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Crack Lip Contact Modeling Based on Lagrangian Multipliers with X-FEM
Jin, Yuan; Pierard, Olivier; Wyard, Eric et al.
2016In Ventura, Guilio; Benvenuti, Elena (Eds.) Advances in Discretization Methods
Peer reviewed
 

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Keywords :
X-FEM; Lagrange multipliers; Contact
Abstract :
[en] 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 singul arities. 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 di scretizing 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.
Disciplines :
Mechanical engineering
Author, co-author :
Jin, Yuan;  CENAERO
Pierard, Olivier;  CENAERO
Wyard, Eric;  CENAERO
Béchet, Eric ;  Université de Liège > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur
Language :
English
Title :
Crack Lip Contact Modeling Based on Lagrangian Multipliers with X-FEM
Publication date :
2016
Main work title :
Advances in Discretization Methods
Author, co-author :
Benvenuti, Elena
Editor :
Ventura, Guilio
Publisher :
Springer
Edition :
SEMA SIMAI Springer Series
ISBN/EAN :
978-3-319-41245-0
Collection name :
Volume 12 2016
Pages :
123-142
Peer reviewed :
Peer reviewed
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