11R2. Nonlinear Continuum Mechanics of Solids: Fundamental Mathematical and Physical Concepts. - Y Basar (Inst fur Statik und Dynamik, Ruhr-Univ Bochum, Universitatsstr 150, Bochum, 44780, Germany) and D Weichert (Inst fur Allgemeine Mech, RWTH Aachen, Templergraben 62, Aachen, 52056, Germany). Springer-Verlag, Berlin. 2000. 193 pp. ISBN 3-540-66601-X. $59.95.
Reviewed by J Petrolito (Sch of Sci and Eng, La Trobe Univ, PO Box 199, Bendigo, Vic 3550, Australia).
As the author states in the preface, “linear elasticity is the ‘mother of all theories’ in continuum physics.” Given this, it is not surprising that there are numerous books that cover the theory at varying levels of sophistication depending on the target audience. Books in this area can generally be grouped depending on whether they concentrate on theory or applications. The current book belongs to the first group, and it aims to provide a concise introduction to the fundamental concepts of the subject. In an unusual development, the book was originally published in a special issue of the Journal of Elasticity.
The book is divided into four chapters that discuss the basic aspects of the theory, namely strain, stress, constitutive equations, and equilibrium. The theory is mainly developed using direct tensor notation, and a good background in tensor analysis is assumed. The book includes a good range of exercises that are partly used to develop the theory.
The first chapter introduces the notion of deformation and strain. It emphasizes the exact nonlinear definition of strain and provides a clear discussion of the small strain approximation. These concepts are illustrated by some representative deformation patterns. Chapter 2 discusses the concept of stress and derives the equilibrium equations via the fundamental balance laws of mechanics. The distinction between equilibrium in the deformed and undeformed positions is also discussed.
Chapter 3 links the notions of strain and stress using linear constitutive relationships. The general relationships are specialized for materials that display symmetry in their behavior and for those that are subjected to internal constraints such as incompressibility. The final chapter combines the previous work by developing the alternative forms of the governing differential equations, including a discussion of variational principles and appropriate boundary conditions.
Given the book’s emphasis on basic theory and its size, there is little in the way of practical applications. Moreover, it is not clear from the book how the theory would be used to solve practical problems. Hence, this limits the book’s usefulness in subjects that include a considerable amount of detail on specific applications. Despite this, Primer in Elasticity offers a clear introduction to the fundamental concepts, and it would be a useful text for graduate students who want to gain an understanding of theoretical aspects of elasticity.