Temperature-Rate-Dependent Thermoelasticity Theory With Memory-Dependent Derivative: Energy, Uniqueness Theorems, and Variational Principle

摘要

This article is focused on developing a new mathematical model on the temperature-rate-dependent thermoelasticity theory (Green-Lindsay), using the methodology of memory-dependent derivative (MDD). First, the energy theorem of this model associated with two relaxation times in the context of MDD is derived for homogeneous, isotropic thermoelas-tic medium. Second, a uniqueness theorem for this model is proved using the Laplace transform technique. A variational principle for this model is also established. Finally, the results for Green-Lindsay model without MDD and coupled theory are obtained from the considered model.