On the theory of thermoelastic materials with a double porosity structure

Abstract

The linear theory of thermoelastic materials with a double porosity structure is considered. In the first part of the article we establish some basic theorems in the dynamical theory. We derive a reciprocity relation which involves two processes at different instants. This result forms the basis of a uniqueness result and a reciprocal theorem. The uniqueness theorem is established with no definiteness assumption on the elastic constitutive coefficients. Then variational theorems of Gurtin type are presented. The propagation conditions and growth equations which govern the propagation of acceleration waves in homogeneous and isotropic solids are investigated. In the equilibrium theory we study the deformation of a hollow cylinder.

Keywords:

• Acceleration waves; porous thermoelastic materials
• reciprocal theorem
• uniqueness
• thermal stresses in hollow cylinders