IDEAS home Printed from
   My bibliography  Save this article

Effective elastic properties of composites of ellipsoids (II). Nearly disk- and needle-like inclusions


  • Wei, Gaoyuan
  • Edwards, S.F.


A general analytic solution has been obtained to effective Poisson ratio and Young's modulus of an isotropic two-phase disordered composite composed of an incompressible matrix and elliptic or ellipsoidal inclusions, each having a Poisson ratio of −1, in the mean-field approximation, which yields a further result that as long as the inclusion area or volume fraction exceeds 0.33, 0.83, 0.42, 0.61 and 0.85 for nearly disc-, blade-, sphere-, disk- and neddle-like inclusions, respectively, it is always possible to make the resulting composite auxetic. Analytic expansions of the effective elastic moduli in the parameters characterizing a small deviation of inclusion shapes from blades or disks or needles have been developed, giving good approximations when truncated at second order. Similar analytic expansions to fifth order of the depolarizing or demagnetizing factors have also been presented. For a matrix having a non-negative Poisson ratio, it is found that auxeticity windows exist only for auxetic inclusions, and a maximum effective Young's modulus occurs at a certain value of volume fraction of auxetic inclusions that are not far from blade- or disk- or needle-like. This maximum-Young's-modulus effect may be advantageously used to produce technologically important high-strength auxetic composites as in the case of nearly disc-like or spherical inclusions studied before.

Suggested Citation

  • Wei, Gaoyuan & Edwards, S.F., 1999. "Effective elastic properties of composites of ellipsoids (II). Nearly disk- and needle-like inclusions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 404-423.
  • Handle: RePEc:eee:phsmap:v:264:y:1999:i:3:p:404-423
    DOI: 10.1016/S0378-4371(98)00464-6

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    As the access to this document is restricted, you may want to search for a different version of it.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:264:y:1999:i:3:p:404-423. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.