Algorithms and Strategies for Treatment of Large Deformation Frictional Contact in the Numerical Simulation of Deep Drawing Process

This paper describes a fully implicit algorithm developed and optimized to simulate sheet metal forming processes. This algorithm was implemented in the in-house code DD3IMP. Attention is paid to the augmented lagrangian method adopted to treat the contact with friction problem. The global resolution of the coupled equilibrium and contact problem is performed in a single loop, with a static implicit iterative Newton-Raphson scheme. This demands particular attention in the contact search algorithm, which in this case adopts a parametric description of the tools. In order to highlight the adopted strategies a review of the state-of-the-art in sheet metal forming simulation is presented, with respect to models reliability and efficiency.

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

[2]  J. Rice,et al.  Finite-element formulations for problems of large elastic-plastic deformation , 1975 .

[3]  Andreas Heege.  Simulation numérique 3D du contact avec frottement et application à la mise en forme , 1992 .

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

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

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

[7]  Peter Wriggers,et al.  A note on the optimum choice for penalty parameters , 1987 .

[8]  Luís Menezes,et al.  Three-dimensional numerical simulation of the deep-drawing process using solid finite elements , 2000 .

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

[10]  Patrick Chabrand,et al.  Complementarity methods for multibody friction contact problems in finite deformations , 2001 .

[11]  G. P. Nikishkov,et al.  Static-explicit FE modeling of 3-d large deformation multibody contact problems on parallel computer , 1998 .

[12]  Laurent Baillet,et al.  Modélisation 3D par éléments finis de fixations ancrées dans une structure en béton , 2000 .

[13]  A. Erman Tekkaya,et al.  State-of-the-art of simulation of sheet metal forming , 2000 .

[14]  Luís Menezes,et al.  Study on the influence of work-hardening modeling in springback prediction , 2007 .

[15]  Z. Tourki,et al.  Finite element simulations of sheet-metal forming processes for planar-anisotropic materials , 2001 .

[16]  Greger Bergman,et al.  A finite element model for thermomechanical analysis of sheet metal forming , 2004 .

[17]  Shaker A. Meguid,et al.  Accurate modeling of contact using cubic splines , 2002 .

[18]  J. Arora,et al.  Review of formulations for elastostatic frictional contact problems , 2000 .

[19]  P. Wriggers,et al.  A method for solving contact problems , 1998 .

[20]  Tod A. Laursen,et al.  Formulation and treatment of frictional contact problems using finite elements , 1992 .

[21]  Gertjan Kloosterman,et al.  Contact methods in finite element simulations , 2002 .

[22]  Tod A. Laursen,et al.  An augmented Lagrangian quasi‐Newton solver for constrained nonlinear finite element applications , 1995 .

[23]  P. Chabrand,et al.  Application of ALE finite elements method to a lubricated friction model in sheet metal forming , 2000 .

[24]  Luís Menezes,et al.  Optimizing the Description of Forming Tools with Bézier Surfaces in the Numerical Simulation of the Deep Drawing Process , 2006 .

[25]  Larsgunnar Nilsson,et al.  A unified contact algorithm based on the territory concept , 1996 .

[26]  S. Sriram,et al.  Adding bending stiffness to 3-D membrane FEM programs , 2000 .

[27]  Rudi ter Haar,et al.  Friction in sheet metal forming, the influence of (local) contact conditions and deformation , 1996 .

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

[29]  K. Bathe,et al.  Fundamental considerations for the finite element analysis of shell structures , 1998 .

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

[31]  Taylan Altan,et al.  Issues in convergence improvement for non‐linear finite element programs , 1997 .

[32]  Klaus-Jürgen Bathe,et al.  On the constraint function method for contact problems , 1997 .

[33]  Diego A. Murio,et al.  3D-IHCP on a finite cube , 1996 .

[34]  Larsgunnar Nilsson,et al.  Automatic contact searching algorithm for dynamic finite element analysis , 1994 .

[35]  A. A. Fernandes,et al.  Analysis of 3D problems using a new enhanced strain hexahedral element , 2003 .

[36]  A. Makinouchi,et al.  Contact strategies to deal with different tool descriptions in static explicit FEM for 3-D sheet-metal forming simulation , 1995 .

[37]  R. H. Wagoner,et al.  Role of plastic anisotropy and its evolution on springback , 2002 .

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

[39]  Abel Dias dos Santos.  Tool descriptions and contact strategies used in the static explicit FEM code ITAS3D for simulation of 3-D sheet metal forming processes , 1993 .

[40]  J. C. Simo,et al.  On the computational significance of the intermediate configuration and hyperelastic stress relations in finite deformation elastoplasticity , 1985 .

[41]  K. Bathe,et al.  Stability and patch test performance of contact discretizations and a new solution algorithm , 2001 .

[42]  Luís Menezes,et al.  Work Hardening Models and the Numerical Simulation of the Deep Drawing Process , 2004 .

[43]  Ted Belytschko,et al.  A three-dimensional impact-penetration algorithm with erosion , 1987 .

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

[45]  A. Makinouchi,et al.  Simulation of multi-step sheet metal forming processes by a static explicit FEM code , 1998 .

[46]  Shaker A. Meguid,et al.  On the modelling of smooth contact surfaces using cubic splines , 2001 .

[47]  J. O. Hallquist,et al.  Improved simulation of thin-sheet metalforming using LS-DyNA3D on parallel computers , 1995 .

[48]  Ted Belytschko,et al.  Smoothing, enrichment and contact in the element-free Galerkin method , 1999 .

[49]  Peter Wriggers,et al.  Numerical derivation of contact mechanics interface laws using a finite element approach for large 3D deformation , 2004 .

[50]  D. A. Hughes,et al.  Numerical simulation and experimental observations of initial friction transients , 1995 .

[51]  Robert H. Wagoner,et al.  Experimental investigation and finite element modeling of hemispherically stretched steel sheet , 1989 .

[52]  Michele Chiumenti,et al.  On the numerical modeling of frictional wear phenomena , 1999 .

[53]  Mark O. Neal,et al.  Contact‐impact by the pinball algorithm with penalty and Lagrangian methods , 1991 .

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

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

[56]  Eugenio Oñate,et al.  Advances in FE explicit formulation for simulation of metalforming processes , 2001 .

[57]  P. Wriggers,et al.  On augmented Lagrangian algorithms for thermomechanical contact problems with friction , 1995 .

[58]  Wei Li Xu,et al.  Rigid‐plastic/rigid‐viscoplastic FE simulation using linear programming for metal forming , 2003 .

[59]  S. Reese.  On a physically stabilized one point finite element formulation for three-dimensional finite elasto-plasticity , 2005 .

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

[61]  A. Klarbring.  Large displacement frictional contact: a continuum framework for finite element discretization , 1995 .

[62]  A. Makinouchi,et al.  Shell-element formulation in the static explicit FEM code for the simulation of sheet stamping , 1995 .

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

[64]  T. Laursen,et al.  Automation and Assessment of Augmented Lagrangian Algorithms for Frictional Contact Problems , 1994 .

[65]  P. Wriggers,et al.  A superlinear convergent augmented Lagrangian procedure for contact problems , 1999 .

[66]  A. Behrens,et al.  2D and 3D simulation of complex multistage forging processes by use of adaptive friction coefficient , 1998 .

[67]  Panayiotis Papadopoulos,et al.  A Novel Three-Dimensional Contact Finite Element Based on Smooth Pressure Interpolations , 2001 .

[68]  Shaker A. Meguid,et al.  On the elastic solution of frictional contact problems using variational inequalities , 1994 .

[69]  Kyung K. Choi,et al.  Meshless shape design sensitivity analysis and optimization for contact problem with friction , 2000 .

[70]  António José Caetano Baptista.  Modelação mecânica e simulação numérica do processo de estampagem multi-etapas : aplicação ao processo de estampagem de chapas soldadas , 2007 .

[71]  Serge Cescotto,et al.  Texture evolution during deep-drawing processes , 2002 .

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

[73]  David J. Benson,et al.  Sliding interfaces with contact-impact in large-scale Lagrangian computations , 1985 .

[74]  Luís Menezes,et al.  Springback Evaluation with Several Phenomenological Yield Criteria , 2004 .

[75]  Zhenhan Yao,et al.  FFS contact searching algorithm for dynamic finite element analysis , 2001 .

[76]  Marta Cristina Cardoso Oliveira.  Algoritmos e estratégias de gestão do problema de contacto com atrito em grandes deformações: aplicação à estampagem de chapas metálicas , 2005 .

[77]  Frédéric Barlat,et al.  A general elasto-plastic finite element formulation based on incremental deformation theory for planar anisotropy and its application to sheet metal forming , 1999 .

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

[79]  Luís Menezes,et al.  Improvement of a frictional contact algorithm for strongly curved contact problems , 2003 .

[80]  Takashi Ishikawa,et al.  FEM simulation of the forming of textured aluminum sheets , 1998 .

[81]  David F. Shanno,et al.  Implementing Barrier Methods for Nonlinear Programming , 1996 .

[82]  T. Hughes,et al.  Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis , 1980 .

[83]  Carlos Alberto Conceição António,et al.  Algorithms for the analysis of 3D finite strain contact problems , 2004 .

[84]  Hiroto Suzuki,et al.  Shape error evaluation method of free-form surfaces , 1999, Comput. Aided Des..

[85]  Y. Yamada,et al.  Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method , 1968 .

[86]  B. Fredriksson.  Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems , 1976 .

[87]  Klaus-Jürgen Bathe,et al.  On the State of Finite Element Procedures for Forming Processes , 2004 .

[88]  V. T. Meinders,et al.  Developments in numerical simulations of the real-life deep drawing process , 2000 .

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

[90]  Peter Frederic Thomson,et al.  Quadratic programming method in numerical simulation of metal forming process , 2002 .

[91]  T. Hughes.  Generalization of selective integration procedures to anisotropic and nonlinear media , 1980 .

[92]  Ferdinando Auricchio,et al.  AUGMENTED LAGRANGIAN FINITE-ELEMENTS FOR PLATE CONTACT PROBLEMS , 1996 .

[93]  Luís Filipe Martins Menezes.  Modelação tridimensional e simulação numérica dos processos de enformação por deformação plástica : aplicação à estampagem de chapas metálicas , 1995 .

[94]  Shaker A. Meguid,et al.  A new strategy for the solution of frictional contact problems , 1998 .

[95]  Shen-Haw Ju,et al.  A new symmetric contact element stiffness matrix for frictional contact problems , 1995 .

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

[97]  T. Belytschko,et al.  A monolithic smoothing‐gap algorithm for contact‐impact based on the signed distance function , 2002 .

[98]  Faker Ben Belgacem,et al.  The mortar finite element method for contact problems , 1998 .

[99]  van der Erik Giessen,et al.  SIMULATION OF MATERIALS PROCESSING: THEORY, METHODS AND APPLICATIONS , 1998 .

[100]  Weimin Han,et al.  Inexact Uzawa algorithms for variational inequalities of the second kind , 2003 .

[101]  Jue Wang,et al.  A practical large‐strain solid finite element for sheet forming , 2005 .

[102]  E. Oñate,et al.  Numerical modelling and simulation of frictional contact using a generalised coulomb law , 1995 .

[103]  R. H. Wagoner,et al.  Simulation of springback , 2002 .

[104]  Luís Menezes,et al.  Modelling of anisotropic work-hardening behaviour of metallic materials subjected to strain-path changes , 2005 .

[105]  Jean-Loup Chenot,et al.  Physical modelling and numerical prediction of defects in sheet metal forming , 1992 .

[106]  Tod A. Laursen,et al.  On the constitutive modeling and finite element computation of rate-dependent frictional sliding in large deformations , 1997 .

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

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

[109]  J. O. Hallquist,et al.  Use of a coupled explicit—implicit solver for calculating spring-back in automotive body panels , 1995 .

[110]  A. A. Ball,et al.  Approximating circular arcs by Bézier curves and its application to modelling tooling for FE forming simulations , 2001 .

[111]  J. Huetink,et al.  A geometrical-based contact algorithm using a barrier method , 2001 .

[112]  J. A. Tanner,et al.  Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire , 1996 .

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

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

[115]  Dong-Yol Yang,et al.  FE-analysis of sheet metal forming processes using continuous contact treatment , 2007 .