9R4. Wave Processes in Solids With Microstructure (Stability, Vibration and Control of Systems, Series A). - Edited by VI Erofeyev (Russian Academy, Russia). World Science Publications, Singapore. 2003. 255 pp. ISBN 981-238-227-5.

Reviewed by A Giannakopoulos (Dept of Civil Eng, Univ of Thessaly, Pedion Areos 38334, Volos, Greece).

The book presents a good account of the mathematics of wave processes in solids with microstructure. The Introduction sets the general outline of the book and presents a good historical background on the topic. The Introduction includes the major part of a valuable list of references, especially from the extensive work of the author. The first chapter gives the main constitutive and equilibrium equations for the specific mathematical models of solids with microstructure (Cosserat, Le Roux, and two-solid mixture). The second chapter presents dispersion and dissipation analysis for various types of traveling waves (longitudinal, shear, surface, and noise). The analysis follows from classical assumptions of the traveling waveforms that influence directly the kinematics (displacements and/or rotations). In some cases, nonclassical assumptions are used successfully. The second chapter includes quasi-harmonic wave interactions (nonlinear resonant and high frequency interactions of waves). Chapter 3 introduces the damaged medium and the magnetoelastic medium. The context of this chapter is somehow out of the essential theme of the book. The author should have tried to show more connections of the context of Chapter 3 with the rest of the book (as he has done successfully with Chapter 7). Chapter 4 clarifies the results for the Cosserat continuum, Chapter 5 for the two-components mixture and Chapter 6 for the micromorphic solids in Mindlin’s spirit. Chapter 7 makes a successful connection of the medium with dislocations, with Cosserat type of continuum. Finally, Chapter 8 describes wave problems of micropolar fluids. The last chapter seems to be written in a rather uncoordinated way with the co-author mentioned in the Preface. It definitely needs thorough revision. The bibliography is very extensive and very adequate, however, there are also some references that have not been linked to the text. The index suffers also from link problems with the text. It is on the positives of the book the realistic examples that are presented, although it is not always clear why the models do better than traditional models with direct inhomogeneities and anisotropies.

There are numerous typos and occasionally severe language problems in the text, which make the book very difficult to follow in certain cases. Symbols often change meaning, sometimes even in the same chapter, creating confusion. A careful and dedicated reader can overcome these problems. The book is on a topic that has a lot of renewed interest. It can serve as an advanced textbook to complement wave mechanics standard books. The book can also serve as reference, but the reader is advised to read several key papers beforehand, to get a clear picture of the mathematical models of solids with microstructure, especially from the constitutive point of view. The book can be of general interest and should be in libraries that specialize in wave mechanics. It is recommended to researchers that have special interest in topics of mathematical treatment of solids with microstructure, keeping in mind that issues of initial and boundary conditions are not covered in the book.