Advertisement

The Effective Properties of Brittle/Ductile Incompressible Composites

  • Pedro Ponte Castañeda
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

A new variational method for estimating the effective properties of nonlinear composites in terms of the corresponding properties of linear composites with the same microstructural distributions of phases is applied to an isotropic, incompressible composite material containing a brittle (linear) and a ductile (nonlinear) phase. More specifically, in this particular work the prescription is used to obtain bounds of the Hashin-Shtrikman type for the effective properties of the nonlinear composite in terms of the well-known linear bounds. It can be shown that in some cases the method leads to optimal bounds.

Keywords

Variational Principle Effective Property Effective Energy Nonlinear Material Rigid Inclusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. CHRISTENSEN, R. M. (1979) Mechanics of Composite Materials, Wiley Interscience, New York.Google Scholar
  2. FRANCFORT, G. and MURAT, F. (1987) Archive Rat. Mech. and Analysis 94, 307.CrossRefGoogle Scholar
  3. HASHIN, Z. and SHTRIKMAN, S. (1962) J. Mech. Phys. Solids 10, 335.CrossRefGoogle Scholar
  4. HILL, R. (1963) J. Mech. Phys. Solids 11, 357.CrossRefGoogle Scholar
  5. HUTCHINSON, J.W. (1990) Private communication.Google Scholar
  6. KOHN, R. V. (1990) Private communication.Google Scholar
  7. LEE, B.J. and MEAR, M.E. (1990) Submitted for publication.Google Scholar
  8. PONTE CASTAÑEDA, P. (1990c) To appear.Google Scholar
  9. PONTE CASTAÑEDA, P. (1990b) To appear.Google Scholar
  10. PONTE CASTAÑEDA, P. (1990a) J. Mech. Phys. Solids, in press.Google Scholar
  11. PONTE CASTAÑEDA, P. and WILLIS, J. R. (1988) Proc. R. Soc. Lond. A 416, 217.CrossRefGoogle Scholar
  12. TALBOT, D. R. S. and WILLIS, J. R. (1985) IMA J. Appl. Math. 35, 39.CrossRefGoogle Scholar
  13. VAN TEEL, J. (1984) Convex Analysis, Wiley, New York.Google Scholar
  14. WILLIS, J. R. (1982) In Mechanics of Solids, The Rodney Hill 60 th anniversary volume (ed. H.G. Hopkins & M.J. Sewell), Pergamon Press, Oxford, 653.Google Scholar
  15. WILLIS, J. R. (1990) J. Mech. Phys. Solids, to appear.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Pedro Ponte Castañeda
    • 1
  1. 1.Mechanical EngineeringThe Johns Hopkins UniversityBaltimoreUSA

Personalised recommendations