Nonlinear time-domain finite element analysis to transient thermoelastic diffusion responses of 2D metallic structure with high-order temperature-dependent material properties

The structural transient thermoelastic-diffusive (TED) impact responses are crucial for understanding multi-field coupling interactions, which help mitigate unwanted dynamic responses in advanced vibration control systems, especially with the widespread use of ultrafast heating techniques in the fabrication and precision machining of metallic components. However, in such conditions, the effects of higher-order temperature-dependent material properties on dynamic TED responses have not been fully explored, and the underlying mechanisms remain unclear. To address this gap, the present study establishes a new Cattaneo-type TED model with high-order nonlinear temperature dependency for metallic material properties. A novel approach combining the principle of virtual work with a nonlinear finite element strategy is developed to directly solve the governing nonlinear finite element equations, significantly reducing the computational precision losses compared to existing transformation-based methods. The proposed model and numerical approach are applied to investigate the transient impact responses of a 2D isotropic homogeneous rectangular metallic plate subjected to zonal, time-dependent temperature and chemical potential shock loading. The results show that an increase in the temperature-dependent higher-order terms in the material properties of metal parts can effectively capture the accelerated propagation of heat and diffusion waves and minimize the structural stresses and deformations induced during temperature changes.