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Dynamic crack propagation using the XFEM

Dynamic crack propagation using the XFEM

Led by:  P. Wriggers, S. Löhnert
Team:  D. Nolte
Year:  2012
Is Finished:  yes

The objective of the project is to extend the application range of the eXtended Finite Element Method (XFEM) to three-dimensional dynamic crack propagation for heterogeneous materials. These heterogeneous structures can be observed in most materials at certain scales. Imperfections in those materials often lead to crack nucleation and propagation. Crack nucleation can be described by means of an elastoplastic material model including non-local damage.

For the simulation of cracks the XFEM has proven to be adequate to handle cracks in a precise geometrical and numerical framework. This method allows the calculation of the displacement field including discontinuities without remeshing the domain for crack propagation processes. The crack propagates if a local material instability occurs. The propagation speed for ceramic materials could be near the Rayleigh wave speed and can be different within the material.

Cracks are specified with Level-Set-Functions. The problem domain is separated in a continuous part, describing the total domain, and a discontinuous part at the crack. Nodes of elements completely cut by a crack are enriched with the Heaviside-Function. The displacements at the domain of the crack front, the so called process-zone, are augmented with the crack-tip-enrichments describing the characteristics of the crack front. Because of the additional local enrichments at the crack the transition to the non-enriched nodes does not fulfill the partition of unity concept. A special function, the so called ramp-function is used to satisfy this condition. For the simulation of dynamic crack propagation with the XFEM the displacement, velocity and acceleration field need to be mapped from the old crack configuration to the new one.

Numerical challenges are the incorporation of the inelastic material behavior during crack propagation as well as the accurate prediction of 3D fracture processes in heterogeneous materials.

This project is part of the International Research and Training Group, “IRTG 1627: Virtual Materials and Structures and their Validation” of the DFG (deutsche Forschungsgesellschaft). It is incorporated in the Graduate School MUSIC in collaboration with the Ecole Normale Superieure de Cachan, France.