Effect of local deformation on the coupling between diffusion and stress in lithium-ion battery

It is known that the local deformation in electrode plays an important role in controlling the migration rate of lithium in lithium-ion battery, which can alter the stress state in electrode. This work derives a new diffusion equation, which takes account of the effect of the local velocity in an electrode, to describe the migration of lithium in the electrode. The effects of the local velocity on the lithium migration and stress evolution are analyzed, using the derived diffusion equation and the theory of linear elasticity. Numerical analysis of diffusion-induced stress in an isotropic, spherical electrode is performed. The numerical results show that there is a larger concentration gradient in the spherical electrode with the effect of local velocity than that without the effect of local velocity, which results in larger magnitudes of radial stress, hoop stress, and von-Mises stress than the corresponding magnitudes without the effect of local velocity. The effects of the current density on the distributions of the lithium concentration and stresses are also analyzed. For a small lithiation rate, the concentration gradient is relatively small, and the stresses in the spherical electrode are small. The results suggest that using small lithiation rates can retard the electrode from fast capacity fading and mechanical degradation.