Advertisement

Investigation of Contact Pressure Oscillations with Different Segment-to-Segment Based Isogeometric Contact Formulations

  • Vishal Agrawal
  • Sachin S. Gautam
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

Contact problems are considered to be highly sensitive to the geometrical approximation and to the choice of the contact constraint treatment procedures. NURBS based isogeometric analysis of contact problems has recently gained a lot of attention due to the ability of isogeometric analysis to exactly represent the surface of the contacting bodies. It has been observed that for the isogeometric based simulation of contact problems, both the segment-to-segment based non-mortar and mortar contact algorithms have been extensively applied for the treatment of the contact constraints. In this contribution, a comparative study between the non-mortar and mortar contact algorithms to investigate the differences between their accuracy and efficiency is carried out. The performance of each contact algorithm is demonstrated by means of the Hertz contact problem.

Keywords

Contact mechanics Isogeometric analysis NURBS Mortar method 

Notes

Acknowledgment

The authors are grateful to the SERB, DST for supporting this research under project SR/FTP/ETA-0008/2014.

References

  1. 1.
    Laursen, T.A.: Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Wriggers, P.: Computational Contact Mechanics. Springer, Berlin, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Cottrell, J.A., Hughes, T.J.R., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, New York (2009)CrossRefGoogle Scholar
  4. 4.
    Padmanabhan, V., Laursen, T.A.: A framework for development of surface smoothing procedures in large deformation frictional contact analysis. Finite Elem. Anal. Des. 37(3), 173–198 (2011)CrossRefGoogle Scholar
  5. 5.
    Wriggers, P., Krstulovic-Opara, L., Korelc, J.: Smooth \({C}^{1}\)-interpolations for two-dimensional frictional contact problems. Int. J. Numer. Methods Eng. 51(12), 1469–1495 (2001)CrossRefGoogle Scholar
  6. 6.
    Stadler, M., Holzapfel, G.A., Korelc, J.: \({C}^{n}\)-continuous modelling of smooth contact surfaces using NURBS and application to 2D problems. Int. J. Numer. Methods Eng. 57(15), 2177–2203 (2003)CrossRefGoogle Scholar
  7. 7.
    De Lorenzis, L., Wriggers, P., Hughes, T.J.R.: Isogeometric contact: a review. GAMM-Mitteilungen 37(1), 85–123 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Method Appl. Mech. Eng. 194(39–41), 4135–4195 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Agrawal, V., Gautam, S.S.: IGA: a simplified introduction and implementation details for finite element users. J. Inst. Eng. (India) Ser. C (2018).  https://doi.org/10.1007/s40032-018-0462-6
  10. 10.
    Temizer, İ., Wriggers, P., Hughes, T.J.R.: Contact treatment in Isogeometric analysis with NURBS. Comput. Methods Appl. Mech. Eng. 200(9–12), 1100–1112 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lu, J.: Isogeometric contact analysis: geometric basis and formulation for frictionless contact. Comput. Methods Appl. Mech. Eng. 200(5–8), 726–741 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kim, J.Y., Youn, S.K.: Isogeometric contact analysis using mortar method. Int. J. Numer. Methods Eng. 89(12), 1559–1581 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    De Lorenzis, L., Wriggers, P., Zavarise, G.: A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method. Comput. Mech. 48(1), 1–20 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Dimitri, R., De Lorenzis, L., Scott, M.A., Wriggers, P., Taylor, R.L., Zavarise, G.: Isogeometric large deformation frictionless contact using T-splines. Comput. Methods Appl. Mech. Eng. 269, 394–414 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Temizer, İ., Hesch, C.: Hierarchical NURBS in frictionless contact. Comput. Methods Appl. Mech. Eng. 299, 161–186 (2016)MathSciNetCrossRefGoogle Scholar
  16. 16.
    De Lorenzis, L., Temizer, İ., Wriggers, P., Zavarise, G.: A large deformation frictional contact formulation using NURBS-based isogeometric analysis. Int. J. Numer. Methods Eng. 87(13), 1278–1300 (2011)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Temizer, İ., Wriggers, P., Hughes, T.J.R.: Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS. Comput. Methods Appl. Mech. Eng. 209–212, 115–128 (2012)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Dimitri, R., De Lorenzis, L., Wriggers, P., Zavarise, G.: NURBS-and T-spline-based isogeometric cohesive zone modeling of interface debonding. Comput. Mech. 52(2), 369–388 (2014)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Zimmermann, C., Sauer, R.A.: Adaptive local surface refinement based on LR NURBS and its application to contact. Comput. Mech. 60(6), 1011–1031 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Maleki-Jebeli, S., Mosavi-Mashhadi, M., Baghani, M.: A large deformation hybrid isogeometric-finite element method applied to cohesive interface contact/debonding. Comput. Methods Appl. Mech. Eng. 330, 395–414 (2018)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Sauer, R.A.: Local finite element enrichment strategies for 2D contact computations and a corresponding post-processing scheme. Comput. Mech. 52, 301–319 (2013)MathSciNetCrossRefGoogle Scholar
  22. 22.
    De Falco, C., Reali, A., Vãzquez, R.: GeoPDEs: a research tool for isogeometric analysis of PDEs. Adv. Eng. Softw. 42(12), 1020–1034 (2011)CrossRefGoogle Scholar
  23. 23.
    Piegl, L., Tiller, W.: The NURBS book. Monographs in Visual Communication. Springer, Heidelberg (2012)zbMATHGoogle Scholar
  24. 24.
    Fischer, K.A., Wriggers, P.: Frictionless 2D contact formulations for finite deformations based on the mortar method. Comput. Mech. 36(3), 226–244 (2005)CrossRefGoogle Scholar
  25. 25.
    Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1987)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Indian Institute of Technology GuwahatiGuwahatiIndia

Personalised recommendations