A three-dimensional finite element formulation coupling electrochemistry and solid mechanics on resolved microstructures of all-solid-state lithium-ion batteries

Abstract

In this paper we present an all-solid-state lithium-ion battery (ASSB) model that considers electrochemistry and solid mechanics in a fully coupled manner. The model spatially resolves the three-dimensional microstructure of an ASSB cell and is based on non-linear continuum mechanics. The coupling of electrochemistry and solid mechanics is incorporated via lithiation-dependent volumetric changes of the active materials and the consistent formulation of the electrochemical governing equations on deformed geometries resulting in changed percolation paths. As the volumetric changes due to (de-)lithiation are reported to be large for several active materials, we introduce this effect using a multiplicative split of the deformation gradient. To also allow for large deformations in the mass conservation equation, an Arbitrary Lagrangian–Eulerian formulation is employed. Furthermore, we show the central steps to deduce the finite element formulation of our model as well as the adopted monolithic solution procedure to solve this strongly coupled non-linear problem. The linear solver used for large problem setups is adjusted from the advanced, physics-oriented preconditioning technique published in our previous work. In the numerical examples, we investigate three different geometries with up to about 1.3 million degrees of freedom and thereby prove that our approach is applicable to geometrically large and complex scenarios. Moreover, we show that our approach consistently introduces the mass and charge conservation on deformed meshes. Furthermore, the numerical examples demonstrate the high relevance to incorporate current collectors into the ASSB cell simulations. Finally, we show that solid mechanics and the coupling effects have indeed a large impact on the ASSB cell performance and their incorporation is therefore vital for precise results and predictions.