A mathematical model that calculates volume expansion and contraction and concentration and stress profiles during lithium insertion into and extraction from a spherical particle of electrode material has been developed. The maximum stress in the particle has been determined as a function of dimensionless current, which includes the charge rate, particle size, and diffusion coefficient. The effects of pressure-driven diffusion and nonideal interactions between the lithium and host material have also been described. The model predicts that carbonaceous particles will fracture in high-power applications such as hybrid-electric vehicle batteries
Stress generation and fracture in lithium insertion materials
Christensen, J., & Newman, J. (2006). Stress generation and fracture in lithium insertion materials. Journal of Solid State Electrochemistry, 10(5), 293-319.