Comparison of Different Elastic Strain Definitions for Largely Deformed SEI of Chemo-Mechanically Coupled Silicon Battery Particles

Abstract

Amorphous silicon is a highly promising anode material for next-generation lithium-ion batteries. Large volume changes of the silicon particle have a critical effect on the surrounding solid-electrolyte interphase (SEI) due to repeated fracture and healing during cycling. Based on a thermodynamically consistent chemo-elasto-plastic continuum model we investigate the stress development inside the particle and the SEI. Using the example of a particle with SEI, we apply a higher order finite element method together with a variable-step, variable-order time integration scheme on a nonlinear system of partial differential equations. Starting from a single silicon particle setting, the surrounding SEI is added in a first step with the typically used elastic Green--St-Venant (GSV) strain definition for a purely elastic deformation. For this type of deformation, the definition of the elastic strain is crucial to get reasonable simulation results. In case of the elastic GSV strain, the simulation aborts. We overcome the simulation failure by using the definition of the logarithmic Hencky strain. However, the particle remains unaffected by the elastic strain definitions in the particle domain. Compared to GSV, plastic deformation with the Hencky strain is straightforward to take into account. For the plastic SEI deformation, a rate-independent and a rate-dependent plastic deformation are newly introduced and numerically compared for three half cycles for the example of a radial symmetric particle.

Figures (3)

• Figure 1: Dimension reduction of a three-dimensional unit sphere with surrounded SEI to the one-dimensional interval, based on castelli2021numerical.
• Figure 2: Radial (a) and tangential (b) Cauchy stress over the radius ($0 \leq r \leq 1.0$ for $\Omega_{\text{h}, \text{P}}$, $1.0 \leq r \leq 1.1$ for $\Omega_{\text{h}, \text{S}}$) at the end of the simulation; for the 1.) purely elastic (ela.) case with the GSV strain approach (Lag. ela.), the simulation stopped at $\text{SOC}= 0.34$, see \ref{['fig:voltage']}(a), whereas all other cases (2.) elastic, 3.) plastic (pla.) and 4a.), 4b.) viscoplastic (vis.)) for the logarithmic (Log.) Hencky strain approach reached the final simulation time.
• Figure 3: Electrical voltage $U$ over SOC for three half cycles for different elastic strain approaches for elastic and plastic cases with aborted GSV Lagrangian approach for the elastic case in orange (a) and tangential Cauchy SEI stress over SOC at the particle SEI interface with increasing stress-overrelaxation for smaller $\dot{\varepsilon}_0$ (blue arrow) in the viscoplastic case (b).