Skip to main content
Top

2015 | OriginalPaper | Chapter

Modeling of Textiles as Nets of One-Dimensional Hyperelastic Strings with Friction Controlled by Capstan Equation

Authors : Vladimir Shiryaev, Julia Orlik

Published in: Numerical Methods and Applications

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper deals with the computational modeling of the in-plane stretch behavior of knitted textiles. Yarns in textiles are modeled as one-dimensional hyperelastic strings with frictional contact. The model is the limiting case of the three-dimensional contact model, as diameters of the yarns’ cross-sections tend to zero. The model is analyzed theoretically and solved by the finite element method with one-dimensional hyperelastic truss elements, with an extension to frictional point-to-point contact. Numerical results for in-plane loading experiments obtained by this approach are discussed and compared with results of real measurements.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
2.
go back to reference Ciarlet, P.: Mathematical Elasticity: Three-Dimensional Elasticity. Studies in Mathematics and Its Applications. North-Holland, Amsterdam (1993) Ciarlet, P.: Mathematical Elasticity: Three-Dimensional Elasticity. Studies in Mathematics and Its Applications. North-Holland, Amsterdam (1993)
3.
go back to reference Gralén, N., Olofsson, B.: Measurement of friction between single fibers. Text. Res. J. 17(9), 488–496 (1947)CrossRef Gralén, N., Olofsson, B.: Measurement of friction between single fibers. Text. Res. J. 17(9), 488–496 (1947)CrossRef
4.
go back to reference Gupta, P.K.: Simple method for measuring the friction coefficient of thin fibers. J. Am. Ceram. Soc. 74(7), 1692–1694 (1991)CrossRef Gupta, P.K.: Simple method for measuring the friction coefficient of thin fibers. J. Am. Ceram. Soc. 74(7), 1692–1694 (1991)CrossRef
5.
go back to reference Johnson, K.: Contact Mechanics. Cambridge University Press, Cambridge (1987) Johnson, K.: Contact Mechanics. Cambridge University Press, Cambridge (1987)
6.
go back to reference Kikuchi, N., Oden, J.: Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia (1987) Kikuchi, N., Oden, J.: Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia (1987)
7.
go back to reference Mielke, A., Rossi, R.: Existence and uniqueness results for general rate-independent hysteresis problems. Math. Models Methods Appl. Sci. 17(01), 81–123 (2007)CrossRefMATHMathSciNet Mielke, A., Rossi, R.: Existence and uniqueness results for general rate-independent hysteresis problems. Math. Models Methods Appl. Sci. 17(01), 81–123 (2007)CrossRefMATHMathSciNet
8.
go back to reference Mielke, A., Roubíček, T.: A rate-independent model for inelastic behavior of shape-memory alloys. Multiscale Model. Simul. 1(4), 571–597 (2003)CrossRefMATHMathSciNet Mielke, A., Roubíček, T.: A rate-independent model for inelastic behavior of shape-memory alloys. Multiscale Model. Simul. 1(4), 571–597 (2003)CrossRefMATHMathSciNet
10.
11.
go back to reference Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton (1997)MATH Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton (1997)MATH
12.
go back to reference Trabucho, L., Viaño, J.: Mathematical modelling of rods. In: Ciarlet, P., Lions, J. (eds.) Handbook of Numerical Analysis, vol. 4, pp. 487–974. Elsevier Science (1996) Trabucho, L., Viaño, J.: Mathematical modelling of rods. In: Ciarlet, P., Lions, J. (eds.) Handbook of Numerical Analysis, vol. 4, pp. 487–974. Elsevier Science (1996)
13.
go back to reference Wriggers, P.: Nonlinear Finite Element Methods. Springer, Heidelberg (2008)MATH Wriggers, P.: Nonlinear Finite Element Methods. Springer, Heidelberg (2008)MATH
Metadata
Title
Modeling of Textiles as Nets of One-Dimensional Hyperelastic Strings with Friction Controlled by Capstan Equation
Authors
Vladimir Shiryaev
Julia Orlik
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-15585-2_25

Premium Partner