A C1-continuous formulation for 3D finite deformation frictional contact

Abstract A new 3D smooth triangular frictional node to surface contact element is developed using an abstract symbolical programming approach. The C1-continuous smooth contact surface description is based on the six quartic Bézier surfaces. The weak formulation and the penalty method are formulated for the description of large deformation frictional contact problems. The presented approach, based on a non-associated frictional law and elastic-plastic tangential slip decomposition, results into quadratic rate of convergence within the Newton-Raphson iteration loop. The frictional sliding path for the smooth, as well as the simple frictional node to surface contact element presented herein, is defined by the mapping of the current in the last converged configuration. Examples demonstrate the performance of symbolically developed contact elements, as well as the stability and more realistic contact description for the smooth elements in comparison with the simple ones.

[1]  M. Cooper,et al.  Thermal contact conductance , 1969 .

[2]  Z. Mroz,et al.  Associated and non-associated sliding rules in contact friction problems. , 1978 .

[3]  R. F. Kulak,et al.  Accurate Numerical Solutions for Elastic-Plastic Models , 1979 .

[4]  David Tabor,et al.  Friction—The Present State of Our Understanding , 1981 .

[5]  J. Nagtegaal.  On the implementation of inelastic constitutive equations with special reference to large deformation problems , 1982 .

[6]  Igorʹ Viktorovich Kragelʹskiĭ,et al.  Friction and wear: Calculation methods , 1982 .

[7]  Wolfgang Böhm,et al.  A survey of curve and surface methods in CAGD , 1984, Comput. Aided Geom. Des..

[8]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[9]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[10]  Michael Ortiz,et al.  An analysis of a new class of integration algorithms for elastoplastic constitutive relations , 1986 .

[11]  A. Klarbring.  A mathematical programming approach to three-dimensional contact problems with friction , 1986 .

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

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

[14]  M. Yovanovich,et al.  Explicit relative contact pressure expression - Dependence upon surface roughness parameters and Vickers microhardness coefficients , 1987 .

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

[16]  A. Giannakopoulos.  The return mapping method for the integration of friction constitutive relations , 1989 .

[17]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[18]  A. Klarbring,et al.  Rigid contact modelled by CAD surface , 1990 .

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

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

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

[22]  Peter Wriggers,et al.  On the treatment of nonlinear unilateral contact problems , 1993 .

[23]  R. Taylor,et al.  A simple algorithm for three-dimensional finite element analysis of contact problems , 1993 .

[24]  J. C. Simo,et al.  A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems , 1993 .

[25]  Rüdiger Braun,et al.  Analysis mit Maple , 1995 .

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

[27]  Pierre Alart,et al.  A FRICTIONAL CONTACT ELEMENT FOR STRONGLY CURVED CONTACT PROBLEMS , 1996 .

[28]  Stephen Wolfram,et al.  The Mathematica book (3rd ed.) , 1996 .

[29]  Joze Korelc,et al.  Symbolic approach in computational mechanics and its application to the enhanced strain method , 1996 .

[30]  H. Parisch,et al.  A formulation of arbitrarily shaped surface elements for three-dimensional large deformation contact with friction , 1997 .

[31]  Henryk K Stolarski,et al.  A contact algorithm for problems involving quadrilateral approximation of surfaces , 1997 .

[32]  Joachim Schöberl,et al.  NETGEN An advancing front 2D/3D-mesh generator based on abstract rules , 1997 .

[33]  C. A. Saracibar.  A new frictional time integration algorithm for large slip multi-body frictional contact problems , 1997 .

[34]  S. Wang,et al.  The inside–outside contact search algorithm for finite element analysis , 1997 .

[35]  P. W. Christensen,et al.  Formulation and comparison of algorithms for frictional contact problems , 1998 .

[36]  Shen-Haw Ju,et al.  A Three-Dimensional Frictional Contact Element Whose Stiffness Matrix is Symmetric , 1999 .

[37]  C1-conforming subdivision elements for thin-shell analysis , 2000 .

[38]  M. Ortiz,et al.  Subdivision surfaces: a new paradigm for thin‐shell finite‐element analysis , 2000 .

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