Dynamical theoretical model and variational principles for coupled temperature-diffusion-mechanics

In this paper, firstly, the acceleration of the temperature and concentration are assumed to need the extra increment of the heat and energy. The inertial entropy and the inertial chemical potential were proposed by Kuang (Acta Mech 203:1-11, 2009, Acta Mech 214:275-289, 2010). Secondly, the expressions of dissipative energy produced by the variation of the temperature and concentration are derived by using the second law of thermodynamics. Finally, several variational principles for coupled temperature-diffusion- mechanics are established, and their corresponding governing equations and boundary conditions are naturally presented. Meanwhile, some numerical simulations are carried out to describe the coupled reciprocity, which shows concentration diffusion with a finite velocity.