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Description
The virtual element method (VEM) is a modern discretization scheme for the numerical solution of boundary value problems on polytopal grids. It has proven to be an efficient alternative to the Finite Element Method (FEM) in recent years and is most prominently known for offering considerable flexibility in the meshing process. In the context of numerical applications of fracture mechanics, one of its most attractive features results from the possibility to employ elements of complex shape with an arbitrary number of nodes, which may be convex as well as non-convex and may even contain crack tips. Consequently, crack growth simulations with the VEM benefit from the fact that incremental changes of the geometry of a crack do not necessitate remeshing, but rather crack paths can traverse through the existing elements, enabling the realization of simulations with significantly reduced computational cost. While classical methods for crack analysis have already been successfully applied within the VEM framework, further research is still required regarding the implementation of efficient and precise methods to evaluate crack tip loading and crack deflection. Therefore, the concept of configurational forces in material space is employed, which already proved to be highly effective for the calculation of these quantities in the context of the FEM. However, the calculations yield certain challenges that need to be dealt with, e.g., due to discontinuous stresses and strains across element edges in the vicinity of the crack tip, and require additional effort in connection with curved crack faces. This work discusses the theoretical and computational aspects of employing configurational forces for mixed-mode crack analysis within the VEM. A methodology for calculating nodal configurational forces is presented and comparative studies are conducted, carefully investigating challenges and opportunities emerging from the discretization method for assessing crack tip loading and crack path prediction, with results benchmarked against analytical and FEM-based solutions.
