A study on generalized thermoelasticity theory based on non-local heat conduction model with dual-phase-lag

Abstract

Non-local continuum theory helps to analyze the influence of all the points of the body at a material point. Involvement of non-local factor, i.e., size effect in heat conduction theory enhances the microscopic effects at a macroscopic level. The present work is concerned with the generalized thermoelasticity theory based on the recently introduced non-local heat conduction model with dual-phase-lag effects by Tzou and Guo. We formulate the generalized governing equations for this non-local heat conduction model and investigate a one-dimensional elastic half-space problem. Danilovskaya’s problem is taken, i.e., we assume that thermal shock is applied at the traction free boundary of the half-space. Laplace transformation is used to solve the problem and numerical method is applied to solve the problem by finding Laplace inversion through the Stehfest method. Various graphs are plotted to analyze the effects of different parameters and to mark the variation of this non-local model with previously established models.