On the Incremental Problem in Thermoelasticity with Microstructure

Abstract

It is usually accepted that the work of Cosserat and Cosserat [1] can be seen as the starting point of the study of solids with microstructure. In the sixties an important effort of several authors gave a relevant development of some theories. In this sense, we recall the monographs by Truesdell and Toupin [2], Eringen and Kafadar [3], Kunin [4, 5] and Capriz [6]. In this paper we restrict our attention to the theory developed by Mindlin [7]. In the book, Ciarletta and Iesan [8] have given a current presentation of this theory. We study the small deformations superposed on a nonlinear general deformation. The current point of view of this problem was given by Iesan [9]. Existence results for the equations of the incremental problem have been presented in [10, 11] for the classical thermoelasticity, in [12] for the thermoelasticity of porous materials and in [13] for the viscoelasticity. Our main aim is to extend these results to the thermoelastic theory of materials with microstructure.