Speaker
Description
Cracks in elastic materials represent an extreme form of notches which, due to high local stress concentrations at their tips, tend to grow even under moderate external loads. This growth can compromise the integrity of technical or natural structures and potentially leads to failure. Highly dynamic loads, such as impacts, further exacerbate this process and may result in catastrophic failure.
For decades, numerical methods have been applied for stress analysis of cracks, making significant contributions to the safety of structures, the prediction of lifetimes, and the enhancement of durability to ensure safe operation. In addition to the Finite Element Method (FEM), which has established as a standard tool for analysing cracks, the Boundary Element Method (BEM) has been extensively studied for applications in fracture mechanics. Particle-based approaches and damage-mechanics models, such as those utilizing phase-field methods, provide qualitative insights but are not suitable for quantitative investigations or validation in safety-critical applications. The Virtual Element Method (VEM) is a generalization of the FEM that employs accurate approximations of virtual shape functions by using suitable projection operators. As a result, VEM allows for discretizations with elements of arbitrary shape, which may even be non-convex and include crack tips. For crack analysis, VEM offers significant advantages due to its high flexibility in element design, enabling accurate calculations of loading quantities and efficient predictions of crack paths.
This presentation focuses on the dynamic analysis of stationary cracks using VEM. Key developments include integrating inertia into VEM, implementing advanced time integration schemes and performing dynamic crack loading analyses as a preparatory step towards simulating dynamic crack propagation. Results are validated against analytical solutions and benchmarks from the literature.
