Generalized thermoelastic medium with diffusion and initial stress with double porosity structure under 3PHL model

Purpose The purpose of this study is to investigate the combined effect of initial stress, diffusion and double porosity on thermomechanical behavior, which was overlooked in previous studies that looked at these elements independently. Understanding how initial stress, diffusion and double porosity interact in thermoelastic media is critical for accurately simulating real-world porous structures like geological formations and smart materials. Most existing studies consider these effects separately, limiting realistic predictions. This work fills that gap by providing a coherent framework with practical applications in geophysics, petroleum engineering and material design. Therefore, this work analyzes the effect of initial stress on a two-dimensional thermoelastic medium with a double-porosity structure in the presence of diffusion based on the generalized thermoelasticity and the three-phase-lag (3PHL) heat conduction model. Design/methodology/approach Analytical solutions were derived with the normal mode method, supported by numerical results under specific boundary conditions. The model captures the interaction between stress, thermal and diffusive processes in a unified way. Findings Results show that changes in relaxation times and initial stress significantly influence the dynamic response of the medium. The study highlights clear coupling between thermal, mechanical and diffusion effects. Research limitations/implications The analysis is limited to a two-dimensional, homogeneous, linear model without experimental validation. Future research should extend it to nonlinear, heterogeneous and three-dimensional systems. Originality/value To the best of authors’ knowledge, this is the first work to integrate initial stress, double porosity and diffusion within a single thermoelastic framework using the 3PHL model. It provides new insights with applications in geophysics, petroleum engineering, rock mechanics and smart material design.