Perturbation finite element solution for chemo-elastic boundary value problems under chemical equilibrium

Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechanical behavior of these solids. In this work, a perturbation finite element (FE) formulation is developed to analyze chemo-elastic boundary value problems (BVPs) under chemical equilibrium. The perturbation method is applied to the FE equations because of the nonlinearity in the chemical potential expression as a function of solute concentration. The compositional expansion coefficient is used as the perturbation parameter. After the perturbation expansion, a system of partial differential equations for the displacement and dimensionless solute concentration functions is obtained and solved in consecutive steps. The presence of a numerical solution enables modeling 3D chemo-elastic solids, such as battery electrodes or ionic gels, of any geometric shape with defects of different shapes. The proposed method is tested in several numerical examples such as plates with circular or elliptical holes, and cracks. The numerical examples showed how the shape of the defect can change the distribution of solute concentration around the defect. Cracks in chemo-elastic solids create sharp peaks in solute concentration around crack tips, and the intensity of these peaks increases as the far field solute concentration decreases.