A Newmark Integral Method in Nonhomogeneous Materials With Parallel Cracks Based on Hyperbolic Heat Conduction

Yanyan Zhang, Tao Zheng, Liangzhong Ao, Shanqiao Huang and Zengtao Chen

Advances in Mathematical Physics, 2025, vol. 2025, 1-16

Abstract: The strong, transient working conditions where heat transfer involves extremely large temperature gradients, extremely large heat fluxes, and extremely short time durations of thermal disturbances may occur in engineering materials and structures. Fourier heat conduction assumes heat propagation at an infinite speed, which is not suitable for strong, transient thermal working conditions. In this paper, a Newmark integral method is presented to deal with the strong, transient heat conduction in nonhomogeneous materials based on the hyperbolic heat conduction theory. The second-order differential equation of the strong transient temperature field is discretized in the spatial and temporal domains through the finite element method (FEM) and the Newmark integral method, respectively. This allows them to be solved directly without the necessity to convert them into a pair of first-order differential equations using the Newmark integral method. Several test examples are presented to demonstrate the application of the current method. Firstly, the stability of the Newmark integral method is analyzed to ensure that the numerical oscillation is suppressed in the calculation. Then the time-related temperature field of functionally graded material (FGM) plate under strong transient thermal shock is analyzed. Finally, the thermal stress intensity factors (TSIFs) in an FGM plate with parallel cracks are extracted after combining with interaction energy integral methods (IEIMs). The results confirm that the Newmark integral method can efficiently address the transient thermal problem and ensure stability. The temperature overshooting phenomenon and thermal wave singularity are visualized at the finite speed of heat propagation. Moreover, the numerical results agree well with analytical solutions. The current method can be well applied to the design and evaluation of thermal protective materials in extreme thermal environments.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:3089008

DOI: 10.1155/admp/3089008

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