Multiscale Methods for Fracturing Solids

In this project, multiscale methods and homogenization techniques for the numerical simulation of three dimensional fracture processes are developed. These methods are important in aerospace and automotive industries and many other fields of mechanical and civil engineering as well as in bio-mechanics and material science.

Specifically, the interaction of macro- and micro cracks in brittle materials is considered. To this end, a multiscale method based on the inherent separation of scales is developed in terms of the three-dimensional eXtended Finite Element Methof (XFEM). In order to achieve highly accurate results in the vicinity of the crack fronts, which is essential for the development of a reliable crack propagation criterion, special measures are taken to improve the standard XFEM. Also, the standard XFEM does not prevent crack face penetration. A remedy to this problem is to incorporate a contact formulation into the XFEM.

Another field of research is to adequately model complex inhomogeneous structures like silicone filled aluminum foams. Again, the XFEM is a suitable tool for this class of applications. In order to model the materials, a metal plasticity, as well as a Neo-Hooke material model, are incorporated into the XFEM for material interfaces.

As within the XFEM, cracks and interfaces are generally modeled with the help of level set functions, a large variety of mesh generators, which are capable to generate appropriate level set fields, are developed.