11R5. Mathematical Theory of Elasticity. - Richard B Hetnarski and Jozef Ignaczak. Taylor & Francis, London. 2004. 821 pp. ISBN 1-591-69020-X. $134.95.
Reviewed by J Petrolito (Sch of Sci and Eng, La Trobe Univ, PO Box 199, Bendigo, Vic 3550, Australia).
This book is an advanced treatise on theoretical elasticity that is aimed at postgraduate students and researchers in the area. It s a long book, with approximately half the book devoted to fundamental principles and half to applications of the theory. The theoretical development uses a mixture of direct tensor and Cartesian tensor notation, which is summarized in the second chapter. This follows a welcome but uncommon brief biographical review of some of the major figures who have contributed to the field.
Chapters 2 to 6 cover the fundamentals of elasticity theory. Chapter 3 discusses the three basic concepts of the theory, namely stress, strain, and constitutive relationships. Chapter 4 combines these concepts to formulate the governing equations for both static and dynamic problems, including thermal effects. Variational formulations of the equations are given in Chapters 5 and 6. While there is a brief discussion on generating approximate solutions using the Rayleigh-Ritz method, these chapters primarily focus on deriving variational principles. These include the standard principles, such as the total potential energy principle, as well as less common ones such as Gurtin’s variational principle in dynamics.
These solutions have both theoretical and practical applications. For example, they could be used as a starting point for boundary element methods. Chapters 8 to 10 present a variety of solutions for static two-dimensional problems. While some examples are standard, many are not usually found in textbooks in the field and are a useful addition to the literature. The last three chapters extend the examples to dynamic problems.
The theory is complemented by many examples and problems, and some the latter are at the research level. There is also an extensive list of references to the literature for further study. The theory and applications are developed in a clear and concise manner that assists in learning. While many proofs are given, some are omitted with appropriate references to other sources.
In summary, Mathematical Theory of Elasticity is a welcome addition to the field. Its range and scope is extensive, and it covers much material that is not usually found together in one text. The early chapters could be used as the basis for an upper-level undergraduate course that emphasizes the theoretical aspects of elasticity. The whole book succeeds in its aim of covering a broad range of elasticity theory and its applications, and can be recommended as a good reference to the field.