A coupled finite element approach to spatially resolved lithium plating and stripping in three-dimensional anode microstructures of lithium-ion cells

Abstract

In this article, we present a coupled finite element approach to spatially resolved lithium plating and stripping in three-dimensional anode microstructures of lithium-ion cells. The local film thickness of plated lithium at the anode-electrolyte interface is treated as a primary variable in addition to the lithium concentration and the electric potential inside both electrodes as well as the lithium concentration and the electrochemical potential inside the electrolyte. We take the electric resistance of plated lithium into account when evaluating the Butler–Volmer charge transfer kinetics at the anode-electrolyte interface. The overall system of nonlinear equations resulting from discretization in time and space is solved in a monolithic, implicit fashion by the iterative Newton–Raphson method. To ensure stable and fast convergence especially during the final stages of lithium stripping, we introduce a novel regularization technique characterized by a trigonometrical regularization function for the purpose of discontinuity removal, and we show that our regularization is indeed necessary and effective while being superior to an existing one from the literature in several respects. The linear solver is derived from an advanced, physics-oriented preconditioning and solution technique established in one of our previous publications. In a large number of numerical examples, we thoroughly study two different lithium-ion cells involving up to approximately 2.3 million degrees of freedom. We thereby prove that our modeling and simulation approach is straightforwardly applicable to large and complex problem setups, and that it is capable of capturing lithium plating and stripping during continuous cell cycling without any interruptions in the corresponding simulations. Besides validating our implementation and examining various electrochemical properties of lithium plating and stripping, we also demonstrate that our approach is physically plausible and sensitive to overcharging, fast charging, and low-temperature charging as the three major causes of lithium plating. Unlike existing and widely used approaches based on geometric homogenization via morphological model parameters such as the porosity and the tortuosity, our approach offers the opportunity to detect spatial inhomogeneities in the propagation and distribution of plated lithium within anode microstructures. Accurate and in-depth numerical investigations of lithium plating and stripping are thus enabled as a potent alternative to elaborate and often costly experimental studies.