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

The model of the equations of generalized thermoviscoelasticity with one relaxation time, when the relaxation effects of the volume properties of the material are taken into account, is established. The state-space approach developed in Bahar and Hetnarski [1] is adopted for the solution of one-dimensional problems. The formulation is valid for problems with or without heat sources. The resulting formulation together with the Laplace transform technique is applied to a variety of problems. The solutions to a thermal shock problem and to a problem of layer media, both without heat sources, are obtained. Also, the effects of a plane distribution of heat sources on the whole and semispace are studied. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory or ignoring the viscous effects of the volume. It is found that the consideration of these effects is to decrease the thermal stresses.