Mechanics of Composite Materials

, Volume 30, Issue 3, pp 234–243 | Cite as

Virial expansions in problems of effective characteristics. 2. Antiplanar deformation of a fiber composite. analysis of self-consistent methods

  • L. N. Germanovich
  • A. V. Dyskin
Article
Received:
Revised:

Conclusion

The virial expansion for the effective shear modulus (condition of antiplanar deformation) was constructed for an isotropic material with parallel cylindrical inclusions and the terms which are quadratic with respect to the concentration of inclusions were precisely calculated. A comparison of the results obtained with the results found with self-consistent methods showed that the differential (step) method gives a precise solution in the case of inclusions which strongly differ in size and a relatively small error (under 25% in the quadratic term) in the case of identical inclusions. The algebraic method and Lorentz method give more significant errors (up to 100 and 50%) in the quadratic term, respectively.

Keywords

Shear Modulus Significant Error Quadratic Term Small Error Isotropic Material 
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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • L. N. Germanovich
    • 1
    • 2
  • A. V. Dyskin
    • 1
    • 2
  1. 1.University of OklahomaNorman
  2. 2.University of Western AustraliaAustralia

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