Generalized thermo-viscoelasticity with memory-dependent derivative: uniqueness and reciprocity

Abstract

This article theoretically demonstrates the reciprocity and uniqueness theorems for generalized theory of thermo-viscoelasticity involving memory-dependent derivative (MDD). To prove the theorems, a thermo-viscoelastic initial-boundary value problem under the domain of three-phase-lag (TPL) model is taken into consideration for an isotropic, homogeneous medium. The theorems are proved with the help of the Laplace transform of the thermophysical quantities. Finally, a few special cases in the generalized theory of thermo-elasticity and thermo-viscoelasticity with MDD and without MDD are derived from the present model.