A simple finite element model of diffusion, finite deformation, plasticity and fracture in lithium ion insertion electrode materials

We describe a finite element method for modeling deformation, diffusion, fracture and electrochemical reactions in materials used as lithium ion insertion electrodes. With a view to modeling high-capacity composite electrode materials such as silicon or tin, the model accounts for finite deformations and plastic flow, and models the evolving electrochemical boundary conditions resulting from the creation of new fracture surfaces using a cohesive zone. In addition, a simple mixed element is used to account for the driving force for diffusion arising from stress gradients. In this approach, the equations for diffusion and deformation are fully coupled, and can be integrated using a stable implicit time-stepping scheme. The method is illustrated by modeling plastic flow and fracture during cyclic lithiation of a thin-film Si electrode and a simple model of a battery microstructure.