Thermo-viscoelastic materials with fractional relaxation operators

The new model of linear thermo-viscoelasticity for isotropic media taking into consideration the rheological properties of the volume with fractional relaxation operators is given. The governing equations are taken in a unified system from which some essential theorems on the linear coupled and generalized theories of thermo-viscoelasticity can be easily obtained. The resulting formulation is applied to several concrete problems, a thermal shock problem and a problem for a half-space subjected to ramp-type heating as well as a problem of a layer media. Laplace transform techniques are used. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effect of fractional relaxation operators and ramping parameter of heating with different theories of thermoelasticity.