Mechanical contact; Penalty Method; Node-to-surface; Higher order of differentiability
Abstract :
[en] The aim of this work is to propose new contact elements of higher order of differentiability for analysing two-dimensional frictionless contact problems. Several methods were proposed in the literature to solve the problem caused by the lack of continuity resulting from the discretization. Among them are Bézier interpolation, Hermitian interpolation and splines. One of the difficulties in using Hermitian interpolation is to verify the partition of unity. Therefore, new elements that satisfy the C1 and C2 continuity at the interface are presented in this paper. These new contact elements are based on Hermitian polynomials for ensuring a higher order of continuity. The advantage is that this approach can be easily developed not only for linear elements but also for quadratic elements with higher order of differentiability. The performance of different surface representations is assessed through a comparison with a C0 surface discretization. Some numerical examples are used for assessing the accuracy and the convergence behaviour
Research Center/Unit :
Department of Advanced Materials and Structures, Centre de Recherche Public Henri Tudor+LTAS, Department of Aerospace and Mechanical Engineering, University of Liège
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Bibliography
P. Wriggers Computational Contact Mechanics 2002 John Wiley & Sons
P. Wriggers, L. Krstulovic-Opara, and J. Korelc Smooth C 1-interpolation for two-dimensional frictional contact problems Internat. J. Numer. Methods Engrg. 57 2001 2177 2203
N. El-Abbasi, S.A. Meguid, and A. Czekanski On the modelling of smooth contact surfaces using cubic splines Internat. J. Numer. Methods Engrg. 50 2001 953 967
J. Muñoz Modelling unilateral frictionless contact using the null-space method and cubic B-spline interpolation Comput. Methods Appl. Mech. Engng. 197 2008 979 993
M. Stadler, G.A. Holzapfel, and J. Korelc Cn continuous modelling of smooth contact surfaces using NURBS and application to 2D problems Internat. J. Numer. Methods Engrg. 57 2003 2177 2203
D. Tan Mesh matching and contact patch test Comput. Mech. 31 2003 135 152
G. Zavarise, and L.D. Lorenzis A modified node-to-segment algorithm passing the contact patch test Internat. J. Numer. Methods Engrg. 79 2009 379 416
M.A. Puso, and T.A. Laursen A mortar segment-to-segment contact method for large deformation solid mechanics Comput. Methods Appl. Mech. Engrg. 193 2004 601 629
M.A. Puso, T.A. Laursen, and J. Solberg A segment-to-segment mortar contact method for quadratic elements and large deformations Comput. Methods Appl. Mech. Engrg. 197 2008 555 566
M. Tur, F. Fuenmayor, and P. Wriggers A mortar-based frictional contact formulation for large deformations using Lagrange multipliers Comput. Methods Appl. Mech. Engrg. 198 2009 2860 2873
S. Hartmann, and E. Ramm A mortar based contact formulation for non-linear dynamics using dual Lagrange multipliers Finite Elem. Anal. Des. 44 2008 245 258
I. Termizer, P. Wriggers, and T.J.R. Hughes Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS Comput. Methods Appl. Mech. Engrg. 209-212 2012 115 128
E. Catmull, and R. Rom A class of local interpolation splines R.E. Barnhill, R.F. Riesenfeld, Computer-Aided Geometric Design 1974
G. Farin Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide 1997 Academic Press
G. Rauchs Optimization-based material parameter identification in identification testing for finite strain elasto-plasticity Z. Angew. Math. Mech. 86 2006 539 562
S. Stupkiewic Extension of the node-to-segment contact element for surface-expansion-dependent contact laws Internat. J. Numer. Methods Engrg. 50 2001 739 759
J. Hallquist, G. Goudreau, and D. Benson Sliding interfaces with contact-impact in large-scale Lagrangian computations Comput. Methods Appl. Mech. Engng. 51 1985 107 137
S. Timoshenko, and J.N. Goodier Theory of Elasticity second ed. 1951 Mc Graw-Hill Book Company, Inc. New York
W. Young Roarks Formulas for Stress and Strain sixth ed. 1989 Mc Graw-Hill Book Company, Inc. New York
C. Luo, and M. Klisinski Application of piece-wise linear weight functions for 2D 8-node quadrilateral element in contact problems Internat. J. Numer. Methods Engrg. 61 2004 159 188
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