Nonlinear time-domain FEM method to non-Fourier thermoelasticity with space-dependent thermal conductivity and impact responses of laser-heated 2D metallic plate

Transient impact thermo-mechanical responses analysis for metallic solids has become critically important to avoid the harmful and unwanted vibration responses with the extensive application of ultrafast heating technology (i.e., laser ablation, etc.) in the processing and manufacturing of metallic devices. Recently, the space-dependent thermal conductivity, which has been experimentally and theoretically verified that is a crucial factor that should be seriously treated in such extreme thermo-mechanical coupling environment, is not considered in the existing non-Fourier thermoelasticity constitutive models. And its influences on the structural dynamic responses are still not reported. To compensate for the deficiencies, the present work aims to establish the multi-field coupling nonlinear model of non-Fourier thermoelasticity with space-dependent thermal conductivity built upon the theories of Lord-Shulman, Green-Lindsay and Green-Naghdi thermoelasticity theories. To directly solve the nonlinear governing equations, the virtual work principle is developed to formulate nonlinear time-domain FEM approach. As numerical example, the proposed theoretical model and numerical method are applied to investigate transient impact thermo-mechanical responses to a two-dimensional homogeneous isotropic copper-metallic plate subjected to ultrafast laser heating. The results show that the space-dependent thermal conductivity parameters increase the thermal wave velocity and reduces the harmful maximum peak values of thermal and mechanical responses.