Micromechanics of Composites

Micromechanics of Composites

Multipole Expansion Approach

2nd Edition - February 15, 2020

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  • Author: Volodymyr Kushch
  • eBook ISBN: 9780128223802
  • Paperback ISBN: 9780128232538

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Micromechanics of Composites: Multipole Expansion Approach, Second Edition outlines substantial recent progress in the development of the multipole expansion method and focuses on its application to actual micromechanical problems. The book covers micromechanics topics such as conductivity and elasticity of particulate and fibrous composites, including those with imperfect and partially debonded interfaces, nanocomposites, cracked solids, and more. Complete analytical solutions and accurate numerical data are presented in a unified manner for the multiple inhomogeneity models of finite, semi-, and infinite heterogeneous solids. This new edition has been updated to include the theories and techniques of the multipole expansion method. Two entirely new chapters covering the conductivity and elasticity of composites with ellipsoidal inhomogeneities and anisotropic constituents have been added. A special emphasis is made on the heterogeneous solids with imperfect interfaces, including the nanoporous and nanocomposite materials.

Key Features

  • Gives a systematic account on the multipole expansion method, including its theoretical foundations, analytical and numerical techniques, and a new, dipole moment-based approach to the homogenization problem
  • Contains detailed analytical and numerical analyses of a variety of micromechanical multiple inhomogeneity models, providing clear insight into the physical nature of the problems under study
  • Provides a reliable theoretical framework for developing the full-field based micromechanical theories of a composite’s strength, brittle/fatigue damage development, and other properties


Academic researchers and professional engineers/material scientists working in mechanics of materials, computational materials science, mechanical and chemical engineering, civil engineering

Table of Contents

  • 1. Multipole expansion approach
    2. Potential fields of interacting spherical inhomogeneities
    3. Periodic multipoles and RUC model of composite
    4. Elastic solid with spherical inhomogeneities
    5. Elasticity of composite half-space, layer and bulk
    6. Conductivity of solid with spheroidal inhomogeneities
    7. Elastic solid with spheroidal inhomogeneities
    8. Composites with transversely isotropic constituents
    9. Conductivity of ellipsoidal particle composite
    10. Elasticity of ellipsoidal particle composite
    11. Circular fiber composite with perfect interfaces
    12. Fibrous composite with interface cracks
    13. Solids with elliptic inhomogeneities
    14. Cracked solids
    15. Elliptic fiber composite with imperfect interface
    16. Fibrous composite with anisotropic constituents

    A. Spherical harmonics and related theory
    B. Spheroidal harmonics and related theory
    C. Ellipsoidal harmonics and related theory
    D. Selected properties of R and X functions
    E. Elliptic harmonics and related theory

Product details

  • No. of pages: 640
  • Language: English
  • Copyright: © Butterworth-Heinemann 2020
  • Published: February 15, 2020
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9780128223802
  • Paperback ISBN: 9780128232538

About the Author

Volodymyr Kushch

Prof. Volodymyr Kushch is Leading Research Scientist, Institute for Superhard Materials of the National Academy of Sciences of Ukraine. He is the author of Micromechanics of Composites as well as dozens of peer-reviewed papers. He has over thirty years of research and industry experience in micromechanics of composites and computational mechanics, with research interests that include advanced analytical and numerical methods in mechanics of heterogeneous solids, suspensions and bubbly liquids, computational materials science, mathematical physics, and more.

Affiliations and Expertise

Head of Laboratory, Institute for Superhard Materials, The National Academy of Sciences of Ukraine

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