A thermal-mechanical coupling modeling with imperfect interfaces: Transition from ballistic to diffusive heat transfer

This paper proposes a generalized thermo-mechanical coupling model to analyze stress distribution in multilayer composites driven by cross-scale heat transfer. The Cattaneo-Fourier (C-F) heat flux model and its associated thermoelastic constitutive framework are revisited within the Green-Lindsay formalism, incorporating transition scales from ballistic to diffusive heat transfer. The resulting thermoelastic formulation predicts thermal stress evolution in layers of varying thicknesses, while the Kapitza thermal interface is modeled as a time-independent algebraic constraint on adjacent interfacial stress. Consequently, the proposed generalized model forms a differential-algebraic system, solved numerically via a fully implicit time integration scheme. Numerical simulations demonstrate the model's accuracy in capturing coupled temperature-mechanical field effects during cross-scale heat transfer, including purely ballistic, ballistic-diffusive, and purely diffusive regimes, as well as perfect and imperfect thermal interfaces. Additionally, a case study of a cracked plate investigates thermoelastic responses under coexisting cracks and imperfect interfaces, revealing temperature-stress evolution dynamics. This computational framework advances theoretical analysis of cross-scale thermo-mechanical coupling in composites, highlighting the critical roles of interfacial effects and heat transfer mechanisms in material behavior.