Stat-Space Approach to Three-Dimensional Thermoelastic Half-Space Based on Fractional Order Heat Conduction and Variable Thermal Conductivity Under Moor–Gibson–Thompson Theorem

Abstract

This study presents a mathematical model of a three-dimensional thermoelastic half-space with variable thermal conductivity under the definition of fractional order heat conduction based on the Moor–Gibson–Thompson theorem. The non-dimensional governing equations using Laplace and double Fourier transform methods have been applied to a three-dimensional thermoelastic, isotropic, and homogeneous half-space exposed to a rectangular thermal loading pulse with a traction-free surface. The double Fourier transforms and Laplace transform inversions have been computed numerically. The numerical distributions of temperature increment, invariant stress, and invariant strain have been shown and analysed. The fractional order parameter and the variability of thermal conductivity significantly influence all examined functions and the behaviours of the thermomechanical waves. Classifying thermal conductivity as weak, normal, and strong is crucial and closely corresponds to the actual behaviour of the thermal conductivity of thermoelastic materials.

Keywords

• thermoelasticity
• Moor–Gibson–Thompson
• variable thermal conductivity
• Laplace transform
• Fourier transform
• fractional order