Micromechanics of Composites

Multipole Expansion Approach


  • Volodymyr Kushch, Ph.D., Head of Laboratory, Institute for Superhard Materials, The National Academy of Sciences of Ukraine

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.
View full description


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.


Book information

  • Published: June 2013
  • ISBN: 978-0-12-407683-9


"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

Table of Contents

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