Time-domain finite element method to generalized diffusion-elasticity problems with the concentration-dependent elastic constants and the diffusivity

The investigations of mechanical-diffusion coupling are of great importance for the micro-electromechanical devices under non-uniform concentration environment, especially with the development of energy storage technology for a rapid charging system. In recent years there have been many experimental and theoretical studies show that the elastic constants and the diffusivity depend on the concentration of diffusing substances. In view of this, present work aims to study generalized diffusion-elasticity problems considering the concentration-dependent elastic constants and the diffusivity by time-domain finite element method. By using principle of virtual work, the obtained nonlinear finite element equations are solved directly in time domain to minimize precision losses in the application of integrated transformation method, and then the nonlinear solutions can be obtained. As numerical examples, the developed method is used to investigate the transient response of a thick circular plate subjected to the shock loading of the concentration. The results demonstrate that the developed method can faithfully predict the deformation of structure and most importantly the diffusive wave feature in both one-/two-dimensional solids whilst it is commonly difficult to model, especially for two-dimensional case, by using transform method. Parametric studies are performed to evaluate and discuss the effects of concentration-dependent elastic constants and diffusivity on the structural dynamic responses.