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

Abstract

Silicon (Si) is considered as 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, 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, diffusion coefficient, electrode geometry, and geometrical constraints affect the fracture behavior of Si electrodes.

Fracture behavior in battery materials

“…Computational methods based on these crack initiation and crack propagation criteria can be used to predict the fracture behavior of materials. The phase field model [16][17][18]54] and cohesive zone model [55][56][57][58][59][60][61][62][63] are the most common computational models. The phase field model employs a continuous field variable to represent cracks.…”

“…Computationally, various chemomechanical models have been developed to simulate the fracture process. In these models, the Li concentration distribution, responding stress distribution, and fracture initiation and propagation criteria have been considered [16][17][18][19]. Scanning electron micrograph of LiNi0.8Co0.15Al0.05O2 primary and secondary particles.…”

Mixed isogeometric analysis of strongly coupled diffusion in porous materials

“…This work is expected to provide a framework for more application‐based problems such as geometrical instabilities() observed in swelling hydrogels due to coupled diffusion() or a diffusion‐induced fracture. ()…”

Mixed Arlequin method for multiscale poromechanics problems

“…To obtain an incremental energy functional of the poromechanics problem, we adopt an approach used in other variational frameworks [54][55][56][57] that performs temporal discretization first and then spatial discretization. In fact, this discretization sequence is the opposite to the typical sequence in poromechanics formulations (e.g., [16,50,[58][59][60]) whereby the spatial domain is discretized first.…”