On a strain gradient theory of porous thermoelastic solids

Abstract

The interest in the gradient theory of elasticity is stimulated by the fact that this theory is adequate to investigate important problems related to size effects and nanotechnology. In this paper, we use the theory of microstretch solids and the Green-Naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of porous thermoelastic bodies, which is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor. A uniqueness theorem for the mixed problem is presented. In the case of isotropic solids we establish the continuous dependence of solutions upon initial data and body supplies. The problem of a concentrated heat source is also investigated.