广义热弹模型的热力学基础与瞬态响应

The rapid development of micro/nano technology and the wide application of ultrashort pulsed laser technology have put forward an urgent need for generalized heat conduction and thermoelastic coupling theory to describe ultrafast thermal shock at micro/nano scale. Based on extended thermodynamic principle, a generalized thermoelastic coupling theory considering the dual-phase-lagging effect of heat conduction and the rate of higher order heat flux is established. Inspired by Green-Naghdi (GN) generalized heat conduction model, thermal "elastic" and "viscous" element models are proposed, which are similar to the series and parallel models of viscoelastic constitutive relations in the field of mechanics. The Cattanoe-Vernotte (CV), GN, dual-phase-lag (DPL) and Moore-Gibson-Thompson (MGT) heat conduction models were obtained by series and parallel methods. Theoretical derivation further shows that the newly formulated model corresponds to the Burgers model of heat conduction. In these models, the proportional relationship between the relaxation time of each phase lag is also obtained. Laplace transform method is used to study the transient response of one-dimensional structure under thermal shock and moving heat source. The results show that the present model overcomes the paradox of infinite thermal wave velocity. When the boundary thermal shock load is applied, the results obtained by the new model have higher peak and the smallest affected region. And under the effect of moving heat source, the new model can generate a larger peak response. The new model could coupled with the classical elastic theory and built a generalized thermoelasticity. With this theory, the jump of stress at wavefront of thermal wave and elastic wave can be clearly observed. Theoretically, this paper promotes the combination of extended thermodynamics and continuum mechanics, which is of enlightening significance to the study of fundamental theoretical problems far from equilibrium of extreme mechanics. For applications, this work can provide theoretical basis and numerical method for the transient response analysis under the moving heat sources.