The influence of plasticity on cavity expansion in lithium-ion battery electrodes

We examine the expansion of a small cavity within a spherical electrode of lithium-ion batteries (LIBs) during the galvanostatic charging process. Nonlinear theories are applied to account for the large deformations typical of silicon-based electrodes. Our analysis focuses on how plasticity influences the evolution of the cavity’s radius by associating an elastic potential with the particle and considering a chemical potential that may depend on stress or be independent of it. We find that when plasticity is taken into account, the behaviour of a small hole undergoes complex changes. The mathematical problem at hand involves coupled nonlinear partial differential equations, which we solve numerically. We assume elastic incompressibility, enabling a simple numerical scheme that can be implemented in any programming language without relying on commercial finite element software typically used in this context. • Expansion of a small cavity during the lithiation of a rubber-type electrode. • Plastic effects produce complex and highly nonlinear behaviour. • Diffusion-induced stresses around the cavity are analysed. • A finite difference scheme is outlined to solve the nonlinear coupled problem.