A variational framework to model diffusion induced large plastic deformation and phase field fracture during initial two-phase lithiation of silicon electrodes

Silicon (Si) is considered to be a promising next-generation anode material for lithium-ion batteries. However, the large volume change during (de)lithiation processes causes fracture of Si electrodes, thereby limiting Si's practical application in lithium-ion batteries. In this work, we formulate a variational-based fully chemo-mechanical coupled computational framework to study diffusion induced large plastic deformation and phase field fracture in Si electrodes. Into this framework we incorporate a recently developed reaction-controlled diffusion model to predict two-phase lithiation for amorphous Si (a-Si) and crystalline Si (c-Si) as well as diffusion induced anisotropic deformation for c-Si. The variational formulation suggests to consider the deformation field, the chemical potential, and the damage field as primary unknowns. The concentration field is considered as a local variable and is recovered from the chemical potential on the element level. We carry out several numerical simulations to show the performance of our computational model and point out the significance of accurately accounting for the presence of the reaction front when modeling diffusion induced fracture problems for both a-Si and c-Si electrodes. In addition, we investigate how the fracture energy release rate, electrode geometry, and geometrical constraints affect the fracture behavior of Si electrodes.