Memory-dependent response of the thermoelastic two-dimensional functionally graded rectangular plate

This article uses a memory-dependent derivative (MDD) — which may be better than a fractional derivative — to develop a novel heat conduction problem in a functionally graded material (FGM) layer with a distinct exponential gradient model. A theoretical framework is designed for a functionally graded plate (FGP) incorporating the fractional heat conduction theory that incorporates single-phase-lag (SPL) and two-temperature discrepancy factors to capture the thermoelastic response and the memory-dependent effect. Then, the modified model is used to investigate the thermoelastic response of an FGP subjected to thermal shock at the left surface of the plate, keeping other faces at zero temperature. The temperature change is determined using the integral transform technique, and the solution is obtained in the Laplace transform domain. The transient temperature response in the time domain is evaluated through numerical inversion of the Laplace transform to generate numerical data. The general solutions of the governing equation of stress function are obtained by utilizing material attributes represented by the exponential-law index. The transient responses, namely temperature, displacement, and stress, are graphically depicted. FGP is composed of partially stabilized zirconia (PSZ) particles, and the austenitic stainless steel (SUS304) matrix was used in the analysis. The use of FGM requires careful compositional choices to prevent thermal stresses from being generated in the FGP. The study compares temperature distributions using non-Fourier and classical Fourier models, revealing wave-like phenomena in fractional heat transfer, which are undetected in classical Fourier heat conduction.