A Three-Dimensional, Thermodynamically and Variationally Consistent, Fully Coupled, Electro-Chemo-Thermo-Mechanical Model of Solid-State Batteries

Abstract

We present a theoretical framework for high fidelity modeling of three-dimensional electro-chemo-thermo-mechanical coupled systems such as solid-state batteries. The framework provides a useful means of utilizing molecular level information to predict the overall performance of the system at the continuum level. The central statement of the theoretical framework is a thermodynamically consistent inf-sup problem. The total potential of the coupled system consists of the Helmholtz free energy, the electrical kinetic potential, the chemical potential, the Fourier potential, the chemical reaction potential, and the external power expenditure. All governing equations derive from variational principles. We also show that the resulting initial-boundary-value problem (IBVP) is consistent with existing, widely adopted equations for modeling batteries. Moreover, the IBVP can be naturally discretized using the (variational) finite element method to simulate practical solid-state batteries with arbitrary geometries. Several examples illustrate multiphysics coupling between pairs of the physical field equations, culminating in a comprehensive three-dimensional model of charge-discharge in a solid state battery.