A stable 3D contact formulation using X-FEM

By S. Géniaut, Patrick Massin, Nicolas Moës. 2007

57 citations recorded by the source corpus.

This paper presents a 3D non-locking contact approach, within the eXtended Finite Element Method (X-FEM) framework. X-FEM allows one to introduce interface independently of the mesh. The contact problem on the interface leads to an Augmented Lagrangian formulation derived from the discretization of its continuous formulation. It is shown that a simple choice of the Lagrange multiplier space is not suitable and leads to contact pressure oscillations. An algorithm for the restriction of the Lagrange multiplier approximation space is proposed to stabilize the formulation. The stability of the mixed displacement-contact pressure formulation is discussed in terms of convergence of the energy error. Numerical examples performed with the Finite Element software Code_Aster illustrate this approach while solving three-dimensional problems with contact.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ae71f2dbdce6fa698dda7ed733fa1cdc41be3b33

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method (2009, methodology): “A second algorithm was then proposed in (Géniaut, Massin, and Moës 2007), and it is currently extended for large sliding (Nistor, Guiton, Massin, Moës, and Géniaut 2008).”
A contact algorithm for frictional crack propagation with the extended finite element method (2008, methodology): “To address this concern, we also consider an augmented Lagrangian technique [43–45] and monitor”
Level set topology optimization of structural problems with interface cohesion (2017, methodology): “A Lagrange multiplier formulation has been used in a few approaches [41, 42].”
On methods for stabilizing constraints over enriched interfaces in elasticity (2009, background): “This approach has since been extended to contact conditions [6].”
An extended stochastic finite element method for solving stochastic partial differential equations on random domains (2008, methodology): “For example, the methodology proposed in [42,43] can be used.”