1R20. Mechanics of Periodically Heterogenous Structures. Foundations of Engineering Mechanics. - Edited by LI Manevitch, IV Andrianov, VG Oshmyan (Inst of Chem Phys, 4 Kosygin St, Moscow, 117977, Russia). Springer-Verlag, Berlin. 2002. 264 pp. ISBN 3-540-41630-7. $89.95.
S Abrate (Col of Eng, Southern Illinois Univ, Mailcode 6603, Carbondale IL 62901-6603).
This book, written by three members of the Institute of Chemical Physics in Moscow, Russia, is dedicated to the application of the Mathematical Homogenization Theory (MHT). As indicated in the preface, many publications provide a rigorous presentation of the theory. Instead, these authors decided to focus on applications to composite materials and heterogeneous plates and shells. In their introduction, the authors state that “researchers often restrict their study to the proof of the solution existing” and that to solve practical problems effective analytical or numerical procedures are needed. The authors have made many contributions in this area as indicated by the 50 articles listed in the list of references for which one of them is listed as author or co-author.
The first chapter presents basic definitions and results from homogenization theory as it applies to heterogeneous solids with periodic microstructure. The following chapters deal with applications to composite materials, beams with concentrated masses and discrete elastic supports, reinforced plates, reinforced shells, corrugated plates, perforated plates and shells, and other periodic structures. A list of 218 references is also provided. As indicated in the introduction, the MHT was developed by many researchers in France, Italy, Russia, the USA, and the Ukraine. Contributions from Russian and Ukrainian scientists are featured prominently in this book, but contributions from other researchers are cited as well. A systematic approach is taken throughout the book to show how the MHT is used to study many problems through examples. The major steps are clearly explained, and major results are usually presented in graphical form. The book is well written and provides an uncluttered view of how homogenization theory can be applied to mechanics problems. The book is well produced and easy to read, but the quality of some the figures is lacking.
The authors do not define the intended audience for this book. It can be said that it is not written as a textbook or as a reference for experienced researchers in that field, but rather as an introduction for new researchers. There are several well-known books in this area: Bensoussan et al. (1978), Sanchez Palencia (1980, 1987), Kalamkarov (1992), and Lewinki and Talega (2000). In comparison, the present text purposely skips mathematical considerations that can be overwhelming and focuses more on applications via examples. The result is a concise presentation that is much more accessible. The background required to appreciate this book includes calculus, partial differential equations, theory of elasticity, theory of beams, plates, and shells. Mechanics of Periodically Heterogenous Structures should be of interest to researchers wanting to familiarize themselves with the MHT and could serve as a basis for a course for advanced graduate students.