Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids

Abstract

In this work a model and solution strategy are developed to describe a class of coupled thermo-chemo-mechanical systems involving the solid-state diffusion of a dilute solute into a multiphase solid material, the subsequent reactions, production of heat, changes in the stress fields, and the evolution of material degradation and inelastic strains in the solid. The algorithm involves recursive staggering, whose convergence is dependent on the discretized time step size. Because the multifield coupling can change, becoming stronger, weaker, or possibly oscillatory, it is extremely difficult to ascertain a-priori the time step size needed to meet a prespecified tolerance on the staggering error, i.e. the incomplete resolution of the interaction between the fields. The solution process involves time step size adaptivity to control the contraction mapping constant of the multifield system operator in order to induce desired staggering rates of convergence within each time step, and hence, the staggering error. Three-dimensional numerical experiments are performed to illustrate the behavior of the model and the solution strategy.