A chemo-mechanics framework for elastic solids with surface stress

Elasticity problems involving solid-state diffusion and chemo-mechanical coupling have wide applications in energy conversion and storage devices such as fuel cells and batteries. Such problems are usually difficult to solve because of their strongly nonlinear characteristics. This study first derives the governing equations for three-dimensional chemo-elasticity problems accounting for surface stresses in terms of the Helmholtz potentials of the displacement field. Then, by assuming weak coupling between the chemical and mechanical fields, a perturbation method is used and the nonlinear governing equations are reduced to a system of linear differential equations. It is observed from these equations that the mechanical equilibrium equations of the first two orders are not dependent on the chemical fields. Finally, the above chemo-mechanics framework is applied to study the stress concentration problem of a circular nano-hole in an infinitely large thick plate with prescribed mechanical and chemical loads at infinity. Explicit expressions up to the third order are obtained for the stress and solute concentration fields. It is seen from these solutions that, different from the classical elasticity result, the stress concentration factor near the nano-hole depends on the surface stress, applied tensile load and prescribed solute concentration at infinity.