The Virtual Element Method for dynamic crack analysis

Abstract

The Virtual Element Method (VEM) constitutes a generalization of the standard Finite Element Method (FEM), allowing for substantially more flexibility in the mesh design. This feature makes the method particularly suitable for problems with evolving discontinuities and singularities, and thus for crack problems. Dynamic crack analyses oftentimes incorporate impact loads, requiring sophisticated procedures of time integration, which are known from the FEM. Furthermore, the crack tip loading quantities are highly dependent on structural damping, while algorithmic damping is inevitable for numerical stability. Established approaches to quantify crack tip loading are basically applicable within the VEM framework, however, have to be adapted to characteristics like the absence of shape functions within elements. The Displacement Interpretation Method (DIM), the Modified Crack Closure Integral and the J-integral are elaborated in this context, restricting analyses to linear elastic fracture mechanics and stationary cracks. The accuracy of the approaches is verified comparing results of analytical and other numerical calculations. Numerical studies reveal the impact of physical parameters associated with structural damping and load rate, as well as of numerical factors such as approximation order, contour of the J-integral, extrapolation domain of the DIM and algorithmic damping. After all, the VEM appears to be a highly suitable numerical approach for dynamic fracture mechanics with a view to future crack growth simulations.