Classical thermoelastic analysis within the framework of classical elasticity and Fourier’s heat conduction cannot meet the increasing demand with the rapid development of new technologies and new materials. Fourier heat conduction theory indicates the speed of thermal propagation is infinite, and any disturbance should be felt everywhere instantaneously, which is obviously unphysical as heat dispersion will indeed require a certain time to propagate in the material. The classical Fourier heat conduction is inapplicable particularly for heat conduction involving a very small characteristic length (10^-8~10^-6 m), very short time scale(10^-11~10^-15 s), or very low temperature (1-10 K), where the time lag between the heat flux and temperature rise becomes significant. Therefore, non-Fourier heat conduction models have been proposed to account for the time lag between heat dispersion and temperature change, such as the hyperbolic heat conduction theory, dual-phase-lag (DPL) model. Besides, with the wider applications of soft materials, the viscous effect should be taken into consideration in the thermoelastic analysis of the cracked media to characterize the thermal stress concentration induced fracture of the material. Moreover, in the past decades, advanced materials or devices have been downsized to micrometer/nanometer scales. In these scales, the effective thermal and mechanical properties differ significantly than bulk materials, and neither the Fourier heat conduction nor classical continuum mechanics can explain these discrepancies.

Taking the aforementioned, unclassical problems into account, the non-Fourier heat conduction, nonlocal heat conduction, and nonlocal elasticity are introduced in the thermoelastic analysis in this thesis. The main contributions are summarized as follows:​

1. A thermo-viscoelastic model is developed for the crack problem in an infinite, functionally graded half plane under a thermal shock.
2. A thermoelastic analytical model is established for a functionally graded half-plane containing a crack under a thermal shock in the framework of hyperbolic heat conduction theory.
3. By extending the fractional calculus to DPL heat conduction theory, the transient thermal-mechanical response in cracked viscoelastic materials under thermal shock is analyzed.
4. A modified nonlocal DPL theory is formulated to account for the heat conduction at the nanoscale. Both the temporally and spatially nonlocal effects are considered in heat conduction, which are verified experimentally by the size-dependent thermal conductivity of silicon nano-films and the transient temperature variation during the femtosecond laser heating of gold films. A generalized, uncoupled, nonlocal thermoviscoelastic theory is hence proposed.
5. The interface crack problem between a functionally graded coating and the homogenous substrate is analyzed within the framework of the nonlocal continuum theory. The nonlocal elasticity is extended to interface crack problems under thermal loading for the first time to eliminate the stress singularities at the crack tips and address size effects on the thermoelastic response.