Modeling and Simulation of Chemo-Elasto-Plastically Coupled Battery Active Particles

Abstract

As an anode material for lithium-ion batteries, amorphous silicon offers a significantly higher energy density than the graphite anodes currently used. Alloying reactions of lithium and silicon, however, induce large deformation and lead to volume changes up to 300%. We formulate a thermodynamically consistent continuum model for the chemo-elasto-plastic diffusion-deformation behavior of amorphous silicon and it's alloy with lithium based on finite deformations. In this paper, two plasticity theories, i.e. a rate-independent theory with linear isotropic hardening and a rate-dependent one, are formulated to allow the evolution of plastic deformations and reduce occurring stresses. Using modern numerical techniques, such as higher order finite element methods as well as efficient space and time adaptive solution algorithms, the diffusion-deformation behavior resulting from both theories is compared. In order to further increase the computational efficiency, an automatic differentiation scheme is used, allowing for a significant speed up in assembling time as compared to an algorithmic linearization for the global finite element Newton scheme. Both plastic approaches lead to a more heterogeneous concentration distribution and to a change to tensile tangential Cauchy stresses at the particle surface at the end of one charging cycle. Different parameter studies show how an amplification of the plastic deformation is affected. Interestingly, an elliptical particle shows only plastic deformation at the smaller half axis. With the demonstrated efficiency of the applied methods, results after five charging cycles are also discussed and can provide indications for the performance of lithium-ion batteries in long term use.

Figures (11)

• Figure 1: Computational domains in 1D in \ref{['fig:geometry_1d']} and 2D in \ref{['fig:geometry_2d']} used for the numerical simulations.
• Figure 2: Numerical results for the elastic (Ela.), plastic (Pla.) and viscoplastic (Vis.) approaches of the 1D radial symmetric case at $\text{SOC} = 0.92$ over the particle radius $r$: concentration $c$ in (a), equivalent plastic strain $\varepsilon_\text{pl}^{\text{eq}}$ in (b) and tangential Cauchy stress $\sigma_\phi$ in (c) as well as tangential Cauchy stress $\sigma_\phi$ at the particle surface $r=1.0$ over $\text{SOC}$ in (d).
• Figure 3: Influence of the different plasticity approaches in (a) and of the maximal yield stress of the viscoplasticity approach in (b) for the tangential Cauchy stress $\sigma_\phi$ at the particle surface $r=1.0$.
• Figure 4: Tangential Cauchy stress $\sigma_\phi$ over SOC at the particle surface $r=1.0$ for varying C-rate in (a) and particle size in (b).
• Figure 5: Advantages of the adaptive solution algorithm: time step size $\tau_n$ over simulation time $t$ for two half cycles (one lithiation and one delithiation) in (a) and concentration $c$ as well as refinement level of the spatial discretization over the particle radius $r$ at $\text{SOC} = 0.92$ in (b).