A mathematical formulation for analysis of diffusion-induced stresses in micropolar elastic solids

This paper develops a coupled chemo-mechanical model for stress-assisted diffusion in the framework of micropolar elasticity. The two-way interaction of mechanical and chemical driving forces as well as internal microstructure of the polar media is taken into account. The fundamental governing equations of chemo-mechanics with kinetics driven by diffusion and stress are developed, and mathematical expressions for stress and concentration fields are derived. Using Airy stress functions, a simplified formulation for two-dimensional chemo-elasticity problems under chemical equilibrium is presented. Using a perturbation approach to solve the presented system of equations, closed-form expressions for different field parameters can be obtained. As an illustrative case study, expressions for the stress and solute concentration in an infinite plate with circular hole embedded in a chemical medium have been written. The derived equation and proposed solution approach can be applied to various plane micropolar chemo-elasticity problems for studying the interaction between mechanical and chemical driving forces as well as material length-scale parameters.