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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bridgens, B., Gosling, P.: Direct stress-strain representation for coated woven fabrics. Comput. Struct. 82, 1913–1927 (2004)
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)
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)
Fischer, M.: Carat++ Dokumentation. Lehrstuhl für Statik - Technische Universität München (2008)
Gosling, P., Bridgens, B.: Material testing and computational mechanics: a new philosophy for architectural fabrics. Int. J. Space Struct. 23(4), 215–232 (2008)
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)
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)
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)
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)
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)
Linhard, J.: Numerish-mechanische Betrachtung des Entwurfsprozesses von Membrantragwerken. Ph.D. thesis, Technischen Universität München, Fakultät für Bauingenieur- und Vermessungswesen (2009)
Münsch, R., Reinhardt, H.W.: Zur Berechnung von Membrantragwerken aus beschichteten Geweben mit Hilfe genäherter elastischer Materialparameter. Bauingenieur 70(6), 271–275 (1995)
Piegl, L.: On NURBS: a survey. IEEE Comput. Graphics Appl. 11(1), 55–71 (1991)
Piegl, L., Tiller, W.: The NURBS Book. Springer (1997)
Rogers, D.F.: An Introduction to NURBS: With Historical Perspective, 1st edn. Morgan Kaufmann (2000)
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), 315–330
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)
Simo, J., Hughes, T.: Computational Inelasticity, vol. 7. Springer (1998)
Simo, J.C., Taylor, R.L.: Consistent tangent operators for rate-independent elastoplasticity. Comput. Methods Appl. Mech. Eng. 48, 101–118 (1985)
Souza Neto, E., Perić, D., Owen, D.: Computational Methods for Plasticity: Theory and Applications. Wiley (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Coelho, M., Roehl, D., Bletzinger, KU. (2016). Material Model Based on Response Surfaces of NURBS Applied to Isotropic and Orthotropic Materials. In: Muñoz-Rojas, P. (eds) Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials. Advanced Structured Materials, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-04265-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-04265-7_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04264-0
Online ISBN: 978-3-319-04265-7
eBook Packages: EngineeringEngineering (R0)