Static Solutions for Plane Strain Problem of Coupled Diffusion and Deformation

The diffusion and deformation coupled problem are considered in many material and engineering areas, and it has been studied on both theory and solution methods. However, the analytical solutions for this problem are relatively fewer, especially for two-dimensional problems. In this paper, based on a diffusion and mechanical coupled continuum model, the plane strain problem in the polar coordinates considering mass diffusion was studied. The relationship between volume strain and mass concentration was deduced by using a displacement potential function, and the analytical expression for concentration was then deduced. To comply with the mechanical boundary conditions, the Airy stress function was applied. The analytical expressions for stress components were also completely determined. After that, a numerical example of a cylinder with variant concentration distribution on its cylindrical surface was given, the results showed that concentration gradient distribution would cause the generation of stresses and the value of stresses positive correlated to the concentration gradient.