Diffusion-induced stress of electrode particles with spherically isotropic elastic properties in lithium-ion batteries

Mechanical degradation generated by crack nucleation and pulverization can lead to the capacity fade in lithium-ion batteries, which has been attributed to diffusion-induced stress inside battery electrodes in recent years. However, not much attention has been directly taken to the models of diffusion-induced stress for anisotropic electrodes. In this work, we develop an analytical model of diffusion-induced stress for spherically isotropic elastic electrodes under potentiostatic and galvanostatic operation. It is shown that the stresses depend strongly on the lithiation expansion coefficient ratio and the elastic modulus ratio of tangential direction to radial direction. The stresses have the different evolution under potentiostatic and galvanostatic control, but have a common feature that they are all affected by the initial condition. From the standpoint of mechanics, our results indicate that extracting more lithium before lithiation (or inserting lower lithium before delithiation) is a good strategy to minimize stress and thus enhance capacity retention for spherically isotropic electrodes.