Micromechanics of Composites

Micromechanics of Composites, 1st Edition

Multipole Expansion Approach

Micromechanics of Composites, 1st Edition,Volodymyr Kushch,ISBN9780124076839






240 X 197

Introduces micromechanics researchers to the multipole expansion approach, a highly efficient analytical method that can be practiced without the expensive software and powerful computers required by computational micromechanics

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Key Features

  • Contains detailed analytical and numerical analyses of a variety of micromechanical multiple inclusion models, providing clear insight into the physical nature of the problems under study
  • Provides researchers with a reliable theoretical framework for developing the micromechanical theories of a composite’s strength, brittle/fatigue damage development and other properties
  • Includes a large amount of highly accurate numerical data and plots for a variety of model problems, serving as a benchmark for testing the applicability of existing approximate models and accuracy of numerical solutions


Micromechanics of Composites: Multipole Expansion Approach is the first book to introduce micromechanics researchers to a more efficient and accurate alternative to computational micromechanics, which requires heavy computational effort and the need to extract meaningful data from a multitude of numbers produced by finite element software code. In this book Dr. Kushch demonstrates the development of the multipole expansion method, including recent new results in the theory of special functions and rigorous convergence proof of the obtained series solutions. The complete analytical solutions and accurate numerical data contained in the book have been obtained in a unified manner for a number of the multiple inclusion models of finite, semi- and infinite heterogeneous solids. Contemporary topics of micromechanics covered in the book include composites with imperfect and partially debonded interface, nanocomposites, cracked solids, statistics of the local fields, and brittle strength of disordered composites.


A multidisciplinary audience consisting of researchers, professionals and graduate students in materials science, mechanics, engineering, applied mathematics, physics and related areas dealing with heterogeneous solids.

Volodymyr Kushch


Dr. Volodymyr Kushch has thirty years of successful experience in Micromechanics of Composite Materials and Computational Mechanics, including - Advanced analytical and numerical methods in composite mechanics; - Particulate and fiber reinforced solid composites; - Suspensions and bubbly liquids; - Multiscale analysis of composite materials; - Computational solid mechanics and materials science; - Methods of mathematical physics and theory of special functions; - FEA simulation of technological processes; - Applied software development.

Affiliations and Expertise

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

Micromechanics of Composites, 1st Edition

Introduction; Potential fields of interacting spherical inclusions; Periodic multipoles: application to composites; Elastic solid with spherical inclusions; Elasticity of composite half-space, layer and bulk; Conductivity of a solid with spheroidal inclusions; Elastic solid with spheroidal inclusions; Composites with transversely isotropic constituents; Circular fiber composite with perfect interfaces; Fibrous composite with interface cracks; Solids with elliptic inclusions; Fibrous composite with anisotropic constituents; References

Quotes and reviews

"Kushch presents the multipole expansion method as an alternative to computational micromechanics for analyzing heterogeneous materials on the level of individual constituents. Being mostly analytical in nature, he says, it constitutes a theoretical basis for high-performance computational algorithms and has found applications in astronomy, physics, chemistry, engineering, statistics, and other fields."--Reference & Research Book News, October 2013

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