Spatiotemporal Nonlocal Thermoelastic Model with Caputo-Tempered Fractional Derivatives for Infinite Thermoelastic Porous Half-Space with Voids

This study presents a novel generalized nonlocal thermoelastic model for porous materials with voids, addressing key limitations in traditional thermoelasticity frameworks. The proposed model builds on the two-phase lag (TPL) theory, incorporating spatial and temporal nonlocal effects to account for microscale and memory-dependent behaviors in porous structures. A significant innovation lies in integrating Caputo-tempered fractional derivatives, which introduce exponential tempering to mitigate the long-range memory effects associated with standard fractional derivatives. This refined mathematical framework provides an enhanced and accurate representation of the dynamic thermomechanical behavior of elastic materials with voids. To validate the model, the transient response of a semi-infinite porous medium subjected to a non-Gaussian laser-shaped heat flux on its free, stress-free surface is analyzed. This study fills a critical research gap by evaluating the combined influence of nonlocal spatial-temporal effects, phase delay, and tempered fractional parameters on the size-dependent thermomechanical responses of half-space porous nanostructures. Key findings reveal that incorporating tempered fractional derivatives significantly improves the predictability of thermal and mechanical responses while offering a more realistic depiction of energy dissipation and wave propagation. These contributions highlight the potential of the proposed model for advancing the understanding and optimization of porous nanostructures in engineering applications.