ECCOMAS 2024

Mixed finite elements for crack propagation

  • Runcie, Callum (University of Glasgow)
  • Shvarts, Andrei (University of Glasgow)
  • Kaczmarczyk, Lukasz (University of Glasgow)
  • Pearce, Chris (University of Glasgow)

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Following recent developments in open-source finite element software, MoFEM [1], a computational framework to model crack propagation along contact interfaces was presented [2]. This implicit computational framework is based on configurational mechanics and utilises a monolithic arbitrary Lagrangian-Eulerian (ALE) formulation to resolve the crack propagation and mortar contact constraints simultaneously through the finite element method. This methodology was developed with close collaboration with industrial partners, that required robust and accurate prediction of fracture in irradiated graphite bricks under various contact and loading conditions. However, this approach lacks robustness with the resolution of the crack surface. In the current work, the recent developments to consider a mixed finite element approach to crack propagation will be presented. In the novel approach, the displacement field is approximated in L2 space while the stress field will be approximated in the H(div) (Raviart-Thomas) space with weakly enforced symmetry [3]. Furthermore, in this approximation, the continuity of displacement is weakly enforced a posteriori. As a result, introducing a displacement discontinuity, such as fracture, is straightforward to consider by eliminating stress field degrees of freedom on the faces where crack is extended. Moreover, utilising mixed finite elements provides accurate methods for estimation of crack release energy which is used as a crack propagation criterion. A wide range of benchmark numerical examples will be considered to verify and validate the results of this novel approach.