A Computational Model for All-Solid-State Batteries Coupling Electrochemistry and Solid Mechanics on Resolved Microstructures Enabling Optimization of Battery Electrode Design
Authors: Schmidt Christoph Paul , Sinzig Stephan , Robalo Rei Gil , Wall Wolfgang A. 
Published: February 2024

All-Solid-State Batteries (ASSB) are a promising technology to replace conventional Lithium-Ion Batteries (LIB) since the energy density and fast charging capability of LIBs are projected to reach a physical limit soon. In this regard, the ASSB technology is considered superior, especially if the incorporation of the lithium metal anode, or other high-capacity anode materials like silicon is achieved. However, these systems still require intensive research as many physical effects, especially those concerning the interaction of electrochemistry and solid mechanics, are to date not well understood [1]. Most experimental investigations on ASSB cells are performed on laboratory scale and are usually operated at elevated mechanical pre-stress to obtain satisfactory system performance. The delamination of active materials and solid electrolyte during cycling is expected to be one of the key effects for the required mechanical pre-stress. Furthermore, a lot of experimental research focuses on the development of new material classes and their stability in the cell compound, while a systematic optimization of the cell setup is missing.
Comprehensive computational models can help to generate insights in these regards as they allow for detailed investigations of local effects, which is often not possible in experimental setups. Another advantage of computational models compared to experiments is the ability to change input parameters in a fast and systematic way to quantify their influence on the battery cell performance and thereby help to speed up the optimization of battery designs. Since the multitude of physical effects that are relevant in ASSB are computationally challenging, a lot of modeling approaches rely on numerous simplifications like spatial homogenization or neglect of mechanical effects to name just two. However, such assumptions can significantly limit the validity of the model.
We propose a novel computational model for ASSB [2] to thoroughly investigate the interdependence of electrochemistry and solid mechanics on resolved microstructures that vastly influence the behavior and the performance of an ASSB cell. It is based on nonlinear continuum mechanics and accounts for large deformations due to lithiation dependent volume changes of the active materials. The mass and charge conservations are consistently formulated to also ensure the conservation property in large deformation scenarios. Furthermore, the model is extended by interaction effects of electrochemistry and solid mechanics like a nonlinear contact formulation at the electrode-electrolyte interfaces to account for delamination phenomena and the subsequent absence of charge transfer reaction (see Fig. 1). We thereby show how delamination phenomena drastically change available percolation paths in the microstructure. The efficient parallel implementation of the computational model allows to investigate realistic three-dimensionally resolved microstructures of ASSB cells while accounting for the coupling effects of electrochemistry and solid mechanics. A combination of elaborate physical models and probabilistic methods enables to gain further understanding and to quantify main influencing factors on the cell performance. To showcase these capabilities and how they can be exploited to increase system understanding, we analyze how statistical values like the porosity, or the composition of the electrode microstructure influence the capacity of an ASSB cell and thereby contribute to find optimal electrode designs.
References:
[1]: J. Janek, W.G. Zeier, Challenges in speeding up solid-state battery development, Nature Energy 8, 230–240 (2023) https://doi.org/10.1038/s41560-023-01208-9
[2]: C.P. Schmidt, S. Sinzig, V. Gravemeier, W.A. Wall, A Three-Dimensional Finite Element Formulation Coupling Electrochemistry and Solid Mechanics on Resolved Microstructures of All-Solid-State Lithium-Ion Batteries, 2022, preprint: https://ssrn.com/abstract=4189627.

Figure 1