An enriched finite element algorithm for numerical computation of contact friction problems

In this paper, the extended finite element method (XFEM) is employed to model the presence of discontinuities caused by frictional contact. The method is used in modeling strong discontinuity within a standard finite element framework. In extended finite element method (XFEM) technique, the special functions are included in standard FEM to simulate discontinuity without considering the boundary conditions in meshing the domain. In this study, the classical finite element approximation is enriched by applying additional terms to simulate the frictional behavior of contact between two bodies. These terms, which are included for enrichment of nodal displacements, depend on the contact condition between two surfaces. The partition of unity method is applied to discretize the contact area with triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, numerical examples are presented to demonstrate the applicability of the XFEM in modeling of frictional contact behavior.

[1]  A. Khoei Computational Plasticity in Powder Forming Processes , 2005 .

[2]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[3]  J. C. Simo,et al.  A perturbed Lagrangian formulation for the finite element solution of contact problems , 1985 .

[4]  D. Chopp,et al.  Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method , 2003 .

[5]  P.M.S.T. de Castro,et al.  Interface element including point‐to‐surface constraints for three‐dimensional problems with damage propagation , 2000 .

[6]  T. Belytschko,et al.  Arbitrary branched and intersecting cracks with the eXtended Finite Element Method , 2000 .

[7]  Roland W. Lewis,et al.  Adaptive finite element remeshing in a large deformation analysis of metal powder forming , 1999 .

[8]  D. Chopp,et al.  Extended finite element method and fast marching method for three-dimensional fatigue crack propagation , 2003 .

[9]  Peter Wriggers,et al.  A note on tangent stiffness for fully nonlinear contact problems , 1985 .

[10]  R. Taylor,et al.  A mixed formulation for the finite element solution of contact problems , 1992 .

[11]  Ted Belytschko,et al.  Discontinuous enrichment in finite elements with a partition of unity method , 2000 .

[12]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[13]  H. Parisch A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis , 1989 .

[14]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[15]  A. Curnier,et al.  A finite element method for a class of contact-impact problems , 1976 .

[16]  A. Curnier A Theory of Friction , 1984 .

[17]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[18]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[19]  O. C. Zienkiewicz,et al.  A note on numerical computation of elastic contact problems , 1975 .

[20]  Anil Chaudhary,et al.  A solution method for static and dynamic analysis of three-dimensional contact problems with friction , 1986 .

[21]  Xiaoyan Lei Contact friction analysis with a simple interface element , 2001 .

[22]  G. Bfer,et al.  An isoparametric joint/interface element for finite element analysis , 1985 .

[23]  J. J. Anza,et al.  A mixed finite element model for the elastic contact problem , 1989 .

[24]  D. Owen,et al.  Computational model for 3‐D contact problems with friction based on the penalty method , 1992 .