Coupled chemomechanics and phase field modeling of failure in electrode materials of Li‐ion batteries

Abstract

We propose a canonical finite strain theory for diffusion-mechanics coupling for the intercalation induced stress generation in Li-ion electrode particles. The intrinsic coupling arises from both mechanical pressure gradient-induced diffusion of Li-ion particles and diffusion induced swelling/shrinkage leading to mechanical stresses. In addition, we extend the finite strain theory for diffusion-mechanics coupling to chemomechanical fracture of electrode particles by introducing a nonlocal crack phase field which replaces a sharp crack topology with a smooth diffuse interpolation between the intact and broken states of the material. We employ a semi-implicit Galerkin-type finite element method for the solution of resulting set of differential equations. In addition to the mechanical, chemical and crack phase field, we introduce the pressure as an independent field variable in order to reduce the smoothness requirements on the interpolation functions. We illustrate characteristic features of the proposed model by means of representative initial-boundary value problems.