A High-Order Virtual Element Method for the Analysis of Dynamic Crack Growth
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The continuous development of computational discretization methods represents a significant research-related driving force in the field of numerical fracture mechanics. Modern polygonal and polytopal methods are especially interesting from a fracture mechanics point of view, since they effectively incorporate cracks in existing mesh topologies. The Virtual Elements Method (VEM), introduced by Beirão Da Veiga et. al in 2013, is a stabilized Bubnov-Galerkin method, which stands out in this class with its extraordinary versatility in element design, and poses considerably lower requirements on meshes than comparable discretization methods. The advantages in terms of meshing result from an implicit definition of the functional space used, and have been successfully exploited by, e.g., Wriggers et al., Choi et al. or Chen et al. for modeling quasi-static fracture. Dynamic fracture mechanics comes with new challenges, including the need to numerically solve and model time-dependent processes, which must be countered using suitable time integration methods and high approximation orders. Modeling cracks within the classical context of strong discontinuities, dynamic crack tip loading, crack deflection and crack growth velocity are issues that need to be addressed. Beyond that, exploiting the VEM-specific advantages for analyzing dynamic crack growth in combination with the FEM appears to be extremely valuable and computationally efficient in an elastodynamic setting. This paper demonstrates a high-order 2D VEM for application in the field of dynamic fracture mechanics and crack growth simulations. For this purpose, crack tip loading analyses in time and frequency domains, based on techniques such as the crack closure or the dynamic J-integral, are presented. Furthermore, our latest research in the context of dynamic crack growth simulations, exploiting VEM-specific advantages, will be presented, and established FEM-based approaches will be compared and critically discussed.
