On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative

Abstract

The research article theoretically deals with the three-phase-lag (TPL) heat conduction model of generalized thermoelasticity, reformulated in terms of the memory-dependent derivative (MDD). The energy theorem and the variational principle of this proposed model are established for an isotropic, homogeneous, thermoelastic continuum. The uniqueness theorem is derived from the energy theorem, and a few special cases are also obtained from the present model. For numerical simulation of the present model, a one-dimensional thermoelastic problem in a semi-infinite medium subjected to a time-dependent thermal shock on its bounding plane is considered. The Laplace transform together with its numerical inversion is adopted to obtain the solutions in the physical domain. The influence of the kernel function and time delay on the variation of the non-dimensional thermophysical quantities are studied graphically and finally some remarkable points are mentioned as conclusions.