Investigation of thermoelastic response in porous materials with memory effects under ramp-type heating using dual phase lag theory

The main aim of this article is to investigate the memory effect in an isotropic porous medium within the dual-phase-lag (DPL) model under transient conditions induced by ramp-type heating. The model captures the influence of thermo-mechanical memory effects through memory-dependent derivative (MDD) and addresses the complexities arising from voids within the material. To solve the governing equations, joint Fourier–Laplace transform is applied to derive the field variables in the transformed domain. The numerical inversion of these transforms is carried out using the Stehfest method along with a Gaussian quadrature method. The graphical results illustrate the influence of the ramp-type heating parameter, different model variations, and the kernel function on the spatial distribution along the considered variable. Additionally, 3D figures corresponding to the displacement components, stress components, volume fraction, and temperature are included in our study.