The relaxation effects of the volume properties of viscoelastic material in generalized thermoelasticity

A new model of the equations of generalized thermoviscoelasticity for isotropic media taking into consideration the rheological properties of the volume is given. The formulation is applied to both generalizations, Lord–Shulman theory and the Green–Lindsay theory, as well as to the coupled theory. The state space approach is adopted for the solution of one-dimensional problems in the absence or presence of heat sources. The Laplace-transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. Numerical results for the stress distribution are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the three theories, or ignoring the viscous effects of the volume. It is found that the consideration of these effects is to decrease the thermal stresses.