A semi-analytical method for thermo-elastic analysis of dual-phase-lag conduction models in coated materials

Modification of the classical heat conduction theory makes the new heat conduction theory and its thermo-elastic problems become the research focus. In this paper, the thermo-elastic response of a half space three-dimensional coating-substrate structure with a dual-phase-lag (DPL) heat conduction theory is studied. First, the frequency response function (FRFs) which is the analytical solution of the thermo-elastic issue is derived by using Fourier transform (FT) and Laplace transform (LT). Then the inverse Laplace transform (IFT) and discrete-convolution fast Fourier transform (DC-FFT) are employed to solve the temperature fields and stress fields. Finally, the effects of phase lag parameters on thermo-elastic are investigated. The results show that compared with the data obtains by the finite element method, the results get from the semi-analytic method in this paper have a high consistency. In addition, the phase lag parameters have an effect on the thermo-elastic response results. With the increase of phase lag of heat flux, the maximum temperature and maximum stress will decrease, while the increase of phase lag of temperature gradient will lead to the hysteresis of temperature field and the increase of maximum stress in the heating stage. This semi-analytical method provides a novel way to address three-dimensional thermo-elastic problems of dual-phase-lag conduction.