Skip to main content
SpringerLink
Log in

Nets with Hexagonal Cell Structure

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

We establish a continuum theory of inextensible nets with hexagonal cell structure. Some qualitative properties of the equilibrium problem and possible singularities are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Caillerie, D., Mourad, A., Raoult, A.: Cell-to-muscle homogenization. Application to a constitutive law for the myocardium. ESAIM: Math. Model. Numer. Anal. 37(4), 681–698 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Caillerie, D., Mourad, A., Raoult, A.: Discrete homogenization in graphene sheet modeling. J. Elast. 84, 33–68 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Olhoff, N., Taylor, J.E.: On structural optimization. Trans. ASME Ser. E J. Appl. Mech. 50, 1139–1151 (1983)

    MATH  MathSciNet  Google Scholar 

  4. Pipkin, A.C.: Inextensible networks with slack. Q. Appl. Math. 40(1), 63–71 (1982)

    MATH  MathSciNet  Google Scholar 

  5. Pipkin, A.C.: Continuously distributed wrinkles in fabrics. Arch. Ration. Mech. Anal. 95, 93–115 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Pipkin, A.C.: Some examples of crinkles. In: Ericksen, J., Kinderlehrer, D., Kohn, R., Lions, J.-L. (eds.) Homogenization and Effective Moduli of Materials and Media, vol. 1, of IMA vol. Math. its Appl., pp. 182–195. Springer-Verlag (1986)

  7. Pipkin, A.C.: Relaxed energy densities for large deformations of membranes. IMA J. Appl. Math. 52(7), 297–308 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Pipkin, A.C.: Energy theorems for infinitesimal plane wrinkling of inextensible networks. IMA J. Appl. Math. 54, 285–299 (1995)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Pipkin, A.C., Rogers, T.G.: Infinitesimal plane wrinkling of inextensible networks. J. Elast. 17(1), 35–52 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Pitteri, M., Zanzotto, G.: Continuum models for phase transitions and twinning in crystals, volume 19 of Applied Mathematics (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2003.

  11. Rivlin, R.S.: Plane strain of a net formed by inextensible cords. J. Rational Mech. Anal. 4, 951–974 (1955)

    MathSciNet  Google Scholar 

  12. Rivlin, R.S.: The deformation of a membrane formed by inextensible cords. Arch. Ration. Mech. Anal. 2, 447–476 (1959)

    Article  MathSciNet  Google Scholar 

  13. Steigmann, D.J.: Proof of a conjecture in elastic membrane theory. J. Appl. Mech., ASME 53, 955–956 December (1986)

    Article  MATH  Google Scholar 

  14. Steigmann, D.J., Pipkin, A.C.: Finite deformations of wrinkled membranes. Q. J. Mech. Appl. Math. 42(3), 427–440 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  15. Steigmann, D.J., Pipkin, A.C.: Equilibrium of elastic nets. Phil. Trans. R. Soc. Lond., A 335, 419–454 (1991)

    Article  MATH  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Georisorse e Territorio, Università di Udine, Via del Cotonificio 114, 33100, Udine, Italy

    C. Davini

  2. Dipartimento di Progettazione e Costruzione dell‘Ambiente, Università di Camerino, Viale della Rimembranza, 63100, Ascoli Piceno, Italy

    P. Governatori

Authors
  1. C. Davini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Governatori
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Davini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davini, C., Governatori, P. Nets with Hexagonal Cell Structure. J Elasticity 92, 35–59 (2008). https://doi.org/10.1007/s10659-007-9148-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10659-007-9148-7

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation