ECCOMAS 2024

The Efficient Simulation of Fracture with an Extended Phase-Field Method

  • Curoșu, Verena (TUD Dresden University of Technology)
  • Krüger, Christian (TUD Dresden University of Technology)
  • Loehnert, Stefan (TUD Dresden University of Technology)

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Recently, an enriched/extended phase-field approach to fracture (XPFM) has been proposed, which combines the advantages of the XFEM/GFEM and those of the classical phase-field method. In this presentation, the latest developments of the method are presented, with a particular focus on an improved displacement field enrichment. The phase-field is reproduced by a transformed ansatz which resembles the analytical solution for a 1D phase-field problem. The phase-field profile can be reproduced independently of the element orientation which is a prerequisite for the accurate and mesh-independent representation of the crack also within a coarse mesh. Furthermore, the displacement ansatz function is extended by a term holding information about the nature of the high gradients across the crack to be expected within the displacement field. Here, modified shape functions are utilised. They are calculated for each enriched element on a subgrid by considering the local stiffness reduction due to the phase-field. Since these shape functions are directly coupled to the phase-field ansatz, no additional discretisation of the crack geometry is required. Both, the transformation of the phase-field and the enrichment of the displacement field allow for a significant reduction of degrees of freedom in comparison to the classical phase-field method where very fine meshes are required. This potentially leads to a significant reduction in computational effort. The effectiveness and efficiency of the new method compared to the classical phase-field approach are shown by its application to common academic examples.