General and fundamental solutions for isotropic thermo-chemo-elasticity with multi-species diffusion in a steady state

Abstract

In this paper, a 3D steady-state general solution for isotropic thermo-chemo-elastic media with multi-species diffusion is derived by introducing two displacement functions and utilizing the rigorous operator theory together with generalized Almansi's theorem. Based on the derived general solution, fundamental solutions for the problems of intact half-infinite, infinite, and bi-material bodies subjected to point loading are obtained by the potential theory method. The fundamental solution to a penny-shaped crack problem is also derived on basis of the general solution and by using the generalized potential theory. Several numerical calculations for specific thermo-chemo-elastic materials are carried out to verify the present analytical solutions and to analyze the 3D distributions of field variables. Furthermore, the transformation relationships among these fundamental solutions are discussed. The present general and fundamental solutions can be served as a basis for deriving analytical or numerical solutions to various boundary value problems in the context of thermo-chemo-elasticity.