Meshfree Multiscale Methods

Prediction of material failure and fracture behavior

The prediction of material failure and fracture behavior of large components plays a crucial role in many industrial sectors. An example is the lifetime prediction of dams, of railway tires, or of aircrafts.

In the new business area "Meshfree Multiscale Methods" therefore new efficient multi-scale methods are developed. These include meshfree methods such as particle-based multiscale methods and the generalization of finite element methods.

These modern methods are suitable for solving problems in which large changes of geometry and changes of topology occur – for example, large deformations or free surfaces. Since no consistent global mesh generation is necessary in these cases, these methods are superior in comparison with classic mesh-based methods.

One focus of our work is on the development of the partition of unity method – a meshfree generalization of the finite element method. It supports the direct use of problem-dependent enrichment functions. These application-specific basis functions may be given analytically or only as numerical or experimental data. Overall, this approach provides a much better approximation with fewer degrees of freedom.