We present a multi-scale finite element model to study the evolution of non-local damage in the electrode active materials. The electrochemical and mechanical phenomena in the separator, porous electrode with solid active materials and liquid electrolyte are described through a multi-scale modeling approach. Our multi-scale model accounts for the interactions between different physical phenomena at different computational scales. Three different length scales are distinguished in our multi-scale model: at the macro-scale, the electrochemical and mechanical interactions of the entire battery cell are characterized through the transport of Li⁺, the electric potential in the solid and liquid phases, and macroscopic mechanical deformation; at the micro-scale, the performance of a single representative active particle is modeled through the concentration of lithium in the electrode active particles, microscopic mechanical deformation, and hydrostatic stress; and at the meso-scale, the homogenization methods are used to relate the interactions between macro- and micro-scales. The evolution of damage in the electrode active materials, caused by the diffusion induced stresses, is described by a non-local damage model that solves the Helmholtz-type differential equation. To trigger the influence of damage evolution on transport properties and the electrochemical performance of the battery, the diffusivity of the electrode is coupled with the damage evolution parameters. The influences of damage evolution on the electrochemical and mechanical performance of the battery are evaluated through numerical examples. Our preliminary results reveal the influence of particle shape and discharge rate on the damage evolution and electrochemical and mechanical performance of the battery. The results also show that there is a significant influences of the damage evolution on capacity fade and reduction in the electrochemical-mechanical performance of the battery.

Figure 1: The influences of damage evolution and electrode shape on capacity fade and the electrochemical performance of the battery.