Skip to main content

Vectorial Microstructures: Applications to Fabrics and Granular Media

  • Chapter
Mechanics of Microstructured Solids 2

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 50))

  • 1067 Accesses

Abstract

Textile fabrics and 2D granular media can be modelled by means of non-classical nonlinear elasticity, in particular using the theory of vectorial microstructures. The field equations are obtained via a variational principle and suitable constitutive relations are given in both cases. The microstructure takes into account the micro-ondulation of the fibres in textiles and the grains in granular media.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Casasso, A., Pastrone, F.: Nonlinear Waves Motion in Complex Elastic Structures. Rend. Circ. Palermo. Serie II 78(suppl.), 45–58 (2006)

    MathSciNet  Google Scholar 

  2. Engelbrecht, J.: Nonlinear wave dynamics. Complexity and simplicity. Kluwer, Dordrecht (1997)

    MATH  Google Scholar 

  3. Engelbrecht, J., Pastrone, F., Braun, M., Berezovski, A.: Hierarchy of waves in non-classical materials. In: Delsanto, P.P. (ed.) The universality of nonclassical nonlinearity, with applications to NDE and Ultrasonics. Springer, New York (2006)

    Google Scholar 

  4. Indelicato, G.: Mechanical models for 2D fiber networks and textiles, PhD Thesis, Torino (2008)

    Google Scholar 

  5. Indelicato, G.: Inextensible networks with bending and twisting effects. Rend. Sem. Mat. Un. Pol. Torino 65(2), 261–268 (2007)

    MATH  MathSciNet  Google Scholar 

  6. Indelicato, G.: The influence of the twist of individual fibers in 2D fibered networks. Intl. J. Solids and Structures 46(3-4), 912–922 (2009)

    Article  Google Scholar 

  7. Luo, C., Steigmann, D.J.: Bending and Twisting Effects in the Three-Dimentional Finite Deformations of an Inextensible Network. In: Advances in the Mechanics of Plates and Shells, pp. 213–228. Kluwer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  8. Maugin, G.A.: Nonlinear Waves in Elastic Crystal. Oxford University Press, UK (1999)

    Google Scholar 

  9. Mindlin, R.D.: Microstructure in linear elasticity. Arch. Ratl. Mech. and Anal. 1, 51–78 (1964)

    MathSciNet  Google Scholar 

  10. Pastrone, F.: Mathematical Models of Microstructured Solids. Lect. Notes Mech. 4/04 Tallinn Tech. Univ. Tallinn (2004)

    Google Scholar 

  11. Pastrone, F.: Waves Propagation in Microstructured Solids. Mathematics and Mechanics of Solids 10, 349–357 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Pastrone, F.: Nonlinearity and complexity in Elastic Wave Motion. In: Delsanto, P.P. (ed.) The universality of nonclassical nonlinearity, with applications to NDE and Ultrasonics. Springer, New York (2006)

    Google Scholar 

  13. Pastrone, F.: Microstructures and granular media. Rend. Sem. Univ. Pol. Torino 65(2) (2007)

    Google Scholar 

  14. Pipkin, A.C.: Some Developments in the Theory of Inextensible Networks. Quart. Appl. Math. 38, 343–355 (1980)

    MATH  MathSciNet  Google Scholar 

  15. Samsonov, A.M.: Strain soliton in solids and how to construct them. Chapman & Hall/CRC, New York (2000)

    Google Scholar 

  16. Wang, W.B., Pipkin, A.C.: Inextensible Networks with Bending Stiffness. Q. Jl. Mech. Appl. Math. 39, 359–434 (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Pastrone, F. (2010). Vectorial Microstructures: Applications to Fabrics and Granular Media. In: Ganghoffer, JF., Pastrone, F. (eds) Mechanics of Microstructured Solids 2. Lecture Notes in Applied and Computational Mechanics, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05171-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-05171-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05170-8

  • Online ISBN: 978-3-642-05171-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics