics and Applications, ICMA-MU 2007, Aug 2007, Thailand. 15p. ⟨hal-00744182⟩