The anode material Sn used in sodium-ion batteries displays high theoretical capacity, complex phase transformation, and significant volume change during the charging/discharging process. In particular, the effects of small scale on the mechanical behavior of Sn anode at the nanoscale are very active research fields. However, the majority of these results are based on nonlocal gradient formulations. In this study, we proposed and established a model that combines the electrochemical reaction with stress-driven nonlocal integral elasticity for the nanoelectrode to analyze the evolution of diffusion-induced deformation during the sodiation process. Several critical features, such as the small-scale parameter, two-phase reaction, and concentration-dependent elastic modulus, were incorporated into the established model. The model demonstrated that a small scale could significantly affect the deformation behavior. The results obtained using the finite element method showed that the mechanical reliability of the Sn anode could be significantly enhanced when the anode was sodiated with larger nonlocal parameters and smaller slenderness. In addition, the axial action force exhibited a strong size effect and was influenced by the nondimensional thickness parameter of the anode. This work provides a framework for multi-scale research on high-capacity sodium-ion battery electrodes.

钠离子电池负极材料Sn具有理论容量高、相变复杂、充放电过程中体积变化显着等特点。特别是，小尺度对纳米尺度锡阳极机械行为的影响是非常活跃的研究领域。然而，这些结果大部分都是基于非局部梯度公式。在本研究中，我们提出并建立了一个将电化学反应与纳米电极应力驱动的非局部积分弹性相结合的模型，以分析钠化过程中扩散引起的变形的演变。几个关键特征，如小尺度参数、两相反应和浓度依赖性弹性模量，被纳入所建立的模型中。该模型表明，小尺度可以显着影响变形行为。有限元分析结果表明，当阳极钠化处理具有较大的非局部参数和较小的细长尺寸时，Sn阳极的机械可靠性能显着提高。此外，轴向作用力表现出较强的尺寸效应，并受到阳极无量纲厚度参数的影响。这项工作为高容量钠离子电池电极的多尺度研究提供了框架。