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Abstract Stress intensity factor is a crucial parameter for modeling and predicting structural fracture failure. The evaluation of the dynamic stress intensity factor for three-dimensional dynamic fracture problem is studied by the adaptive phantom node method. This method combines the phantom node method with adaptive mesh refinement, automating the generation of dense mesh around the crack. In this approach, strong discontinuities at cracks are modeled using the technique of phantom nodes without the crack tip enrichment functions or the corresponding extra degrees of freedom. The theoretical framework of this technique is straightforward and easy to implement based on the finite element method, but it requires a relatively dense mesh to ensure computational accuracy. Adaptive mesh refinement technology and criterion suitable for crack problems are introduced into the phantom node method, thus the globally dense mesh with high computational consumption is not needed and the computational accuracy and efficiency are improved. A concise approach, known as constrained approximation, is adopted to deal with hanging nodes presented in the locally refined mesh. It is convenient to implement numerically, does not involve special elements or complex shape functions and retains the interpolation and numerical integration of the standard finite element method. The stress intensity factors for several three-dimensional crack problems are evaluated using the adaptive phantom node method and compared with the theoretical solutions and numerical results obtained by the standard phantom node method. It is found that the numerical results of this method are in good agreement with the theoretical solutions, and the computational accuracy is effectively improved compared to the standard phantom node method. Additionally, compared to locally pre-refined mesh with equivalent accuracy, adaptive refined mesh exhibits higher computational efficiency and reduced computational consumption. This holds considerable potential value for the efficient simulation and prediction of dynamic fracture failure in large-scale complex engineering structures.
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Received: 28 November 2023
Published: 02 July 2024
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2024, Vol. 45 
