Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

A three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the contact surface is inherited directly from the NURBS discretization of the volume, the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative Lagrange discretizations independent of the discretization order. These enable the achievement of improved smoothness in global contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume.

[1]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[2]  P. Wriggers,et al.  Smooth C1‐interpolations for two‐dimensional frictional contact problems , 2001 .

[3]  T. Hughes,et al.  Efficient quadrature for NURBS-based isogeometric analysis , 2010 .

[4]  Peter Wriggers,et al.  Contact treatment in isogeometric analysis with NURBS , 2011 .

[5]  Panayiotis Papadopoulos,et al.  A Novel Three-Dimensional Contact Finite Element Based on Smooth Pressure Interpolations , 2000 .

[6]  T. Laursen,et al.  A framework for development of surface smoothing procedures in large deformation frictional contact analysis , 2001 .

[7]  Gerhard A. Holzapfel,et al.  Cn continuous modelling of smooth contact surfaces using NURBS and application to 2D problems , 2003 .

[8]  Jia Lu,et al.  Isogeometric contact analysis: Geometric basis and formulation for frictionless contact , 2011 .

[9]  Wolfgang A. Wall,et al.  A finite deformation mortar contact formulation using a primal–dual active set strategy , 2009 .

[10]  Alexander Konyukhov,et al.  Geometrically exact theory for contact interactions of 1D manifolds. Algorithmic implementation with various finite element models , 2012 .

[11]  Panayiotis Papadopoulos,et al.  An analysis of dual formulations for the finite element solution of two-body contact problems , 2005 .

[12]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

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

[14]  Panayiotis Papadopoulos,et al.  A family of simple two-pass dual formulations for the finite element solution of contact problems , 2007 .

[15]  Thomas J. R. Hughes,et al.  A large deformation, rotation-free, isogeometric shell , 2011 .

[16]  Peter Betsch,et al.  A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems , 2009 .

[17]  J. C. Simo,et al.  A perturbed Lagrangian formulation for the finite element solution of contact problems , 1985 .

[18]  G. Sangalli,et al.  Isogeometric analysis in electromagnetics: B-splines approximation , 2010 .

[19]  Cv Clemens Verhoosel,et al.  A phase-field description of dynamic brittle fracture , 2012 .

[20]  Roger A. Sauer,et al.  Enriched contact finite elements for stable peeling computations , 2011 .

[21]  I. Akkerman,et al.  Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method , 2010, J. Comput. Phys..

[22]  Richard W. Johnson.  Higher order B-spline collocation at the Greville abscissae , 2005 .

[23]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

[24]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[25]  G. Zavarise,et al.  A non-consistent start-up procedure for contact problems with large load-steps , 2012 .

[26]  Ernst Rank,et al.  A comparison of the h-, p-, hp-, and rp-version of the FEM for the solution of the 2D Hertzian contact problem , 2010 .

[27]  I. Temizer,et al.  A mixed formulation of mortar-based frictionless contact , 2012 .

[28]  Panayiotis Papadopoulos,et al.  A Lagrange multiplier method for the finite element solution of frictionless contact problems , 1998 .

[29]  Stephen J. Piazza,et al.  Robust contact modeling using trimmed NURBS surfaces for dynamic simulations of articular contact , 2009 .

[30]  Alexander Konyukhov,et al.  Incorporation of contact for high-order finite elements in covariant form , 2009 .

[31]  Barbara Wohlmuth,et al.  Thermo-mechanical contact problems on non-matching meshes , 2009 .

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

[33]  E. Rank,et al.  Erratum to: A comparison of the h-, p-, hp-, and rp-version of the FEM for the solution of the 2D Hertzian contact problem , 2010 .

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

[35]  Alexander Konyukhov,et al.  Geometrically Exact Theory for Contact Interactions , 2012 .

[36]  Alexander Konyukhov,et al.  Geometrically exact covariant approach for contact between curves , 2010 .

[37]  T. Hughes,et al.  ISOGEOMETRIC COLLOCATION METHODS , 2010 .

[38]  T. Hughes,et al.  Local refinement of analysis-suitable T-splines , 2012 .

[39]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

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

[41]  A. Curnier,et al.  Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment , 1999 .

[42]  T. Belytschko,et al.  A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM , 2010 .

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

[44]  Mark A. Ganter,et al.  Real-time finite element modeling for surgery simulation: an application to virtual suturing , 2004, IEEE Transactions on Visualization and Computer Graphics.

[45]  Elaine Cohen,et al.  Optimization-based virtual surface contact manipulation at force control rates , 2000, Proceedings IEEE Virtual Reality 2000 (Cat. No.00CB37048).

[46]  Barbara Wohlmuth,et al.  A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems , 2005 .

[47]  Barbara Wohlmuth,et al.  A primal–dual active set strategy for non-linear multibody contact problems , 2005 .

[48]  T. Hughes,et al.  Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations , 2010 .

[49]  Jakub Lengiewicz,et al.  Automation of finite element formulations for large deformation contact problems , 2010 .

[50]  P. Wriggers,et al.  A C1-continuous formulation for 3D finite deformation frictional contact , 2002 .

[51]  J. Tinsley Oden,et al.  Computational methods in nonlinear mechanics , 1980 .

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

[53]  L. Herrmann.  Finite Element Analysis of Contact Problems , 1978 .

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

[55]  T. Hughes,et al.  Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes , 2010 .

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

[57]  Tod A. Laursen,et al.  Mortar contact formulations for deformable–deformable contact: Past contributions and new extensions for enriched and embedded interface formulations , 2012 .

[58]  John A. Evans,et al.  Isogeometric Analysis , 2010 .

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

[60]  Tod A. Laursen,et al.  A mortar segment-to-segment frictional contact method for large deformations , 2003 .

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

[62]  B. Simeon,et al.  Adaptive isogeometric analysis by local h-refinement with T-splines , 2010 .

[63]  John A. Evans,et al.  Isogeometric finite element data structures based on Bézier extraction of NURBS , 2011 .

[64]  David A. Hills,et al.  Mechanics of elastic contacts , 1993 .

[65]  Panagiotis D. Kaklis,et al.  An isogeometric BEM for exterior potential-flow problems in the plane , 2009, Symposium on Solid and Physical Modeling.

[66]  Tod A. Laursen,et al.  A segment-to-segment mortar contact method for quadratic elements and large deformations , 2008 .

[67]  Peter Wriggers,et al.  A large deformation frictional contact formulation using NURBS‐based isogeometric analysis , 2011 .