An introduction to the theory of elasticity

This textbook is a companion text to that of A. J. M. Spencer (Continuum Mechanics, Longman, London, 1980), and is written in a similar concise style. It provides a selfcontained brief introduction to the theory of elasticity (both infinitesimal and finite theory) suitable for undergraduates and beginning graduate students in applied mechanics, applied mathematics, and materials science. It is published in the series of Longman Mathematical Texts (edited by A. Jeffrey), a set of concisely written (and inexpensively produced) introductory textbooks used primarily in British universities. The major novelty of this textbook on elasticity is that it begins with the finite (i.e., nonlinear) theory (covering the first half of the book) and then proceeds to the infinitesimal (linear) theory, which is shown to be a special case of the former. In this reviewer's opinion, such a treatment in the textbook literature on elasticity is long overdue and the authors are to be commended on their originality in this regard, especially in an introductory book. The first chapter, entitled Deformation and Stress, summarizes those general principles of continuum mechanics that are necessary for the foundations of elasticity. Chapter 2, entitled Finite Elasticity: Constitutive Theory outlines the theory of constitutive equations in finite elasticity both for compressible and incompressible materials. The various forms of strain-energy functions which have been proposed in the literature are described, with citation of some original references. In Chapter 3, entitled Exact Solutions, some of the most important solutions of equilibrium problems in finite elasticity are discussed. Thus, homogeneous and nonhomogeneous deformations are described, together with associated experimental results. These first three chapters form a well-written, self-contained (but, of course, brief) introduction to finite elasticity. The remainder of the book, in four chapters, is concerned with various topics in the classical linear theory of isotropic elasticity governing infinitesimal deformations. Chapter 4, entitled Infinitesimal Theory discusses the process of linearization as well as considerations of uniqueness. Other topics considered include problems involving spherical symmetry, displacement potentials, and solutions for some point force problems. Chapter 5, entitled Antiplane Strain, Plane Strain, and Generalized Plane Stress provides a brief account of the two-dimensional theories of elasticity governing the deformations of the chapter title, including a concise treatment of the complex variable approach for such problems. In Chapter 6, entitled Extension, Torsion, and Bending, the classical Saint-Venant problems of the chapter title are considered, with emphasis on the torsion problem. Curiously, the flexure problem (bending by terminal loads) is not mentioned. The book concludes with Chapter 7, entitled Elastic Waves, which contains a short summary of the most important results in linear isotropic elastodynamics. The style of this book is, by its very nature, overly concise. This is a serious shortcoming in the second half of the book where the treatment of linear elasticity is uneven, with various topics included apparently at random. Those items that are covered are not distinguished by any originality in exposition. Thus, the present book is inferior to the standard textbooks on linear elasticity currently available. However, the first half of the book goes a long way toward remedying this. Here the authors have provided a readable condensed account of finite elasticity theory accessible to the beginner. In view of the current flourishing research activity in mechanical and mathematical aspects of this theory, the contribution of such an introduction for beginning students is a welcome addition to the textbook literature.