Analysis of thermomechanical responses of functionally graded unbounded materials using an advanced dual‐phase delay heat transfer model with higher‐order fractional derivatives

Abstract

The present article provides a theoretical investigation into the thermoelastic behavior of functionally graded materials (FGMs) using modified thermoelastic conduction models. These enhanced models have potential applications in various engineering fields, including aerospace, pressure vessels, and structural engineering. The research delves into examining a thermoelastic scenario concerning an infinite FGM with a spherical cavity exposed to thermal shock. This analysis is framed within the dual‐phase‐lag (DPL) thermoelasticity theory and incorporates higher‐order fractional derivatives. The analysis employs the Laplace transform method to address the problem, utilizing the Taylor series expansion of higher‐order fractional derivatives as proposed by Caputo and Fabrizio. This approach enables advanced approximations of heat flux, temperature gradients, and thermal displacements. The study assumes that the thermal and mechanical properties of the FGM vary as a power function of the radial coordinate. The results are presented graphically, showing temperature distributions, stress fields, and displacement profiles. Additionally, the study explores how variations in the gradation parameter and the coefficient of fractional derivatives impact the thermoelastic behavior of the material.