Thermo-Chemo-Elasticity Considering Solid State Reaction and the Displacement Potential Approach to Quasi-Static Chemo-Mechanical Problems

Abstract

Engineering materials and structures represent complex behaviors when reacting to superposed influences of mechanical forces, high temperature, diffusion and reaction of chemicals, which could cause large internal stresses and further induce cracks or failure. To determine the material reliability and integrity, the multi-field interactions and stresses/strains evolutions need to be identified at first. We proposed a theory of thermo-chemo-elasticity considering solid state reactions between the solid phase and absorbed chemicals in a stressed-solid. Both diffusion–reaction induced chemical strains and thermal dilations are taken into account as functions of species concentration, reaction extent and temperature. The fully coupled conservation laws, constitutive equations and chemical kinetics are formulated for the initial-boundary problem. For isotropic solids, we developed a displacement potential approach for steady-state 3D problems of thermo-chemo-elasticity. Solutions can be found from particular solutions of displacement potential and homogeneous solution of thermo-chemo Lamé equation. This approach is also available for transient chemo-mechanical problems in thermal equilibrium providing that quasi-static conditions are introduced. We exemplified the model with a reaction-dominated problem of a core–shell structure subjected to chemo-mechanical loading and the results demonstrate the capability of the model in dealing with comprehensive influences of solid state reaction and species diffusion on solids.