Damage model for diffusion-induced structural degradation of metal-ion battery

Understanding structural durability and safety of metal-ion batteries, such as lithium-ion battery and sodium-ion battery, is of practical importance for applications in electric vehicles and hybrid electric vehicles. Following the method used in damage mechanics, we introduce an isotropic damage state variable in the deformation analysis of electrode during electrochemical cycling. The evolution of the damage state variable is dependent on chemical reaction, reaction-released heat, and stress state of the electrode, and the elastic constants and the molar volume of the electrode material are dependent implicitly on the damage state variable. Provided that the contribution of higher orders of the concentration of diffusive constituent and diffusion flux to the structural damage/degradation is negligible, we propose an approximated expression for the damage states corresponding to individual cycle for respective insertion and de-insertion process. Assuming negligible effect of stress on insertion/diffusion of diffusive constituent, we analyze the effect of structural damage/degradation on the bending of an electrode beam during the first insertion. The numerical results reveal that the structural damage/degradation reduces the minimum radius of curvature that an electrode beam can reach. There exists the damage-induced relief of the diffusion-bending moment that is introduced by the insertion of the diffusive constituent.