Spatial behavior in the electromagnetic theory of microstretch elasticity

AbstractThis paper is concerned with the electromagnetic theory of microstretch elasticity. First, the initial boundary value problem is formulated in the framework of the linear dynamic theory of microstretch magnetoelectroelastic solids. Then, the spatial behavior of solutions is studied in both bounded and unbounded regions. The obtained result gives an exact idea of the domain of influence, in the sense that for each fixed time in a given interval, the entire activity vanishes at distanced from the support of the given data greater than a time-dependent threshold value. The study of spatial behavior is completed by an exponential decay estimate inside the domain of influence. As a by product a uniqueness result holding for both bounded and unbounded bodies is derived. Finally, the effect of a concentrated microstretch body force is studied

A Mixture Theory for Micropolar Thermoelastic Solids

We derive a nonlinear theory of heat-conducting micropolar mixtures in Lagrangian description. The kinematics, balance laws, and constitutive equations are examined and utilized to develop a nonlinear theory for binary mixtures of micropolar thermoelastic solids. The initial boundary value problem is formulated. Then, the theory is linearized and a uniqueness result is established

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