Robust implementation of contact under friction and large sliding with the eXtended finite element method

An X-FEM formulation is proposed for the case of large sliding frictional interfaces. A continuous augmented lagrangian framework is adopted for contact and friction. We provide an algorithm for the selection of an appropriate discrete space for the lagrange multipliers, accounting for the transition between contact and free zones, and also between sliding and adherent zones. A 3D numerical test is realized with Code_Aster free software for the compression of a cylinder cut along a radial section and shows the ability of the model to capture such transitions.

[1]  Ronaldo I. Borja,et al.  A contact algorithm for frictional crack propagation with the extended finite element method , 2008 .

[2]  I. Babuska.  The finite element method with Lagrangian multipliers , 1973 .

[3]  Jean E. Roberts,et al.  Mixed and hybrid finite element methods , 1987 .

[4]  Samuel Geniaut,et al.  A stable 3D contact formulation using X-FEM , 2007 .

[5]  Georges Dumont,et al.  Algorithme de contraintes actives et contact unilatéral sans frottement , 1995 .

[6]  Nicolas Moës,et al.  A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method , 2009 .

[7]  Nicolas Moës,et al.  Imposing Dirichlet boundary conditions in the extended finite element method , 2006 .

[8]  Samuel Geniaut,et al.  A stable 3D contact formulation for cracks using X-FEM , 2006 .

[9]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[10]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[11]  K. Bathe,et al.  The inf-sup test , 1993 .

[12]  Ted Belytschko,et al.  An extended finite element method for modeling crack growth with frictional contact , 2001 .

[13]  Nicolas Moës,et al.  Fissuration avec X-Fem et contact , 2005 .

[14]  Isaac Harari,et al.  A bubble‐stabilized finite element method for Dirichlet constraints on embedded interfaces , 2007 .

[15]  Samuel Geniaut,et al.  An X‐FEM approach for large sliding contact along discontinuities , 2009 .

[16]  Malek Zarroug,et al.  Hybrid frictional contact particles-in elements , 2002 .

[17]  A. Khoei,et al.  Contact friction modeling with the extended finite element method (X-FEM) , 2006 .