Analytical solution for one-dimensional coupled non-Fick diffusion and mechanics

On the basis of the developed coupled non-Fick diffusion and mechanics theory, the approximate analytical solutions of concentration, stress and displacement are respectively derived by using the Laplace transform and inverse Laplace transform. There exist two discontinuous points in both the stress and concentration solutions, while the displacement is continuous. Moreover, the two discontinuous points verify the interaction between the non-Fick diffusion and mechanics. Then, numerical examples about the stress, concentration and displacement field are carried out to show the coupled behavior. Finally, the non-Fick effect is graphically obvious in the results.