In this paper, a thermodynamically consistent chemo-thermo-mechanical coupled constitutive relationship is developed based on the local energy conservation equation, the entropy inequality and mass conservation equation, and the constitutive relation for chemo-mechanical coupled problem was degraded when the temperature was kept constant. The governing equations of chemo-mechanical coupling model were established by combining the force balance equation with the Fick diffusion equation. Then we considered a case of a sphere with symmetrical boundary and initial conditions, and the diffusion conducted along the radial direction. Using the symmetry of the spherical structure, the chemo-mechanical coupled governing equation was simplified, and then analytically solved by the separation variable method. The analytical expressions of concentration and displacement were obtained, and the variations of stresses, concentration, displacement and chemical potential with time were deduced. The results showed that the deformation of the sphere and species diffusion was not independent, but interacts with each other. The chemical potential in the sphere could be affected by both of them.

中文翻译：

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具有质量扩散的可变形球体中化学-机械耦合问题的解析解

本文基于局部能量守恒方程、熵不等式和质量守恒方程建立了热力学一致的化学-热力-机械耦合本构关系，并在一定温度下降低了化学-机械耦合问题的本构关系。持续的。将力平衡方程与Fick扩散方程相结合，建立了化学-机械耦合模型的控制方程。然后我们考虑了具有对称边界和初始条件的球体的情况，并且扩散沿径向进行。利用球体结构的对称性，简化了化学-机械耦合控制方程，然后用分离变量法解析求解。得到浓度和位移的解析表达式，推导出应力、浓度、位移和化学势随时间的变化。结果表明，球体的变形和物种扩散不是独立的，而是相互影响的。球体中的化学势可能会受到两者的影响。