A Time-Domain Boundary Element Method for Size-Dependent Micropolar Porous Thermoelasticity with Non-Fourier Heat Conduction

A fully coupled convolution-quadrature time-domain boundary element method (BEM) formulation is presented for the transient analysis of size-dependent porous micropolar solids under rapid thermal loading. The formulation unifies the theories of modified couple stress micropolar elasticity, Cowin-Nunziato porosity theory, and non-Fourier heat conduction with the refined Lord-Shulman model. This allows for the simultaneous consideration of size effects, porosity effects, and finite-speed heat conduction phenomena. The governing multi-field equations are transformed into boundary integral form and solved using quadratic boundary elements combined with convolution quadrature, retaining the boundary-oriented computational structure of the Boundary Element Method while efficiently treating the additional domain integrals arising from thermo–poro–micropolar coupling terms. The proposed framework captures strong thermo-mechanical coupling and dispersive wave phenomena that are inaccessible to classical Fourier-based and size-independent models. Validation against benchmark solutions demonstrates excellent numerical robustness and convergence. Parametric studies indicate that intrinsic length-scale effects enhance the displacement and microrotation responses, the thermal relaxation effects delay the penetration of the thermal field, and the porosity coupling effects dominate the internal damping. These studies demonstrate the importance of the microstructure effects and the non-Fourier effects in the transient thermoelastic response. The proposed BEM formulation provides an efficient computational tool for the analysis of advanced microstructured materials and porous composites in thermal shock situations.