The relaxation effects of a saturated porous media using the generalized thermoviscoelasticity theory

In this paper, a model of the generalized thermoviscoelasticity for a saturated porous media is used. Taking the rheological properties of the volume into consideration, it is developed on the basis of the thermo-hydro-elastodynamic model proposed by the authors. The formulation is applied to the generalized porous thermoviscoelasticity theories: coupling theory, Lord–Shulman theory and Green–Lindsay theory. The general characteristic equations for arbitrary coordinate system are derived using a semi-analytical approach in the Laplace domain. Exact solutions of the saturated porous thermoviscoelastic media, with a cylindrical cavity that is subjected to a time dependent thermal load, are obtained in the absence of heat sources. Numerical results are illustrated graphically employing numerical method for inverting the Laplace transform. Comparisons are made with the results predicted by these theories and the classical theory. In addition, the influence of rheological parameters on the thermoviscoelastic property is analyzed.