Fractional Order Theory of Thermoelasticity for Elastic Medium with Variable Material Properties

Abstract

In this work, a new theory of generalized thermoelasticity for elastic media with variable properties has been constructed in the context of the fractional order heat conduction. The Clausius inequality and the higher expansions of the free energy are used to derive the formulations of anisotropic heterogeneous material with temperature-dependent material properties. The governing equations for the isotropic homogeneous material are also obtained, and which can be reduced to the corresponding L-S theory and the classical coupled theory for the different values of the fractional order parameter, respectively. Furthermore, a uniqueness theorem of the initial mixed boundary value problem for this new theory is stated and proved.

Keywords:

• Fractional order heat conduction
• Generalized thermoelasticity
• Uniqueness theorem
• Variable material properties