Computational assessment of mechanical damage in a thermoelastic rod under hyperbolic two-temperature theory with nonlocal and memory effects

Abstract

The present work is devoted to study the thermoelastic interaction for a homogeneous thermoelastic rod, exposed to a moving heat source under the purview of hyperbolic two-temperature thermoelasticity. The constitutive relations for the present problem has been framed in the context of nonlocal elasticity theory taking into account the mechanical damage. The heat conduction equation in the present situation has been established taking into account the Moore–Gibson–Thompson generalized heat equation within a slipping interval on assimilating the memory-dependent derivative. The rod is assumed to be fixed at both ends and thermally insulated. The governing equations have been solved by the Laplace transform mechanism and in order to arrive at the solutions in real space–time domain, inversion of the Laplace transform has been performed using the method of Zakian. The computational results have been obtained for various values of damage parameter to reveal significant effect of various parameters such as hyperbolic two-temperature parameter, classical two-temperature parameter, various kernel function, nonlocal parameter and the time delay also. Various comparative studies have been performed to analyze the impact of damage on each physical fields. Moreover, a comparative study between hyperbolic two-temperature theory and one-temperature theory is also carried out.