Skip to main content

The influence of boundary conditions on the non-local response of a randomly heterogeneous medium

  • Conference paper
IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 97))

Abstract

In this paper, boundary layer effects on the effective non-local response of heterogeneous bodies are studied. Non-local constitutive operators have been obtained in real space for composite materials with a special geometry of the boundary (half space) and for two types of boundary conditions (Dirichlet and Neumann boundary conditions). Finally, the case of periodic laminates has been developed explicitly.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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. Beran, M.J., and McCoy, J.J., 1970, “Mean field variations in a statistical sample of heterogeneous linearly elastic solids”, Int. J. Solids and Structures, Vol. 6, pp. 1035–1054.

    Article  MATH  Google Scholar 

  2. Hashin, Z., and Shtrikman, S., 1962a, “On some variational principles in anisotropic and nonhomogeneous elasticity”, J. Mech. Phys. Solids, Vol. 10, pp. 335–342.

    Article  MathSciNet  ADS  Google Scholar 

  3. Hashin, Z., and Shtrikman, S., 1962b, “A variational approach to the theory of the elastic behavior of multiphase materials”, J. Mech. Phys. Solids, Vol. 11, pp. 127–140.

    Article  MathSciNet  Google Scholar 

  4. Luciano, R., and Willis J.R., 2000, “Bounds on non-local effective relations for random composites loaded by configuration-dependent body forces”, J. Mech. Phys. Solids, Vol. 48, pp. 1827–1849.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Luciano, R., and Willis J.R., 2001a, “Non-local constitutive response of a random laminate subjected to configuration-dependent body forces”, J. Mech. Phys. Solids, Vol. 49, pp. 431–444.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Luciano, R., and Willis J.R., 2001b, “Non-local effective relations for fibre-reinforced composites loaded by configuration-dependent body forces”, to appear in J. Mech. Phys. Solids.

    Google Scholar 

  7. Luciano, R., and Willis J.R., 2001c, “Non-local constitutive equations for functionally graded materials”, to appear in Mechanics of Materials.

    Google Scholar 

  8. Sanchez-Palencia, E., 1987, “Boundary layers and edge effects in composites”, Sanchez-Palencia, E. and Zaoui, A.(Ed.), Homogenization techniques for composite media, Lecture Notes in Physics Vol. 272, Springer Verlag, pp. 121–192.

    Google Scholar 

  9. Willis, J.R., 1982, “Elasticity theory of composites”, Hopkins, H. G. and Sewell, M. J.(Ed.), Mechanics of Solids: The R. Hill 60th Anniversary Volume, Pergamon Press, Oxford, pp. 653–686.

    Google Scholar 

  10. Willis, J.R., 1983, “The overall elastic response of composite materials”, Journal of Applied Mechanics, Vol. 50, pp. 1202–1209.

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Luciano, R., Willis, J.R. (2002). The influence of boundary conditions on the non-local response of a randomly heterogeneous medium. In: Karihaloo, B.L. (eds) IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials. Solid Mechanics and Its Applications, vol 97. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0081-8_28

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0081-8_28

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5977-2

  • Online ISBN: 978-94-017-0081-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics