A modified node‐to‐segment algorithm passing the contact patch test

SUMMARY Several investigations have shown that the classical one-pass node-to-segment (NTS) algorithms for the enforcement of contact constraints fail the contact patch test. This implies that the algorithms may introduce solution errors at the contacting surfaces, and these errors do not necessarily decrease with mesh refinement. The previous research has mainly focused on the Lagrange multiplier method to exactly enforce the contact geometry conditions. The situation is even worse with the penalty method, due to its inherent approximation that yields a solution affected by a non-zero penetration. The aim of this study is to analyze and improve the contact patch test behavior of the one-pass NTS algorithm used in conjunction with the penalty method for 2D frictionless contact. The paper deals with the case of linear elements. For this purpose, several sequential modifications of the basic formulation have been considered, which yield incremental improvements in results of the contact patch test. The final proposed formulation is a modified one-pass NTS algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method. In other words, this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration. Copyright q 2009 John Wiley & Sons, Ltd.

[1]  K. Bathe,et al.  Stability and patch test performance of contact discretizations and a new solution algorithm , 2001 .

[2]  M. A. Crisfield,et al.  Re‐visiting the contact patch test , 2000 .

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

[5]  P. Wriggers,et al.  A segment-to-segment contact strategy , 1998 .

[6]  P. Wriggers,et al.  Real contact mechanisms and finite element formulation—a coupled thermomechanical approach , 1992 .

[7]  Jae Hyuk Lim,et al.  A new computational approach to contact mechanics using variable‐node finite elements , 2008 .

[8]  Stanisław Stupkiewicz,et al.  Extension of the node‐to‐segment contact element for surface‐expansion‐dependent contact laws , 2001 .

[9]  P. Wriggers,et al.  FINITE ELEMENT FORMULATION OF LARGE DEFORMATION IMPACT-CONTACT PROBLEMS WITH FRICTION , 1990 .

[10]  Anil Chaudhary,et al.  A SOLUTION METHOD FOR PLANAR AND AXISYMMETRIC CONTACT PROBLEMS , 1985 .

[11]  C. Felippa,et al.  A simple algorithm for localized construction of non‐matching structural interfaces , 2002 .

[12]  Peter Wriggers,et al.  Computational Contact Mechanics , 2002 .

[13]  David J. Benson,et al.  Sliding interfaces with contact-impact in large-scale Lagrangian computations , 1985 .

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

[15]  Klaus-Jürgen Bathe,et al.  The inf–sup condition and its evaluation for mixed finite element methods , 2001 .

[16]  Reese E. Jones,et al.  A novel finite element formulation for frictionless contact problems , 1995 .

[17]  Bernhard A. Schrefler,et al.  A Contact Formulation for Electrical and Mechanical Resistance , 2002 .

[18]  Carlos Alberto Conceição António,et al.  Algorithms for the analysis of 3D finite strain contact problems , 2004 .

[19]  Toshiaki Hisada,et al.  Development of a Finite Element Contact Analysis Algorithm to Pass the Patch Test , 2006 .