Acta Mechanica

, Volume 230, Issue 3, pp 953–964 | Cite as

A textile architecture-based hyperelastic model for rubbers reinforced by knitted fabrics

  • Rui Li
  • Dianyun ZhangEmail author
Original Paper


A new anisotropic hyperelastic model has been developed to model the deformation response of a knitted-fabric-reinforced rubber composite. The composite has a sandwich structure with a fiber net layer embedded in two rubber layers. Due to the architecture of the knitted fabric, the composite demonstrates an anisotropic hyperelastic response, which is modeled through a strain energy density function that incorporates the effects of deformed rubbers and stretched fibers. The rubber is considered as a neo-Hookean material, while the knitted fabrics are modeled as cords with negligible stiffness in bending. The effect of reinforcement comes from the conservation of the total length of the fiber cords. In addition, a slack variable is proposed to account for the effect of processing-induced fabric pre-stretch or fabric slack on the resulting composite response. This novel approach enables the determination of the constitutive behavior of the composite in closed form based on the constituent rubber and fiber properties and fabric architectures. The proposed analytical model is validated through a full 3D finite element (FE) model, in which the rubber and fiber reinforcement are modeled explicitly. Since the proposed model captures the key parameters that dictate the deformation response of knitted-fabric-reinforced composites, it can be employed as an efficient modeling tool to guide the design of rubbers and fabric architectures with targeted composite performance.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. 1.
    Huang, Z.M., Ramakrishna, S.: Micromechanical modeling approaches for the stiffness and strength of knitted fabric composites: a review and comparative study. Compos. Part A Appl. Sci. Manuf. 31(5), 479–501 (2000)CrossRefGoogle Scholar
  2. 2.
    Leong, K., Ramakrishna, S., Huang, Z., Bibo, G.: The potential of knitting for engineering compositesa review. Compos. Part A Appl. Sci. Manuf. 31(3), 197–220 (2000)CrossRefGoogle Scholar
  3. 3.
    ASTM D412-16, Standard Test Methods for Vulcanized Rubber and Thermoplastic ElastomersTension. ASTM International, West Conshohocken, PA (2016)Google Scholar
  4. 4.
    ASTM D380-94(2012), Standard Test Methods for Rubber Hose. ASTM International, West Conshohocken, PA (2012)Google Scholar
  5. 5.
    ASTM E143-13, Standard Test Method for Shear Modulus at Room Temperature. ASTM International, West Conshohocken, PA (2013)Google Scholar
  6. 6.
    Manach, P.Y.: Mechanical behavior of fabric-reinforced elastomer straight flexible hoses. Appl. Comput. Mech. 2(1), 291–302 (2008)Google Scholar
  7. 7.
    Pidaparti, R.M., May, A.W.: A micromechanical analysis to predict the cord–rubber composite properties. Compos. Struct. 34(4), 361–369 (1996)CrossRefGoogle Scholar
  8. 8.
    Dinh, T., Rezaei, A., Daelemans, L., Mollaert, M., Van Hemelrijck, D., Van Paepegem, W.: A hybrid micro-meso-scale unit cell model for homogenization of the nonlinear orthotropic material behavior of coated fabrics used in tensioned membrane structures. Compos. Struct. 162, 271–279 (2016)CrossRefGoogle Scholar
  9. 9.
    Sun, W., Lin, F., Hu, X.: Computer-aided design and modeling of composite unit cells. Compos. Sci. Technol. 61(2), 289–299 (2001)CrossRefGoogle Scholar
  10. 10.
    Liu, D., Christe, D., Shakibajahromi, B., Knittel, C., Castaneda, N., Breen, D., Dion, G., Kontsos, A.: On the role of material architecture in the mechanical behavior of knitted textiles. Int. J. Solids Struct. 109, 101–111 (2017)CrossRefGoogle Scholar
  11. 11.
    Gough, V.: Stiffness of cord and rubber constructions. Rubber Chem. Technol. 41(4), 988–1021 (1968)CrossRefGoogle Scholar
  12. 12.
    Tangorra, G.: Fiber-reinforced, oriented rubber sheets. In: Proceedings of International Rubber Conference, Moscow, Russia, pp. 459–466 (1969)Google Scholar
  13. 13.
    Pidaparti, R.: Analysis of cord–rubber composite laminates under combined tension and torsion loading. Compos. Part B Eng. 28(4), 433–438 (1997)CrossRefGoogle Scholar
  14. 14.
    Rao, S., Daniel, I.M., Gdoutos, E.E.: Mechanical properties and failure behavior of cord/rubber composites. Appl. Compos. Mater. 11(6), 353–375 (2004)CrossRefGoogle Scholar
  15. 15.
    Qiu, G.Y., Pence, T.J.: Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids. J. Elast. 49, 1–30 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Holzapfel, G.A., Gasser, T.C., Ogden, R.W.: A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. Phys. Sci. Solids 61(1–3), 1–48 (2000)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Holzapfel, G.A., Gasser, T.C., Stadler, M.: A structural model for the viscoelastic behavior of arterial walls: continuum formulation and finite element analysis. Eur. J. Mech. A Solids 21(3), 441–463 (2002)CrossRefzbMATHGoogle Scholar
  18. 18.
    Demirkoparan, H., Pence, T.J.: Swelling of an internally pressurized nonlinearly elastic tube with fiber reinforcing. Int. J. Solids Struct. 44(11), 4009–4029 (2007)CrossRefzbMATHGoogle Scholar
  19. 19.
    Fereidoonnezhad, B., Naghdabadi, R., Arghavani, J.: A hyperelastic constitutive model for fiber-reinforced rubber-like materials. Int. J. Eng. Sci. 71, 36–44 (2013)CrossRefzbMATHGoogle Scholar
  20. 20.
    Yang, H., Yao, X.F., Ke, Y.C., Ma, Y.J., Liu, Y.H.: Constitutive behaviors and mechanical characterizations of fabric reinforced rubber composites. Compos. Struct. 152, 117–123 (2016)CrossRefGoogle Scholar
  21. 21.
    Peng, X.Q., Guo, Z.Y., Moran, B.: An anisotropic hyperelastic constitutive model with fiber-matrix shear interaction for the human annulus fibrosus. J. Appl. Mech. 73, 815–824 (2006)CrossRefzbMATHGoogle Scholar
  22. 22.
    Peng, X., Guo, G., Zhao, N.: An anisotropic hyperelastic constitutive model with shear interaction for cord rubber composites. Compos. Sci. Technol. 78, 69–74 (2013)CrossRefGoogle Scholar
  23. 23.
    Peng, X., Guo, Z., Du, T., Yu, W.R.: A simple anisotropic hyperelastic constitutive model for textile fabrics with application to forming simulation. Compos. Part B Eng. 52, 275–281 (2013)CrossRefGoogle Scholar
  24. 24.
    Nolan, D.R., Gower, A.L., Destrade, M., Ogden, R., McGarry, J.P.: A robust anisotropic hyperelastic formulation for the modelling of soft tissue. J. Mech. Behav. Biomed. Mater. 39, 48–60 (2014)CrossRefGoogle Scholar
  25. 25.
    Chebbi, E., Wali, M., Dammak, F.: An anisotropic hyperelastic constitutive model for short glass fiber-reinforced polyamide. Int. J. Eng. Sci. 106, 262–272 (2016)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of ConnecticutStorrsUSA

Personalised recommendations