In this paper we consider exact solutions for two families of constrained thermoelastic materials whose energy potentials reduce, under isothermal conditions, to the strain energy function of generalized Varga materials. The two families correspond to different ideas of mechanical incompressibility, for the first family the density is independent of deformation and is a function of temperature alone. The second family consists of materials whose density is a function of the specific entropy alone, independent of the deformation.
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