Analysis of the equations governing the motion of a degrading elastic solid due to diffusion of a fluid

Abstract

Degradation of solids bearing load due to the infusion of moisture when exposed to the environment can leads to a decrease in their load carrying capacity and can also lead to the failure of the body from performing its intended task. In this short paper, we study some qualitative properties of the solution to systems of equations that describe the degradation in a linearized elastic solid due to the diffusion of a fluid. The model that is considered allows for the material properties of the solid to depend on the concentration of the diffusing fluid. While the load carrying capacity of a solid could decrease or increase due to the infusion of a fluid, we consider the case when degradation takes place. We are able to obtain results concerning the uniqueness of solutions to the problem under consideration. We also consider special anti-plane and quasi-static deformations of the body.