Analytical Solution for Coupled Diffusion Induced Stress Model for Lithium-Ion Battery

Electric cycling is one of the major damage sources in lithium-ion batteries and extensive work has been produced to understand and to slow down this phenomenon. The damage is related to the insertion and extraction of lithium ions in the active material. These processes cause mechanical stresses which in turn generate crack propagation, material loss and pulverization of the active material. In this work, the principles of diffusion induced stress theory are applied to predict concentration and stress field in the active material particles. Coupled and uncoupled models are derived, depending on whether the effect of hydrostatic stress on concentration is considered or neglected. The analytical solution of the coupled model is proposed in this work, in addition to the analytical solution of the uncoupled model already described in the literature. The analytical solution is a faster and simpler way to deal with the problem which otherwise should be solved in a numerical way with finite difference method or a finite element model. The results of the coupled and uncoupled models for three different state of charge levels are compared assuming the physical parameters of anode and cathode active material. Finally, the effects of tensile and compressive stress are analysed.