Wave propagation in a photo-thermomechanical medium with triple porosity and voids under the Lord–Shulman theory

This paper presents a comprehensive analytical framework for wave propagation in a generalized photo-thermoelastic medium possessing both triple porosity (macro, micro, nano) and voids (empty pores) under the Lord-Shulman (L-S) theory with one thermal relaxation time, further incorporating the photo-thermal (carrier density) effect. The model extends classical poroelasticity, void elasticity, and plasma theories by coupling solid deformation, temperature field, three distinct pore pressures, void volume fraction, and photo-excited carrier density. A homogeneous, isotropic half-space subjected to thermo-mechanical and photo-excitation loading is considered. The coupled system of equations is solved analytically using normal mode analysis, yielding exact expressions for displacements, stresses, temperature, pore pressures, void distribution, and carrier density. Numerical simulations for porous silicon reveal that the carrier density introduces a new slow diffusion wave mode (plasma wave), significantly alters stress concentration patterns, and enhances energy dissipation compared to triple porosity and voids alone. The thermal relaxation time and carrier lifetime critically modulate wave attenuation, thermal diffusion, and plasma transport. The results provide a rigorous foundation for applications in porous semiconductors, optoelectronics, and photothermal therapy.