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.

翻译：作为锂离子电池的负极材料，非晶硅相比目前使用的石墨负极具有显著更高的能量密度。然而，锂与硅的合金化反应会导致大变形并引发高达300%的体积变化。我们基于有限变形理论，建立了描述非晶硅及其锂合金化学-弹塑性扩散-变形行为的热力学一致连续介质模型。本文提出了两种塑性理论（即含线性各向同性硬化的率无关理论与率相关理论），以允许塑性变形的演化并降低产生的应力。采用现代数值技术（如高阶有限元方法及高效的空间与时间自适应求解算法），对两种理论导致的扩散-变形行为进行了比较。为进一步提升计算效率，采用自动微分方案，相比全局有限元牛顿格式的算法线性化，该方案可显著加速组装时间。两种塑性方法均导致更不均匀的浓度分布，并在一个充电周期结束时使颗粒表面转化为拉伸切向柯西应力。不同参数研究表明塑性变形增强的影响机制。有趣的是，椭圆颗粒仅在短半轴方向产生塑性变形。基于所应用方法的高效性，本文还讨论了五个充电周期后的结果，为锂离子电池长期使用性能提供参考依据。