An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact

In this paper we propose an extension of Nitsche’s method for frictional contact in large elastic deformations. In fact we develop an unbiased strategy in which no asymmetry is considered between contact surfaces, conversely to the master–slave strategy. This enables to take into account within the same formalism contact of two elastic bodies as well as self-contact. We provide a numerical study of the performance and robustness of the method.

[1]  Franz Chouly,et al.  A Nitsche-Based Method for Unilateral Contact Problems: Numerical Analysis , 2013, SIAM J. Numer. Anal..

[2]  A. Klarbring,et al.  Continuum Mechanics Modelling of Large Deformation Contact with Friction , 1995 .

[3]  Franz Chouly,et al.  Symmetric and non-symmetric variants of Nitsche's method for contact problems in elasticity: theory and numerical experiments , 2014, Math. Comput..

[4]  M. Puso,et al.  A mortar segment-to-segment contact method for large deformation solid mechanics , 2004 .

[5]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[6]  L. Baillet,et al.  Mixed finite element formulation in large deformation frictional contact problem , 2005, math/0502162.

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

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

[9]  Franz Chouly,et al.  An adaptation of Nitscheʼs method to the Tresca friction problem , 2014 .

[10]  Erik Burman,et al.  A Penalty-Free Nonsymmetric Nitsche-Type Method for the Weak Imposition of Boundary Conditions , 2011, SIAM J. Numer. Anal..

[11]  Peter Wriggers,et al.  Mortar based frictional contact formulation for higher order interpolations using the moving friction cone , 2006 .

[12]  J. Nitsche Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind , 1971 .

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

[14]  Yves Renard,et al.  Generalized Newton’s methods for the approximation and resolution of frictional contact problems in elasticity , 2013 .

[15]  Alexander Konyukhov,et al.  Computational Contact Mechanics , 2013 .

[16]  Peter Hansbo,et al.  The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem , 2016, SIAM J. Numer. Anal..

[17]  P. Alart,et al.  A generalized Newton method for contact problems with friction , 1988 .

[18]  Patrick Hild,et al.  Numerical Implementation of Two Nonconforming Finite Element Methods for Unilateral Contact , 2000 .

[19]  Javier Oliver,et al.  A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis , 2009 .

[20]  T. Laursen,et al.  A mortar‐finite element formulation for frictional contact problems , 2000 .

[21]  Franz Chouly,et al.  An unbiased Nitsche’s approximation of the frictional contact between two elastic structures , 2018, Numerische Mathematik.

[22]  P. Wriggers,et al.  A mortar-based frictional contact formulation for large deformations using Lagrange multipliers , 2009 .

[23]  John E. Dolbow,et al.  A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part II: Intersecting interfaces , 2013 .

[24]  Konstantinos Poulios,et al.  An unconstrained integral approximation of large sliding frictional contact between deformable solids , 2015 .

[25]  Peter Wriggers,et al.  Frictionless 2D Contact formulations for finite deformations based on the mortar method , 2005 .

[26]  Barbara I. Wohlmuth,et al.  Dual Quadratic Mortar Finite Element Methods for 3D Finite Deformation Contact , 2012, SIAM J. Sci. Comput..

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

[28]  T. Laursen Computational Contact and Impact Mechanics , 2003 .

[29]  Wolfgang A. Wall,et al.  Segment-based vs. element-based integration for mortar methods in computational contact mechanics , 2015 .

[30]  Patrick Hild,et al.  A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics , 2010, Numerische Mathematik.

[31]  P. Hansbo,et al.  A finite element method for the simulation of strong and weak discontinuities in solid mechanics , 2004 .

[32]  P. Wriggers,et al.  A formulation for frictionless contact problems using a weak form introduced by Nitsche , 2007 .

[33]  Roger A. Sauer,et al.  An unbiased computational contact formulation for 3D friction , 2015 .

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

[35]  Keith Hjelmstad,et al.  A finite element formulation of non-smooth contact based on oriented volumes for quadrilateral and hexahedral elements , 2007 .

[36]  M. Puso,et al.  A 3D contact smoothing method using Gregory patches , 2002 .