A large deformation frictional contact formulation using NURBS-based isogeometric analysis

International Journal for Numerical Methods in Engineering

Volumn 87, Issue 13, 2011, Pages 1278-1300

  De Lorenzis, L ^a   Temizer, I ^b   Wriggers, P ^c   Zavarise, G ^a  

^a UNIVERSITY OF SALENTO   (Italy)

^b BILKENT UNIVERSITY   (Turkey)

^c LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Contact mechanics; Isogeometric analysis; Mortar method; NURBS

Indexed keywords

ARBITRARY ORDER; CONTACT CONSTRAINT; CONTACT MECHANICS; CONTACT SURFACE; DEFORMABLE BODIES; DISCRETIZATIONS; FRICTIONAL CONTACT; FRICTIONAL CONTACT PROBLEMS; INTEGRATION POINTS; ISOGEOMETRIC ANALYSIS; LAGRANGE; LAGRANGE POLYNOMIALS; LARGE DEFORMATIONS; MORTAR METHOD; NUMERICAL EXAMPLE; NURBS;

DEFORMATION; FRICTION; LAGRANGE MULTIPLIERS; MORTAR; NUMERICAL METHODS;

SPLINES;

EID: 80051946538     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3159     Document Type: Article

References (32)

1. Hughes TJR, Cottrell JA, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering 2005; 194:4135-4195.
2. Bazilevs Y, Hughes T. NURBS-based isogeometric analysis for the computation of flows about rotating components. Computational Mechanics 2008; 43:143-150.
3. Bazilevs Y, Calo V, Hughes T, Zhang, Y. Isogeometric fluid-structure interaction: theory, algorithms and computations. Computational Mechanics 2008; 43:3-37.
4. Bazilevs Y, Gohean J, Hughes T, Moser R, Zhang Y. Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Computer Methods in Applied Mechanics and Engineering 2009; 198:3534-3550.
5. Buffa A, Sangalli G, Vazquez, R. Isogeometric analysis in electromagnetics: B-splines approximation. Computer Methods in Applied Mechanics and Engineering 2010; 199:1143-1152.
6. Cottrell JA, Hughes TJR, Bazilevs Y. Isogeometric Analysis. Wiley: New York, 2009.
7. Zhang Y, Bazilevs Y, Goswami S, Bajaj C, Hughes T. Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Computer Methods in Applied Mechanics and Engineering 2007; 196:2943-2959.
8. Eterovic AL, Bathe KJ. An interface interpolation scheme for quadratic convergence in the finite element analysis of contact problems. Computational Methods in Nonlinear Mechanics. Springer: Berlin, New York, 1991; 703-715.
9. Pietrzak G, Curnier A. Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment. Computer Methods in Applied Mechanics and Engineering 1999; 177:351-381.
10. Padmanabhan V, Laursen T. A framework for development of surface smoothing procedures in large deformation frictional contact analysis. Finite Elements in Analysis and Design 2001; 37:173-198.
11. Wriggers P, Krstulovic-Opara L, Korelc J. Smooth C1-interpolations for two-dimensional frictional contact problems. International Journal for Numerical Methods in Engineering 2001; 51:1469-1495.
12. Krstulovic-Opara L, Wriggers P, Korelc J. A C1-continuous formulation for 3D finite deformation frictional contact. Computational Mechanics 2002; 29:27-42.
13. n continuous modelling of smooth contact surfaces using NURBS and application to 2D problems. International Journal for Numerical Methods in Engineering 2003; 57:2177-2203.
14. Landon RL, Hast MW, Piazza SJ. Robust contact modeling using trimmed NURBS surfaces for dynamic simulations of articular contact. Computer Methods in Applied Mechanics and Engineering 2009; 198:2339-2346.
15. Temizer İ, Wriggers P, Hughes TJR. Contact treatment in isogeometric analysis with NURBS. Computer Methods in Applied Mechanics and Engineering 2011; 200(9-12):1100-1112.
16. Laursen TA. Computational Contact and Impact Mechanics. Springer: Berlin, 2002.
17. Wriggers P. Computational Contact Mechanics (2nd edn). Springer: Berlin, 2006.
18. Zavarise G. Problemi termomeccanici di contatto-aspetti fisici e computazionali, Tesi di Dottorato in Meccanica delle Strutture, Istituto di Scienza e Tecnica delle Costruzioni, Padova, Italy, 1991 (in Italian).
19. Piegl L, Tiller W. The NURBS Book (2nd edn). Springer: Berlin, Heidelberg, New York, 1996.
20. Hughes TJR, Reali A, Sangalli G. Efficient quadrature for NURBS-based isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 2010; 199:301-313.
21. Fischer KA, Wriggers P. Frictionless 2D contact formulations for finite deformations based on the mortar method. Computational Mechanics 2005; 36:226-244.
22. Fischer KA, Wriggers P. Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Computer Methods in Applied Mechanics and Engineering 2006; 2006:5020-5036.
23. Hüeber S, Wohlmuth BI. A primal-dual active set strategy for non-linear multibody contact problems. Computer Methods in Applied Mechanics and Engineering 2005; 194:3147-3166.
24. Puso MA, Laursen TA. A mortar segment-to-segment frictional contact method for large deformations. Computer Methods in Applied Mechanics and Engineering 2004; 193:4891-4913.
25. Puso MA, Laursen TA, Solberg J. A segment-to-segment mortar contact method for quadratic elements and large deformations. Computer Methods in Applied Mechanics and Engineering 2008; 197:555-566.
26. Hesch C, Betsch P. A mortar method for energy-momentum conserving schemes in frictionless dynamic contact problems. International Journal for Numerical Methods in Engineering 2009; 77:1468-1500.
27. Tur M, Fuenmayor FJ, Wriggers P. A mortar-based frictional contact formulation for large deformations using Lagrange multipliers. Computer Methods in Applied Mechanics and Engineering 2009; 198:2860-2873.
28. Hüeber S, Wohlmuth BI. Thermo-mechanical contact problems on non-matching meshes. Computer Methods in Applied Mechanics and Engineering 2009; 198:1338-1350.
29. Nowell D, Hills DA, Sackfield A. Contact of dissimilar elastic cylinders under normal and tangential loading. Journal of the Mechanics and Physics of Solids 1988; 36(1):59-75.
30. Hills DA, Nowell D. Mechanics of Fretting Fatigue. Kluwer Academic Publishers: Dordrecht, 1994.
31. Franke D, Düster A, Nübel V, Rank E. A comparison of the h-, p-, hp-, and rp-version of the FEM for the solution of the 2D Hertzian contact problem. Computational Mechanics 2010; 45:513-522.
32. Yang B, Laursen TA, Meng X. Two dimensional mortar contact methods for large deformation frictional sliding. International Journal for Numerical Methods in Engineering 2005; 62:1183-1225.