Two-temperature Green–Naghdi theory of type III in linear thermoviscoelastic anisotropic solid

The reciprocal theorem is proved and the variational principle is established for the linear two-temperature Green–Naghdi theory of type III in an anisotropic and inhomogeneous thermoviscoelastic solid. A proof of a uniqueness theorem for thermoviscoelasticity  , without restrictions imposed on the relaxation or thermal conductivity tensors, except symmetry conditions, is given. The constitutive equations are derived for the linear two -temperature Green–Naghdi thermoviscoelasticity theory of type III, and the time-independence of the conductivity tensors kijkij and kij∗ is proved. An application is given for isotropic thermoviscoelastic solid and the results are presented graphically. The curves of the stress and temperature distributions are more uniform and the thermodynamic temperature is smaller in magnitude relative to the one-temperature case.