Fractional thermo-viscoelasticity theory with and without energy dissipation

Abstract

In the present paper, a new fractional model of fractional order thermo-viscoelasticity theory with and without energy dissipation is constructed. Some basic theorems can easily obtain in both theories. A three-dimensional model of fractional thermo-viscoelasticity is established. The model is applied to a specific problem of a half space subjected to harmonic heating and traction free surface. The reverses of Fourier transforms and Laplace processes are obtained numerically. Numerical results are given and illustrated graphically for temperature, displacement, and stress distributions. A comparison of coupled and generalized thermo-viscoelasticity theories are made.

KEYWORDS:

• Thermo-viscoelastic theory
• Lord-Shulman theory
• Green-Naghdi without energy dissipation theory (GN-II)
• fractional calculus
• Laplace– double Fourier transform

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.