ON THE TWO-TEMPERATURE GREEN-NAGHDI THERMOELASTICITY THEORIES

The constitutive laws for two-temperature Green-Naghdi theories are given. It is proved that the two-temperature thermoelasticity theory admits dissipation of energy and the theory of elasticity without energy dissipation is valid only when the two-temperatures coincide. The uniqueness and reciprocal theorems are proved for a linear anisotropic and inhomogeneous thermoelastic centro-symmetric solid in the frame of two-temperature Green-Naghdi theories. The convolutional variational principle is established for the two-temperature Green-Naghdi theory of type III. A continuous dependence result is given for an isotropic solid.