Memory-dependent generalized thermoelasticity with finite wave speeds

Abstract

The present article deals with the question: how time dependent non-locality influence the domain of dependency of thermal signals in solids? In order to establish the hypothesis “domain of influence” in an isotropic medium, based on the temperature-rate dependent thermoelasticity (TRDTE) theory, a thermodynamic consistent model is formulated by incorporating memory-dependent derivative (MDD). Firstly, the domain of influence theorem is established followed by a domain of dependence inequality and it certifies that for a finite time t>0 a solution of a given thermo-dynamical problem, corresponding to the data defined in a bounded support, vanishes outside a suitably defined bounded domain D*(t). It physically interprets that an initial perturbation of a bounded thermo-elastic domain generates thermal signals which for any t>0 can not occupy the whole space, i.e. it propagates with a finite speed. Finally, a two-dimensional thermoelastic problem in the isotropic medium is considered for a supporting visualization of the domain of influence theorem of the memory-dependent generalized thermoelasticity theory.