Abstract
A new mathematical model of two-temperature electro-thermo viscoelasticity theory has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative. 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. The exact solutions for temperature, stress and displacement are obtained in the Laplace transform domain for each problem. According to the numerical results and its graphs, conclusion about the new theory has been constructed. The predictions of the theory are discussed and compared with dynamic classical coupled theory. The result provides a motivation to investigate conducting thermoelectric viscoelastic materials as a new class of applicable materials.