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 based on finite deformations. In this paper, a plastic deformation approach with linear isotropic hardening and a viscoplastic deformation ansatz are investigated and compared to allow the evolution of plastic deformations and reduce occurring stresses. For both models, a return mapping can be derived to update the equivalent plastic strain for the next time step. Using a finite element method and an efficient space and time adaptive solution algorithm a large number of charging cycles can be examined. We derive a linearization for the global Newton scheme and compare it to an automatic differentiation technique regarding the numerical performance and physical results. Both plastic approaches lead to a stronger 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，非晶硅相比当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引发大变形，导致体积变化高达300%。基于有限变形框架，我们建立了一个热力学一致的化学-弹塑性扩散-变形连续介质模型。本文研究并比较了采用线性各向同性硬化的塑性变形方法与粘塑性变形策略，以允许塑性变形演化并降低产生的应力。针对两种模型均可推导出返回映射算法，用于更新下一时间步的等效塑性应变。通过有限元方法与高效的空间-时间自适应求解算法，可模拟大量充放电循环。我们推导了全局牛顿法的线性化形式，并与自动微分技术在数值性能及物理结果方面进行了对比。两种塑性方法均导致单次充电循环结束时粒子表面出现更强的非均匀浓度分布，并向拉伸切向柯西应力转变。不同参数研究揭示了塑性变形放大的影响因素。有趣的是，椭圆粒子仅在短半轴方向产生塑性变形。基于所开发方法的高效性，本文还讨论了五个充放电循环后的模拟结果，可为锂离子电池长期使用性能提供参考。