Review of Fundamentals of Micromechanics of Solids by J. Qu and M. Cherkaoui: John Wiley, New York; 2006; 386 pp.

This book is an outgrowth of lectures given in the courses on micromechanics taught by the authors in their respective institutions. The book integrates the various topics of micromechanics and is primarily targeted for graduate and upper-level undergraduate students. In this book, the classical homogenization theories for the micromechanical deformation and material response of heterogeneous solids are developed using a fundamental mathematical approach. Initial development focuses on classical continuum mechanics as applied toward development of field equations for the micromechanics of solids. These first principles are used to rederive exact classical Eshelby solutions for simple microstructures consisting of a single elastic heterogeneity in an elastic matrix. Extension of the field equations to random media, consisting of a representative sample of heterogeneities, is developed, and classical approximate methods used to derive elastic material properties from these field equations, for random media, are discussed. Applications of these developments toward laminated composites and brittle damage in ceramic materials are taken up, and a brief discussion of exact and approximate methods for nonlinear constituents is also presented. Finally, fundamental ideas of material modeling of metallic crystals undergoing phase transformations are discussed.

The development of the book is geared toward a fundamental understanding of the various classical methods used to analyze material response at the mesoscale, with an introduction to methods used at the sub-mesoscale (crystal scale). The material is presented in a clear and concise fashion for readers with at least a senior graduate standing. Sufficient contrast of the various methods developed in the text is provided for readers to appreciate the applicability of these methods in engineering research. References to additional reading materials are good, and indexing of concepts in the book is excellent. The book is more mathematically based. The physics of length scales needs to be elaborated upon with applications to nanostructures. In the future, the authors should consider devoting a chapter on the physics of length scales.

The book, however, reads very much as a research manuscript, with a collection of various topics of interest to young scientists. However, it could also be used as a textbook for graduate engineering education if the authors included more solved examples and geared suggested problems toward more practical engineering applications. It is in this regard that the book has the most potential when compared to previous manuscripts on similar topics. Finally, the focus of the book is geared toward classical methods for analyzing material response in heterogeneous materials. It does not provide (even in an introductory sense) recent advances in numerical simulations, which use these classical approaches to solve a variety of material problems. It would also be useful if the text introduced the reader to concepts in the thermomechanical response (instead of purely mechanical development) of heterogeneous materials.

Overall, this book offers a comprehensive review of research topics dealing with various aspects of micromechanics of solids and will be useful to researchers interested in these topics as well as to graduate students of materials science looking for concrete topics of application of homogenization principles. In the future, the authors should consider devoting a chapter or more on the computational simulation aspects of micromechanics and homogenization.