Simulation of mixed-mode crack propagation in Mindlin plates by a hierarchical quadrature element method with minimal remeshing

In this work, a framework for efficient and automatic crack propagation simulation in Mindlin plates is established, utilizing the hierarchical quadrature element method (HQEM) characterized by p-convergence. The HQEM is combined with the virtual crack closure method to extract mixed-mode moment and shear force intensity factors of cracked Mindlin plates. These fracture parameters are employed to predict the crack propagation direction according to the maximum circumferential tensile stress criterion. A notable advantage of HQEM over conventional h-version FEM is its capacity to achieve highly accurate fracture parameters with a rather coarse mesh. To take advantage of the simplicity of HQEM in pre-processing, a minimal remeshing strategy utilizing NURBS fitting for crack paths is developed. This strategy maintains a minimal or even constant number of elements throughout the crack propagation process, significantly reducing the workload associated with mesh regeneration while preserving the accuracy of fracture parameters and crack propagation paths. The practicality and accuracy of the proposed method are verified through several numerical examples involving a variety of crack configurations, including both infinite and finite geometries, as well as pure mode and mixed mode scenarios. The results for fracture parameters and crack propagation paths align closely with those reported in the literature. This consistency strongly indicates that the proposed method is a promising numerical tool for efficient and reliable crack propagation analysis.