Thermodiffusion in Elastic Materials of Grade Two

The elastic solid of grade two subjected to the process of thermodiffusion is studied in the framework of the nonlinear mechanics of continua. Two independent sets of constitutive quantities are obtained: the first set results from the free energy density as a thermodynamic potential, and second one consists of thermodynamic fluxes. Constitutive equations for thermodynamic fluxes are restricted not only by the entropy inequality, but also by a number of additional conditions following from the entropy inequality. Expanding the free energy density into  a quadratic polynomial and assuming particular forms of constitutive equations for entropy, heat and diffusion fluxes, the linearized field equations for displacements, temperature and concentration of diffused mass are derived.