Reduced mixture model and elastic response of chemically swollen solids: Application to Si oxidation and lithiation

Abstract

This paper presents a mixture model for coupled chemo-mechanical response of the general class of fluid-solid systems undergoing chemical reaction and large deformations. It further investigates our earlier works on the mathematical modeling of chemo-mechanical coupling and material evolution across advancing fronts of reactive fluids. A detailed analysis of the stress response of the chemically evolving solid is carried out, taking into account the changes in the reference unstressed configurations of the unreacted and reacted solid. This yields a systematic way to determine the material parameters required for the material constitutive models. The formulation for the fluid constituent is simplified for the case of slow diffusion, which yields a reduced system of governing equations wherein coercivity of the continuum system is inherited by the discrete system. The resulting nonlinear model lends itself to consistent linearization and is implemented in a finite element method. The nonlinear system of coupled equations is solved monolithically using the Newton-Raphson algorithm and quadratic convergence is attained. The method is applied to investigate the bending-dominated response of a silicon wafer during thermal oxidation, and to the problem of cross-section evolution during lithiation of a silicon nanowire.