Dual-stage method with PINN for coupled strong-form diffusion and energy-based deformation analysis in lithium-ion batteries

Traditional numerical methods, such as finite element analysis, have been extensively used to solve lithiation-induced stress, while they are costly and computationally intensive in solving high-dimensional nonlinear problems. In this work, we combine an alternating iterative method with a deep energy method to study a nonlinear coupling problem associated with the deformation of electrode materials in lithium-ion battery, i.e., the coupling between stress and diffusion during electrochemical cycling. Physics-informed neural networks (PINNs) are established to solve the time-dependent diffusion equation, which captures the evolution of the concentration field under stress-limited diffusion. The concentration field at each specific time serves as a part of the loss function for the Deep Energy Method (DEM)-based model, which computes the corresponding stress field. An alternating iterative approach is used to solve the coupling between diffusion and stress, with the diffusion equation being solved by the trained PINN and the static stress computation by the DEM for the updated concentration field. This sequential and iterative process effectively addresses the interaction between the concentration field and the deformation field, ensuring accurate and efficient analysis of the coupled diffusion-deformation problem. Numerical experiments support the feasibility and robustness of the alternating-iterative method with de-coupled physics-informed neural networks to solve complex problems for various physical scenarios and demonstrate the superior performance of the proposed method. The proposed method offers a simple avenue to solve multi-physics coupling problems with significantly theoretical and practical potential. The code used in this work is available at https://github.com/Owen-Hugh/DEMs.git.