201 Modelling Cracks: Recent Advances and Applications

Qinglin Duan, Dalian University of Technology
Rong Tian, CAEP Software Center for High Performance Numerical Simulation
Haim Waisman, Columbia University
Timon Rabczuk, Bauhaus University Weimar
Crack is one of the primary causes of many catastrophic failures of structures. Numerical modelling of cracks has received significant attention in the community of computational mechanics because it plays an important role in understanding how materials fail as well as in improving the ability to prevent such failures. However, implementation of such modelling is quite difficult due to the presence of strong discontinuity and singularity in crack problems. For multiple cracks, crack interaction and coalescence add even more complexities.
Many efforts have been devoted to developing various models, computational methods and numerical techniques for cracks. For example, the eXtended Finite Element Method (XFEM) currently still under intensive studies is one of the major computational methods for cracks modeled by the traditional fracture mechanics. In recent years, new models for cracks such as the phase-field model and the peridynamic model emerge and attract significant attention.

The purpose of this mini-symposium is to report the new developments of strategies to model cracks numerically. Both the computational methods for cracks such as the XFEM, GFEM, meshfree methods, boundary element methods, etc., and the mathematical models for cracks such as the phase-field model, the peridynamic model, etc., are welcome. In addition, application of these strategies to solve crack problems in engineering is also welcome. In particular, the topics covered include (but not limited to):

- Approximation of the singular fields of crack tip in XFEM, GFEM, meshfree methods, etc;
- Peridynamics for fracture;
- Phase-field models of cracks;
- Dynamic crack propagation, especially the related issues of energy consistency;
- Problems with multiple cracks such as fragmentation, especially the techniques to handle crack interaction and coalescence;
- Geometric description of 3D cracks;
- Adaptive methods for crack propagation;
- Multiscale methods for cracks;
- Fracture criteria for crack initiation and propagation;
- Large scale simulation of cracks using parallel computing;
- Application of numerical modelling to analyze cracks in engineering.