On the Nonlinear Theory of Micromorphic Thermoelastic Solids

This work aims to study some dynamical problems in the framework of nonlinear theory of micromorphic thermoelastic solids. First, the continuous dependence of smooth admissible thermodynamic processes upon initial state and supply terms is investigated in the region of state space where the internal energy is a convex function and the elastic material behaves as a definite conductor of heat. Then, a uniqueness result is demonstrated. 1. Introduction Motivated by experimental studies, various continuous models of deformable bodies have been proposed in literature in order to describe the thermomechanical behavior of media with microstructure. In the micromorphic theory introduced by Eringen and ？uhubi [1] and Eringen [2], a material body is envisioned as a collection of a large number of deformable particles (subcontinua or microcontinua). Each particle possesses finite size and directions representing its microstructure. The microdeformation gives rise to extra degrees of freedom. Thus, the particle has nine independent degrees of freedom describing both rotations and stretches, in addition to the three classical translational degrees of freedom of its center. Many deformable solids point to the necessity for the incorporation of micromotions into mechanics. Porous solids with deformable grains and pores, composites, polymers with deformable molecules, crystals, solids with microcracks, dislocation and disclinations, and biological tissues (bones and muscles) are just a few examples of deformable solids which require the degrees of freedom given by the micromorphic theory. As a consequence, the micromorphic mechanics is the subject of detailed studies both from theoretical and practical reasons. In the linear context, uniqueness theorems have been proved by Soós [3] and Ie？an [4], variational principles have been established by Maugin [5] and Nappa [6], applications to earthquake problems have been suggested by Teisseyre [7], Dresen et al. [8], and Teisseyre et al. [9], plane harmonic waves have been studied by Eringen [2], reciprocal and existence theorems have been demonstrated by Ie？an [4], and material constants for isotropic materials have been determined by Chen and Lee [10]. On the other hand, the theory has been generalized to mixtures of micromorphic materials by Twiss and Eringen [11, 12], to higher-grade materials by Eringen [13], and to electromagnetic micromorphic thermoelastic solids by Eringen [14]. Moreover, the constitutive theory of micromorphic thermoplasticity has been formulated by Lee and Chen [15], the concept of material forces