[en] The aim of this work is to propose a new numerical method for solving the mechanical frictional contact problem in the general case of multi-bodies in a three dimensional space. This method is called adapted augmented Lagrangian method (AALM) and can be used in a multi-physical context (like thermo-electro-mechanical fields problems). This paper presents this new method and its advantages over other classical methods such as penalty method (PM), adapted penalty method (APM) and, augmented Lagrangian method (ALM). In addition, the efficiency and the reliability of the AALM are proved with some academic problems and an industrial thermo-electromechanical problem.
Disciplines :
Mechanical engineering
Author, co-author :
Bussetta, Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Daniel, Marceau; Université du Québec à Chicoutimi (Canada) > Département des sciences appliquées
Ponthot, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Language :
English
Title :
The adapted augmented Lagrangian method: a new method for the resolution of the mechanical frictional contact problem
Publication date :
January 2012
Journal title :
Computational Mechanics
ISSN :
0178-7675
eISSN :
1432-0924
Publisher :
Springer Science & Business Media B.V., New York, United States - New York
Volume :
49
Issue :
2
Pages :
259-275
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
FRQNT - Fonds de Recherche du Québec - Nature et Technologies [CA]
Wriggers P (2006) Computational contact mechanics. Springer, Berlin
Keshavarz Sh, Khoei AR, Khaloo AR (2008) Contact friction simulation in powder compaction process based on the penalty approach. Mater Des 29:1199-1211 (Pubitemid 351396287)
Bayram YB,NiedHF (2000) Enriched finite element-penalty function method for modeling interface cracks with contact. Eng Fract Mech 65:541-557 (Pubitemid 30589533)
Zavarise G, Wriggers P, Stein E, Schrefler BA (1992) Real contact mechanisms and finite element formulation-a coupled thermomechanical approach. Int J Numer Methods Eng 35:767-785
Krstulović-Opara L,Wriggers P, Korelc J (2002) A c1-continuous formulation for 3d finite deformation frictional contact. Comput Mech 29:27-42 (Pubitemid 34882302)
FischerKA, Wriggers P (2006) Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Comput Methods Appl Mech Eng 195:5020-5036 (Pubitemid 43842594)
Elguedj T, Gravouil A, Combescure A (2007) Amixed augmented Lagrangian-extended finite element method for modelling elasticplastic fatigue crack growth with unilateral contact. Int J Numer Methods Eng 71:1569-1597 (Pubitemid 47470920)
Simo JC, Laursen TA (1992) An augmented Lagrangian treatment of contact problems involving friction. Comput Struct 42:97-116
Wriggers P, Zavarise G (1993) Application of augmented Lagrangian techniques for non-linear constitutive laws in contact interfaces. Commun Numer Meth Eng 9:815-824
Baba OA, Radi B, Gelin JC (2000) An augmented Lagrangian treatment of the metal forming process. Math Comput Model 32:1171-1179
Wriggers P (1995) Finite element algorithms for contact problems. Arch Comput Methods Eng 2:1-49
Saleeb AF, Chen K, Chang TYP (1994) An effective two-dimensional frictional contact model for arbitrary curved geometry. Int J Numer Methods Eng 37:1297-1321
Walter H (1999) Modélisation 3D par éléments finis du contact avec frottement et de l'endommagement du béton: application à l'étude de fixation ancrées dans une structure en béton. PhD thesis, École Doctorale mega (in French)
CarpenterNJ, Taylor RL,KatonaMG (1991) Lagrange constraints for transient finite elements surface contact. Int J Numer Methods Eng 32:103-128
Oldenburg M, Nilsson L (1994) The position code algorithm for contact searching. Int J Numer Methods Eng 37:359-386
Klarbring A, Ciavarella M, Barber JR (2007) Shakedown in elastic contact problems with coulomb friction. Int J Solids Struct 44:8355-8365 (Pubitemid 47632564)
Ireman P, Klarbring A, Strömberg N (2002) Finite element algorithms for thermoelastic wear problems. Eur J Mech A Solids 21:423-440
Chamoret D, Saillard P, Rassineux A, Bergheau J-M (2004) New smoothing procedures in contact mechanics. J Comput Appl Math 168:107-116 (Pubitemid 38763320)
Chamoret D (2002) Modélisation du contact: nouvelles approches numériques. PhD thesis, École Centrale de Lyon (in French)
Bussetta P (2009) Modélisation et résolution du probléme de contact mécanique et son application dans un contexte multiphysiques. PhD thesis, Université du Québec à Chicoutimi (in French)
Zavarise G, De Lorenzis L (2009) A modified node-to-segment algorithm passing the contact patch test. Int J NumerMethods Eng 79:379-416
Zavarise G, De Lorenzis L (2009) The node-to-segment algorithm for 2d frictionless contact: classical formulation and special cases. Comput Methods Appl Mech Eng 198:3428-3451
Zavarise G, Wriggers P (1998) A segment-to-segment contact strategy. Math Comput Model 28:497-515 (Pubitemid 28448182)
Wriggers P, Zavarise G (2008) A formulation for frictionless contact problems using a weak form introduced by Nitsche. Comput Mech 41:407-420 (Pubitemid 350211989)
Yang B, Laursen TA, MengX (2005) Two dimensionalmortar contact methods for large deformation frictional sliding. Int J Numer Eng 62:1183-1225 (Pubitemid 40345675)
Puso MA, Laursen TA (2004) A mortar segment-to-segment contact method for large deformation solid mechanics. Comput Methods Appl Mech Eng 193:601-629 (Pubitemid 38187806)
Puso MA, Laursen TA (2004) A mortar segment-to-segment frictional contact method for large deformations. Comput Methods Appl Mech Eng 193:4891-4913 (Pubitemid 39408007)
Oysu C, Fenner RT (2006) Coupled fem-bem for elastoplastic contact problems using Lagrange multipliers. Appl Math Model 30:231-247 (Pubitemid 41748524)
Chernov A, Maischaka M, Stephan EP (2007) A priori error estimates for hp penalty bem for contact problems in elasticity. Comput Methods Appl Mech Eng 196:3871-3880 (Pubitemid 47029546)
Yamazaki K, Sakamoto J, Takumi S (1994) Penalty method for three-dimensional elastic contact problems by boundary element method. Comput Struct 52:895-903
Rodríguez-Tembleque L, Buronia FC, Abascala R, Sáez A (2010) 3D frictional contact of anisotropic solids using bem. Eur J Mech A Solids (in press)
Daux C, Moës N, Dolbow J, Sukumar N, Belytschko T (2000) Arbitrary branched and intersecting cracks with the extended finite element method. Int J Numer Eng 48:1741-1760
Dolbow J, Moës N, Belytschko T (2001) An extended finite element method for modeling crack growth with frictional contact. Comput Methods Appl Mech Eng 190:6825-6846 (Pubitemid 33079936)
Legrain G, Moës N, Verron E (2005) Stress analysis around crack tips in finite strain problems using the extended finite element method. Int J Numer Methods Eng 63:290-314 (Pubitemid 40659666)
Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131-150 (Pubitemid 30508928)
Marceau D (2001) Modélisation du contact tridimensionnel avec frottement en grande transformation et son application á l'étude des dispositifs d'ancragemultitorons. PhD thesis, Université Laval (in French)
Wriggers P, Vu Van T, Stein E (1990) Finite element formulation of large deformation impact contact problem with friction. Comput Struct 37:319-331
Laursen TA, Simo JC (1993) A continuum-based finite element formulation for the implicit solution of multibody, large deformation frictional contact problem. Int JNumer Methods Eng 36:3451-3485
Qiu X, Plesha ME, Meyer D (1991) Stiffness matrix integration rules for contact-friction finite elements. Comput Methods Appl Mech Eng 93:385-399
Lei X (2001) Contact friction analysis with a simple interface element. Comput Methods Appl Mech Eng 190:1955-1965 (Pubitemid 32333692)
El-Abbasi N, Bathe K-J (2001) Stability and patch test performance of contact discretizations and a new solution algorithm. Comput Struct 79:1473-1786
Harnau M, Konyukhov A, Schweizerhof K (2005) Algorithmic aspects in large deformation contact analysis using 'solid-shell' elements. Comput Struct 83:1804-1823 (Pubitemid 40819699)
Bussetta P, Marceau D, Ponthot J-P (2009) Résolution du problème de contact mécanique frottant: méthode du lagrangien augmenté adapté. In: Proceedings of 9éme Colloque National en Calcul des Structures, Giens, France (in French)
Timoshenko S, Goodier JN (1951) Theory of elasticity, 2nd edn. Mc Graw-Hill Book Company, Inc, New York
Marceau D, Pilote S, Désilets M, Bilodeau J-F, Hacini L, Caratini Y (2011) Advanced numerical simulation of the thermo-electromechanical behaviour of hall-héroult cells under electrical preheating. In: Proceeding of the 140th annual meeting & exhibition. Light metals 2011
Dupuis M, Asadi G, Mark Read C, Thellend R, Tomlinson SA, Tabsh I (1993) Thermal study of the coke pre-heating technique for a hall-heroult cell. In: Proceeding of the 32th annual conference of CIM. Light metals section
Goulet P (2004) Modélisation du comportement thermo- électromécanique des interfaces de contact d'une cuve de Hall-Héroult. PhD thesis, Université Laval (in French)
D'Amours G (2004) Développement de lois constitutives thermomécaniques pour les matériaux á base de carbone lors du préchauffage d'une cuve d'électrolyse. PhD thesis, Université Laval (in French)
Mirchi AA, Chen W, Tremblay M (2003) Comparative characterisation of graphitized and graphitic cathode blocks. In: TMS light metals, pp 617-624
Zolochevsky A, Hop JG, Servant G, Foosnaes T, Oye HA (2003) Creep and sodium expansion in a semigraphitic cathode carbon. In: TMS light metals, pp 595-602
