Uzawa and Newton algorithms to solve frictional contact problems within the bi‐potential framework

This paper is concerned with the numerical modeling of three-dimensional unilateral contact problems in elastostatics with Coulomb friction laws. We propose a Newton-like algorithm to solve the local contact non-linear equations within the bi-potential framework. The piecewise continuous contact tangent matrices are explicitly derived. A comparative study is made between the Newton algorithm and the previously developed Uzawa algorithm. A test example is included to demonstrate the developed algorithms and to highlight their performance.

[1]  J. Oden,et al.  Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , 1987 .

[2]  F. Jourdan,et al.  A Gauss-Seidel like algorithm to solve frictional contact problems , 1998 .

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

[4]  Zhi-Qiang Feng,et al.  The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms , 1998 .

[5]  P. Wriggers.  Finite element algorithms for contact problems , 1995 .

[6]  A. Curnier,et al.  An augmented Lagrangian method for discrete large‐slip contact problems , 1993 .

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

[8]  T. Laursen.  Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis , 2002 .

[9]  J. C. Simo,et al.  An augmented lagrangian treatment of contact problems involving friction , 1992 .

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

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

[12]  François Peyraut,et al.  Solution of large deformation contact problems with friction between Blatz-Ko hyperelastic bodies , 2003 .

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

[14]  J. Haslinger,et al.  FETI based algorithms for contact problems: scalability, large displacements and 3D Coulomb friction , 2005 .

[15]  Zhi-Qiang Feng.  2D or 3D frictional contact algorithms and applications in a large deformation context , 1995 .

[16]  G. Saxcé,et al.  New Inequality and Functional for Contact with Friction: The Implicit Standard Material Approach∗ , 1991 .

[17]  Mohammed Hjiaj,et al.  Three-dimensional finite element computations for frictional contact problems with non-associated sliding rule , 2004 .