Crack Lip Contact Modeling Based on Lagrangian Multipliers with X-FEM
The eXtended Finite Element Method (X-FEM), developed intensively in the past 15 years has become a competitive tool for the solution of problems with evolving discontinuities and singularities. In the present study, we focus on the application of X-FEM on frictionless contact problems in the context of fracture mechanics. A promising approach in the literature counting for this problem consists in applying Lagrangian multipliers. Meanwhile, as pointed out in Ji and Dolbow (Int J Numer Methods Eng 61:2508–2535, 2004), a naive choice for Lagrangian multiplier space leads to oscillatory multipliers on the contact surface. This oscillation results from a non-uniform but mesh-dependent inf-sup condition. In this work, we adapt the algorithm proposed in Béchet et al. (Int J Numer Methods Eng 78:931–954, 2009) on crack lip contact by discretizing the displacement field with both scalar and vector tip enrichment functions (Chevaugeon et al., Int J Multiscale Comput Eng 11:597–631, 2013). The influence of the tip enrichment functions on the stability of the formulation is addressed. We show evidences that the vector enrichment functions can improve the conditioning of the problem without jeopardizing the simulation accuracy in the presence of contact.
This work is funded by an SBO Project grant 110070: eSHM with AM of the Agency for Innovation by Science and Technology (IWT). The authors would like to thank C. Friebel and N. Poletz for the insightful discussion about the implementation of the numerical framework.
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