A nonlinear non-Fourier thermoelasticity model with high-order temperature-dependent material properties and time-domain finite element method to impact responses of 2D metallic solids under ultra-short pulsed laser heating

The thermo-mechanical transient impact responses analysis of metallic structures within active vibration control systems is essential for preventing adverse vibration effects, especially with the increasing application of ultrafast heating technologies such as laser ablation in metal processing and fabrication. Under such extreme thermo-mechanical coupling conditions, the high-order temperature-dependent characteristics of materials are the crucial factors. However, these effects have not yet been incorporated into current non-Fourier thermoelastic constitutive formulations, and the impact on structural dynamic behavior remains unexplored. Present work introduces the high-order temperature-dependent material properties and establishes a unified nonlinear non-Fourier thermoelasticity model based on the L-S (Lord-Shulman), G-L (Green-Lindsay), and G-N (Green-Naghdi) models. The virtual work principle is applied for formulating nonlinear time-domain Finite element method to solve the nonlinear governing equations directly. The proposed theoretical model and numerical method are applied to investigate the transient impact thermo-mechanical responses of the 2D homogeneous isotropic cylindrical copper plate subjected to ultrafast laser heating. The dimensionless numerical results reveal that the high-order temperature-dependent thermal modulus enhances the stress and displacement responses. The high-order temperature-dependent specific heat, thermal conductivity and elastic modulus reduce the temperature, stress and displacement responses.