Applied Mathematics and Mechanics

, Volume 19, Issue 9, pp 869–879 | Cite as

Differential geometrical method in elastic composite with imperfect interfaces

  • Tong Jinzhang
  • Guan Lingyun
  • Zhang Qingiie


A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite matarials with imperfect interface which the inclusions are assumed to be ellipsoidal of revolutions. All of the interface integral items participating in forming the potential and complementary energy functionals of the composite materials are expressed in terms of intrinsic quantities of the ellipsoidal of revolutions. Based on this, the upper and the lower bound for the effective elastic moduli of the composite materials with inclusions described above have been derived Under three limiting conditions of sphere, disk and needle shaped inclusions, the results of this paper will return to the bounds obtained by Hashin[6] (1992).

Key words

differential geometrical method composite imperfect interface interface integral effective modulus 


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  1. [1]
    Z. Hashin, Analysis of composite materials—A survey,J. Appl. Mech.,50, 3 (1983), 481–505.MATHCrossRefGoogle Scholar
  2. [2]
    Tong Jinzhang and Wu Xuejun, Differential geometrical structures of a two-phase, elastic composite materials,Modern Mathematics and Mechanics (MMM-V), edited by Chen Zhida, China Institute of Mining and Technology Press (1993), 157–161. (in Chinese)Google Scholar
  3. [3]
    J. D. Achenbach and H. Zhu, Effect of interphases on micro and macromechanical behavior of hexagonal—array fiber composite,J. Appl. Mech.,57, 4 (1990), 956–963.Google Scholar
  4. [4]
    Y. Benveniste, The effective mechanical behavior of composite materials with imperfect contact between the constituents,Mechanics of Materials,4 (1985), 197–208.CrossRefGoogle Scholar
  5. [5]
    Z. Hashin, The spherical inclusion with imperfect interface,J. Appl. Mech.,58, 2 (1991), 444–449.Google Scholar
  6. [6]
    Z. Hashin, Extremum principles for elastic heterogeneous media with imperfect interface and their application to bounding effective moduli,J. Mech. Phys. Solids,40, 4 (1992). 767–781.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Tong Jinzhang, Nan Cewen and Jin Fusheng, Hill decomposition theorem of the four-rank isotropic tensors and its applications,Journal of Wuhan University of Technology,18, 3 (1996), 111–114. (in Chinese)Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Tong Jinzhang
    • 1
  • Guan Lingyun
    • 1
  • Zhang Qingiie
    • 1
  1. 1.Department of Engineering MechanicsWuhan University of TechnologyWuhanP. R. China

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