Four-field formulation and adaptive acceleration for fatigue fracture of lithium-ion battery electrode particles

The phase field method for fracture is effective for simulating fatigue cracking in lithium-ion battery electrode particles, but its application is restricted by high computational cost of cycle-by-cycle simulation, especially for large-scale and high-cycle fatigue problems. To address this issue, this study presents a mixed four-field formulation combined with an efficient adaptive acceleration strategy for fatigue cracking simulation under cyclic lithiation–delithiation. Lithium diffusion governed by chemical potential and concentration equations is fully coupled with the displacement field and phase field, forming a four-field coupled system. An efficient iterative scheme is designed based on the degree of coupling between fields. The proposed acceleration algorithm decomposes the fatigue problem into fast and slow components and uses a predictor–corrector guided cycle-jumping technique to accelerate the simulation. Numerical results show that the algorithm achieves a speedup ratio of up to 3.77 while preserving good accuracy. This method enables efficient quasi-static simulations over thousands of electrochemical cycles and provides a computational framework for investigating the effects of particle size, C-rate, initial crack length, internal cavities, and particle aspect ratio on fatigue crack propagation and battery performance degradation. The predicted fatigue crack evolution trends are qualitatively consistent with reported experimental observations.