A finite deformation mortar contact formulation using a primal-dual active set strategy

被引:111
作者
Popp, Alexander [1 ]
Gee, Michael W. [1 ]
Wall, Wolfgang A. [1 ]
机构
[1] Tech Univ Munich, Inst Computat Mech, D-85747 Garching, Germany
关键词
mortar finite element methods; multibody contact; primal-dual active set strategy; dual Lagrange multipliers; finite deformations; SEMISMOOTH NEWTON METHOD; FRICTIONAL CONTACT; ELEMENT FORMULATION; LAGRANGE MULTIPLIER; MULTIBODY; SPACES; 3D;
D O I
10.1002/nme.2614
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In recent years, nonconforming domain decomposition techniques and, in particular, the mortar method have become popular in developing new contact algorithms. Here, we present an approach for 2D frictionless multibody contact based on a mortar formulation and using a primal-dual active set strategy for contact constraint enforcement. We consider linear and higher-order (quadratic) interpolations throughout this work. So-called dual Lagrange multipliers are introduced for the contact pressure but can be eliminated front the global system of equations by static condensation, thus avoiding an increase in system size. For this type of contact formulation, we provide a full linearization of both contact forces and normal (non-penetration) and tangential (frictionless sliding) contact constraints in the finite deformation frame. The necessity of such a linearization in order to obtain a consistent Newton scheme is demonstrated. By further interpreting the active set search as a semi-smooth Newton method, contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme. This yields a robust and highly efficient algorithm for frictionless finite deformation contact problems. Numerical examples illustrate the efficiency of our method and the high quality of results. Copyright (C) 2009 John Wiley & Sons, Ltd.
引用
收藏
页码:1354 / 1391
页数:38
相关论文
共 37 条
  • [1] [Anonymous], 2002, Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis
  • [2] The mortar finite element method for contact problems
    Belgacem, FB
    Hild, P
    Laborde, P
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 1998, 28 (4-8) : 263 - 271
  • [3] BERNHEIM J, 1994, NEPHROL DIAL TRANS S, V3, P13
  • [4] A fast and robust iterative solver for nonlinear contact problems using a primal-dual active set strategy and algebraic multigrid
    Brunssen, S.
    Schmid, F.
    Schaefer, M.
    Wohlmuth, B.
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2007, 69 (03) : 524 - 543
  • [5] BRUNSSEN S, 2008, THESIS U STUTTGART
  • [6] Christensen PW, 1998, INT J NUMER METH ENG, V42, P145, DOI 10.1002/(SICI)1097-0207(19980515)42:1<145::AID-NME358>3.0.CO
  • [7] 2-L
  • [8] A TIME INTEGRATION ALGORITHM FOR STRUCTURAL DYNAMICS WITH IMPROVED NUMERICAL DISSIPATION - THE GENERALIZED-ALPHA METHOD
    CHUNG, J
    HULBERT, GM
    [J]. JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1993, 60 (02): : 371 - 375
  • [9] Robust adaptive remeshing strategy for large deformation, transient impact simulations
    Erhart, T
    Wall, WA
    Ramm, E
    [J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2006, 65 (13) : 2139 - 2166
  • [10] ERHART T, 2001, P ECCM 01 CRAC POL