Influence of Higher-Order Memory on Thermoelastic Response in a Nonlocal Orthotropic Medium Subjected to Ramp-Type Heating

Abstract The primary objective of this study is to analyze the memory effect in a homogeneous, orthotropic thermoelastic medium modeled as a two-dimensional half-space. This model couples higher-order memory-dependent derivatives with Eringen’s nonlocal elasticity within the framework of the generalized Moore–Gibson–Thompson theory. The half-space surface is subjected to thermal variation induced by ramp-type heating under the assumption of traction-free conditions. The analysis converts the governing equations into a vector–matrix form of ordinary differential equations through Laplace–Fourier transforms, and the solutions in the transformed domain are obtained using the eigenvalue method. The numerical inversion of these transforms is carried out simultaneously using the Stehfest algorithm together with a seven-point Gaussian quadrature scheme. Numerical outcomes are displayed in graphical form to show the influence of kernel functions, the nonlocal parameter, and ramp-type heating parameters on thermophysical fields along spatial direction. A comparative study is performed among the Lord-Shulman model, the Green-Naghdi-III model, and the MGT model with higher-order memory-dependent derivatives parameter.