Advertisement

Material Model Based on Response Surfaces of NURBS Applied to Isotropic and Orthotropic Materials

  • Marianna CoelhoEmail author
  • Deane Roehl
  • Kai-Uwe Bletzinger
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 49)

Abstract

A finite element analysis depends on the material model used to represent the material behavior of a physical phenomenon. Some materials expose a constitutive behavior that cannot be represented by analytical models. Complex material behavior requires the use of appropriate material models able to represent the response under a wide range of load conditions. This contribution uses a response surface based on non-uniform rational B-splines (NURBS) surfaces to define direct biaxial stress–strain relations. For the application in a finite element method, an approach is suggested to compute the matrix of material coefficients from these surfaces. The method was developed for a plane stress condition, which can be used for membranes, beams and thin plates. Two applications of this method are shown: a large strain elastoplastic material behavior with von Mises yield criterion and a linear elastic orthotropic material behavior (Münsch-Reinhardt). The advantage of this material model is that from results of experimental tests, any kind of material can be modeled by fitting the response surface parameters subjected to monotonic load. This approach might be a good alternative to model new fabrics and polymers used in membrane structures.

References

  1. 1.
    Bridgens, B., Gosling, P.: Direct stress-strain representation for coated woven fabrics. Comput. Struct. 82, 1913–1927 (2004)CrossRefGoogle Scholar
  2. 2.
    Coelho, M., Roehl, D., Bletzinger, K.U.: Using NURBS as response surface for membrane material behavior. In: Textile Composites and Inflatable Structures VI, vol. 1, pp. 166–175. Artes Gráficas Torres S.A., Barcelona (2013)Google Scholar
  3. 3.
    Coelho, M.A.O.: Analysis of pneumatic structures considering nonlinear material models and pressure-volume coupling. Ph.D. thesis, Pontificia Universidade Catolica do Rio de Janeiro (2012)Google Scholar
  4. 4.
    Fischer, M.: Carat++ Dokumentation. Lehrstuhl für Statik - Technische Universität München (2008)Google Scholar
  5. 5.
    Gosling, P., Bridgens, B.: Material testing and computational mechanics: a new philosophy for architectural fabrics. Int. J. Space Struct. 23(4), 215–232 (2008)CrossRefGoogle Scholar
  6. 6.
    Gruttmann, F., Taylor, R.: Theory and finite element formulation of rubberlike membrane shells using principal stretches. Int. J. Numer. Methods Eng. 35(5), 1111–1126 (1992)CrossRefzbMATHGoogle Scholar
  7. 7.
    Hughes, T., Cottrell, J., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kiendl, J., Bazilevs, Y., Hsu, M.C., Wüchner, R., Bletzinger, K.U.: The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches. Comput. Methods Appl. Mech. Eng. 199(37–40), 2403–2416 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kiendl, J., Bletzinger, K.U., Linhard, J., Wüchner, R.: Isogeometric shell analysis with Kirchhoff-Love elements. Comput. Methods Appl. Mech. Eng. 198, 3902–3914 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kiendl, J., Schmidt, R., Wüchner, R., Bletzinger, K.U.: Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting. Comput. Methods Appl. Mech. Eng. 274, 148–167 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Linhard, J.: Numerish-mechanische Betrachtung des Entwurfsprozesses von Membrantragwerken. Ph.D. thesis, Technischen Universität München, Fakultät für Bauingenieur- und Vermessungswesen (2009)Google Scholar
  12. 12.
    Münsch, R., Reinhardt, H.W.: Zur Berechnung von Membrantragwerken aus beschichteten Geweben mit Hilfe genäherter elastischer Materialparameter. Bauingenieur 70(6), 271–275 (1995)Google Scholar
  13. 13.
    Piegl, L.: On NURBS: a survey. IEEE Comput. Graphics Appl. 11(1), 55–71 (1991)Google Scholar
  14. 14.
    Piegl, L., Tiller, W.: The NURBS Book. Springer (1997)Google Scholar
  15. 15.
    Rogers, D.F.: An Introduction to NURBS: With Historical Perspective, 1st edn. Morgan Kaufmann (2000)Google Scholar
  16. 16.
    Schmidt, R., Kiendl, J., Bletzinger, K.U., Wüchner, R.: Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis. Comput. Vis. Sci. 13(7), 315–330Google Scholar
  17. 17.
    Sevilla, R., Fernández-Méndez, S., Huerta, A.: 3D NURBS-enhanced finite element method (NEFEM) Sonia Fernández-Méndez. Int. J. Numer. Methods Eng. 88, 103–125 (2011)CrossRefzbMATHGoogle Scholar
  18. 18.
    Simo, J., Hughes, T.: Computational Inelasticity, vol. 7. Springer (1998)Google Scholar
  19. 19.
    Simo, J.C., Taylor, R.L.: Consistent tangent operators for rate-independent elastoplasticity. Comput. Methods Appl. Mech. Eng. 48, 101–118 (1985)CrossRefzbMATHGoogle Scholar
  20. 20.
    Souza Neto, E., Perić, D., Owen, D.: Computational Methods for Plasticity: Theory and Applications. Wiley (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Marianna Coelho
    • 1
    Email author
  • Deane Roehl
    • 2
  • Kai-Uwe Bletzinger
    • 3
  1. 1.Departamento de Engenharia CivilUniversidade do Estado de Santa CatarinaJoinvilleBrazil
  2. 2.Instituto TecgrafPontificia Universidade Catolica do Rio de JaneiroRio de JaneiroBrazil
  3. 3.Lehrstuhl fuer StatikTechnische Universitaet MünchenMünchenGermany

Personalised recommendations