Lithium-ion batteries (LIBs) of high energy density and light-weight design, have found wide applications in electronic devices and systems. Degradation mechanisms that caused by lithiation is a main challenging problem for LIBs with high capacity electrodes like silicon (Si), which eventually can reduce the lifetime of batteries. In this paper, a hybrid phase field model (PFM) is proposed to study the fracture behavior of LIB electrodes. The model considers the coupling effects between lithium (Li) -ion diffusion process, stress evolution and crack propagation. Also, the dependency of Elastic properties on the concentration magnitude of Li-ion is considered. A numerical implementation based on a MATLAB finite element (FE) code is elaborated. Then, the proposed hybrid PF approach is applied to a Nanowire (NW) Si electrode particle. It is shown that the hybrid model shows less tendency to crack growth than the isotropic model.

中文翻译：

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锂离子电池电极颗粒中锂扩散引起断裂的混合相场模型

具有高能量密度和轻量化设计的锂离子电池 (LIB) 在电子设备和系统中得到了广泛的应用。锂化引起的降解机制是具有高容量电极（如硅（Si））的 LIB 的主要挑战问题，最终会缩短电池的寿命。在本文中，提出了一种混合相场模型（PFM）来研究 LIB 电极的断裂行为。该模型考虑了锂（Li）离子扩散过程、应力演化和裂纹扩展之间的耦合效应。此外，还考虑了弹性特性对锂离子浓度大小的依赖性。详细阐述了基于 MATLAB 有限元 (FE) 代码的数值实现。然后，将所提出的混合 PF 方法应用于纳米线 (NW) Si 电极颗粒。