[en] For the two dimensional contact modeling, the standard node-to-segment quadratic contact
elements are known to exhibit oscillations of the contact pressure. This situation is particularly critical when using the penalty method with a high penalty parameter because the amplitude of the oscillations increase with increasing penalty parameter. The aim of this article is to present a method for removing the oscillations of contact pressure observed while using quadratic contact element. For this purpose, the nodal forces at the slave and at the master nodes need to be evaluated appropriately. One possibility is to develop a suitable procedure for computing the nodal forces. In that sake, we selected the approach first proposed in [35] in an appropriate manner. After presenting the improved quadratic contact element, some numerical examples are illustrated in this paper to compare the standard quadratic node-to-segment element with the proposed element. The examples show that the proposed element can strongly reduce the oscillating contact pressure for both plane and curved contact surfaces.
Disciplines :
Mechanical engineering
Author, co-author :
Nguyen, Duc-Tué; Bosch Vietnam
Rauchs, Gast; Department of Materials Research and Technology, Luxembourg Institute of Science and Technology, 41 Brillstrooss, L-4422 Bieles, Luxembourg
Ponthot, Jean-Philippe ; Université de Liège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Language :
English
Title :
A quadratic contact element passing the patch test
Publication date :
2016
Journal title :
Key Engineering Materials
ISSN :
1013-9826
eISSN :
1662-9795
Publisher :
Trans Tech Publications, Aedermannsdorf, Switzerland
Chen, X., Hisada, T.: Development of a finite element contact analysis algorithm to pass the patch test. Japan Society of Mechanical Engineers International Journal 49(4), 483-491 (Series A 2006)
Fischer, K. A., Wriggers, P.: Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Comput. Methods Appl. Mech. Engrg. 195, 5020-5036 (2006)
Hartmann, S., Ramm, E.: A mortar based contact formulation for non-linear dynamics using dual lagrange multipliers. Finite Elem. Anal. Des. 44, 245-258 (2008)
Kim, J. Y., Youn, S. K.: Isogeometric contact analysis using mortar method. Int. J. Numer. Meth. Engng. 89, 1559-1581 (2012)
Krstulovic-Opara, L., Wriggers, P., Korelc, J.: A C1-continuous formulation for 3D finite deformation frictional contact. Comput. Struct 29, 27-42 (2001)
Krstulovic-Opara, L., Wriggers, P., Korelc, J.: A C1-continuous formulation for 3D finite deformation frictional contact. Compt. Mechanics 29, 27-42 (2002)
Lorenzis, L. D., Termizer, I., Wriggers, P., Zavarise, G.: A large deformation frictional contact formulation using NURBS-based isogeometric analysis. Int. J. Numer. Meth. Engng. 10, 31-59 (2011)
Lorenzis, L. D., Wriggers, P., Zavarise, G.: A mortar formulation for 3d large deformation contact using NURBS based isogeometric analysis and the augmented lagrangian method. Comput. Mech. 4, 555-566 (2011)
Luo, C., Klisinski, M.: Application of piece-wise linear weight functions for 2D 8-node quadrilateral element in contact problems. Int. J. Num. Meth. Engng. 61, 159-188 (2004)
Nguyen, D. T.: Modélisation 2D par éléments finis du contact: effet de l'utilisation de méthodes de représentation des surfaces présentant un ordre de continuité élevé et méthodes permettant de passer le patch test (in French).. Ph. D. thesis, University of Liège (Belgium) (2014)
Nguyen, D. T., Rauchs, G., Ponthot, J. P.: The impact of surface higher order differentiability in two-dimensional contact elements. Journal of Computational and Applied Mathematics 246, 195-205 (2013)
Papadopoulos, P., Taylor, R. L.: A mixed formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 94, 373-389 (1992)
Popp, A., Gee, M. W., Wall, W. A.: A finite deformation mortar contact formulation using a primal dual active set strategy. Int. J. Numer. Meth. Engng. 79, 1354-1391 (2009)
Popp, A., Wohlmuth, B., Gee, M., Wall, W.: Dual quadratic mortar finite element methods for 3D finite deformation contact. SIAM J. SCI. COMPUT. 34, 421-446 (2012)
Puso, M. A., Laursen, T. A.: A mortar segment-to-segment contact method for large deformation solid mechanics. Comput. Methods Appl. Mech. Engrg. 193, 601-629 (2004)
Puso, M. A., Laursen, T. A., Solberg, J.: A segment-to-segment mortar contact method for quadratic elements and large deformations. Comput. Methods Appl. Mech. Engrg. 197, 555-566 (2008)
Sauer, R.: Enriched contact finite elements for stable peeling computations. Int. J. Numer. Meth. Engng. 87, 593-616 (2011)
Sauer, R.: Local finite element enrichment strategies for 2D contact computations and a corresponding post-processing scheme. Comput. Mech 52, 301-319 (2013)
Sheng, D., Wriggers, P., Sloan, S. W.: Improved numerical algorithms for frictional contact in pile penetration analysis. Comput. Geotech. 33, 341-354 (2006)
Simo, J., Wriggers, P., Taylor, R.: A perturbed lagrangian formulation for the finite element solution of contact problems. Comput. Methods Appl. Mech. Engrg. 50, 163-180 (1985)
Stupkiewicz, S.: Extension of the node-to-segment contact element for surface-expansiondependent contact laws. Int. J. Num. Meth. Engng. 50, 739-759 (2001)
Taylor, R., Papadopoulos, P.: On a patch test for contact problems in two dimensions. Computational Methods in Nonlinear Mechanics pp. 690-702 (1991)
Termizer, I., Wriggers, P., Hughes, T. J. R.: Contact treatment in isogeometric analysis with NURBS. Comput. Methods. Appl. Mech. Engrg. 200, 1100-1112 (2011)
Timoshenko, S., Goodier, J. N.: Theory of Elasticity. Second Edition, McGraw-Hill Book Company, Inc, New York (1951)
Tur, M., Fuenmayor, F., Wriggers, P.: A mortar-based frictional contact formulation for large deformations using lagrange multipliers. Comput. Methods Appl. Mech. Engrg. 198, 2860-2873 (2009)
Tur, M., Giner, E., Fuenmayor, F., Wriggers, P.: 2D contact smooth formulation based on the mortar method. Comput. Methods Appl. Mech. Engrg. 247-248, 1-14 (2012)
Wriggers, P.: Computational contact mechanics. John Wiley & Sons (2002)
Wriggers, P., Simo, J.: A note on tangent stiffness for fully nonlinear contact problems. Commun. Appl. Numer. Methods 1, 199-203 (1985)
Wriggers, P., Van, T., Stein, E.: Finite element formulation of large deformation impact-contact problems with friction. Comput. Struct 37, 319-333 (1990)
Yang, B., Laursen, T., Meng, X.: Two dimensional mortar contact methods for large deformation frictional sliding. Int. J. Numer. Methods Eng. 62, 1183-1225 (2005)
Zavarise, G., Boso, D., Schrefler, B.: A contact formulation for electrical and mechanical resistance. In Proceedings of CMIS, III Contact Mechanics International Symposium, Martins JAC, Monteiro Marques MDP (eds). Praja de Consolacao: Portugal pp. 211-218 (2001)
Zavarise, G., Lorenzis, L.: The node-to-segment algorithm for 2D frictionless contact: Classical formulation and special cases. Comput. Methods. Appl. Mech. Engrg. 198, 3428-3451 (2009)
Zavarise, G., Lorenzis, L. D.: A modified node-to-segment algorithm passing the contact patch test. Int. J. Num. Meth. Engng. 79, 379-416 (2009)