A consistently coupled multiscale mechanical–electrochemical battery model with particle interaction and its validation

Abstract

As an inherent multiscale structure, a continuum scale battery electrode is composed of many microscale particles. Currently it is generally assumed that each particle is isolated while the stress in a particle only affects solid diffusion. The lack of mechanical interaction between particles and effect of stress on the electrochemical reaction rate makes mechanics and electrochemistry uncoupled at the continuum scale: an applied continuum scale stress in the electrode has no effect on the spatial distribution of electrochemical reaction in the electrode and vice versa. This paper first presents a multiscale model that couples mechanics and electrochemistry consistently at the microscopic and continuum scales. The microscopic particle stress is a superposition of the intra-particle concentration gradient-induced stress and the particle interaction stress, with the latter being related to the continuum scale stress through a representative volume element. The electrochemical charge transfer kinetics is generalized with the stress effect. Diffusion in a particle is described by a chemical potential that includes stress and phase transition. In a parallel effort, we develop a direct three-dimensional particle network model, which consists of realistic active material particles. Unlike the multiscale model, there is no scale separation and homogenization in the particle network model: all particles are modeled explicitly with fully coupled three-dimensional mechanical-electrochemical equations and the finite element method. The results from the particle network model are accurate and can serve as a standard, but the size of particle network that can be calculated is limited due to high computational cost. Comparison of results from the multiscale model and from the particle network model shows that the multiscale model gives good, satisfying accuracy while reducing the computational cost dramatically in comparison to the three-dimensional particle network model. The multiscale model is a power tool to address various coupled problems in the electrode, from inter-particle crack growth to electrode structure design for high performance and long cycle life.