The Virtual Element Method for Efficient Crack Growth Simulations Based on Configurational Forces
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The virtual element method (VEM) [1] is an efficient discretization scheme for the numerical solution of boundary value problems on polytopal grids, which is most prominently known for offering considerable flexibility in the discretization 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 in the geometry of a crack do not require any remeshing of the structure, but rather crack paths can run through already existing elements, enabling the realization of very efficient simulations in terms of computational cost. Although the method provides a valuable tool for modelling crack propagation, there is still further research required regarding the implementation of efficient and precise methods to evaluate crack tip loading quantities and crack deflection criteria. Therefore, the concept of configurational forces in material space is employed, which already proved to be very efficient for the calculation of these quantities in the context of the FEM. However, the calculations yield certain numerical difficulties that need to be dealt with, e.g., due to discontinuous stresses and strains at element edges in the vicinity of the crack tip, and require additional effort in connection with curved crack faces [2]. This work aims to discuss theoretical and computational aspects of employing configurational forces for mixed-mode crack growth simulations in the VEM. A framework 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. Furthermore, crack growth simulations are presented, and results are compared to reference solutions as well as solutions obtained with the FEM. REFERENCES [1] L. Beirão da Veiga et. al. Basic principles of virtual element methods. Mathematical Models and Methods in Applied Sciences, 23(01):199–214, 2013. [2] K. Schmitz and A. Ricoeur. Theoretical and computational aspects of configurational forces in three-dimensional crack problems. Int. J. Solids Struct., 282: 112456, 2023.