Competition between thermal and elastic waves in microscale solids: A generalized Guyer–Krumhansl thermoelastic formulation

Thermoelastic coupling at micro- and nanoscales is strongly influenced by non-Fourier heat transport, where heat-flux relaxation and spatial nonlocality can modify both thermal-wave propagation and the associated mechanical response. In this work, a thermodynamically consistent generalized Guyer–Krumhansl (GK) thermoelastic formulation is developed for microscale solids by incorporating the GK heat-flux law into linear thermoelasticity. Starting from the energy balance and the second law of thermodynamics, the coupled constitutive relations and governing equations are systematically derived, with the heat flux treated as an independent non-equilibrium variable. The resulting model accounts for heat-flux relaxation through a thermal relaxation time and nonlocal heat-flux transport through a characteristic length. The formulation is applied to a one-dimensional thermoelastic boundary-value problem subjected to a short heat pulse. We analyze the transient evolution of temperature, heat flux, strain, and stress fields to clarify the interaction between finite-speed thermal waves and thermally induced longitudinal elastic waves. The results show that localized thermal excitation generate elastic waves through constrained thermal expansion, while the strain-rate field associated with elastic-wave motion feeds back into the temperature response through thermoelastic coupling. This bidirectional interaction gives rise to a double-peak temperature response, whose formation and evolution are governed by the relative propagation characteristics of the thermal wave and the thermally induced elastic wave, together with the strength of thermoelastic coupling. Parametric studies further show that the heat-flux relaxation time mainly controls the thermal-wave propagation, whereas the GK characteristic length governs the degree of spatial nonlocality, broadens the localized thermal response, and suppresses the primary and secondary peaks. The thermal expansion coefficient further regulates the strength of the elastic-wave-induced thermal modulation and thus the prominence of the secondary peak. The pronounced double-peak response is therefore identified as a conditional coupled thermoelastic phenomenon requiring suitable non-Fourier transport characteristics and sufficiently strong thermoelastic coupling. The developed formulation provides a physically grounded basis for interpreting the competition between thermal and elastic waves in microscale solids.