Buckling behavior of a wire-like electrode with a concentration-dependent elastic modulus based on a deformed configuration

Abstract

Abstract Buckling behavior may occur during the lithiation process of wire-like electrodes, and it can cause the mechanical degradation of lithium-ion batteries (LIBs). In this study, we focused on the stress evolution and buckling behavior of wire-like electrodes with a concentration-dependent elastic modulus, and we considered the two-phase reaction. The elastic finite deformation theory was adopted to establish the mechanics equations under the assumption of the elastic modulus being a linear function of the lithium concentration. The modified second moment of area and the Euler-forward finite scheme based on a deformed configuration were adopted to determine the onset of buckling behavior. The mass transport equations were established based on the Cahn-Hilliard phase-field theory to mimic the two-phase reaction during lithiation. The coupled equations were solved with the partial differential equation (PDE) module of COMSOL Multiphysics. The results showed that the concentration-dependent elastic modulus of the silicon electrodes led to the later onset of buckling due to the lithiation-induced softening of the electrodes, and this trend became slight for the electrodes with a large ratio of length to radius, since the phase separation had not yet occurred. The critical buckling state of charge (SOC) of the electrode with a concentration-dependent elastic modulus was larger than that of the electrode with a constant elastic modulus. The critical buckling time decreased with the ratio of the length to the radius of the electrode and the charging rate whether the electrode had a concentration-dependent modulus or a concentration-independent elastic modulus.