Generalized thermo-viscoelasticity with memory-dependent derivatives

A new generalized thermo-viscoelasticity theory with memory-dependent derivatives is constructed. The governing coupled equations with time-delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to one-dimensional problem of a half-space. The bounding surface is taken traction free and subjected to a time dependent thermal shock. The Laplace transforms technique is used to obtain the general solution in a closed form. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory are given. The predictions of the theory are discussed and compared with dynamic classical coupled theory. (C) 2014 Elsevier Ltd. All rights reserved.