Generalized Theory of Thermoviscoelasticity and a Half-Space Problem

In this work, the equations of generalized thermoviscoelasticity for a viscoelastic medium are derived. Also, uniqueness and reciprocity theorems for these equations are proved. In addition, a one-dimensional problem for a viscoelastic half space is considered. The Laplace transform technique is used to solve the problem. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained in an approximate analytical manner using asymptotic expansions valid for small values of time. The temperature, displacement, and stress are computed and represented graphically.