Abstract
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.