An Analytical Solution for Chemo-Mechanical Coupled Problem in Deformable Sphere with Mass Diffusion

Abstract

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.