The author states in the preface to this book that, in the early 1980s, motivated by the upsurge in research on composite materials, he embarked on anisotropic elasticity research "with little background on isotropic elasticity" and "reluctant and apprehensive in venturing into anisotropic elasticity." He need not have worried. The book under review is a masterly account of the fundamental theory of linear anisotropic elasticity and its applications, with emphasis on the two-dimensional theory. The book consists of 15 chapters. Following a brief 30-page introductory chapter on a summary of relevant results from Matrix Algebra, Chapter 2 presents the basic stress-strain laws for general anisotropic elastic materials, including classification of materials according to the number of symmetry planes. Chapter 3 is concerned with the basic theory and applications of antiplane shear deformations. It is refreshing to see this topic treated in a linear elasticity book before embarking on the considerably more-complicated plane problems. Chapter 3 discusses some very recent developments from the research literature on the anti-plane shear theory. The remainder of the book, except for the final Chapter 15, is concerned with the two-dimensional plane theory of elasticity. The well-known Lekhniskii formulation, involving a fourth-order partial differential equation for an Airy stress function, is briefly summarized in Chapter 4 (15 PP). The remaining chapters form the core of this book. The author is one of the pioneers in the use of the Stroh formalism as an alternative to the Lekhnitskii approach, and this method is described in detail in Chapters 5-7 (108 pp). As the author points out in the preface, this algebraic method was first developed by A.N. Stroh in 1958 and 1962; it has been widely used by the physics, materials science, and applied mathematics communities. The present account is the first to appear in book form, and the author clearly hopes to persuade solid mechanics researchers of its utility. A nice personal touch is provided at the end of Chapter 5, where a brief historical account, including a biography of Stroh (1926-1962), is given. Applications of the Stroh formalism to special subjects are presented in Chapters 8-12, whose contents may be surmised from the chapter headings. Topics covered include Green's functions for infinite space, half-space, and composite space; particular solutions, stress singularities, and stress decay; anisotropic materials with an elliptic boundary; anisotropic media

BOOK REVIEWS tively, expanded. Apart from these addenda and some minor corrections the text remains unchanged. Van Dyke's book is no longer the only one which treats the subject of singular perturbations. Moreover the problems on which the techniques are demonstrated are not quite as central to the mainstream of fluid mechanics as they were in 1964. Nevertheless this book continues to provide a valuable first glimpse of singular perturbation theory for prospective researchers.

The Hertz problem for a rigid spherical indenter on a viscoelastic half-space was studied by Lee and Radok [1] in which the radius a(t) of the contact area is a monotonically increasing function of time t. Later, Hunter [2] studied the rebound of a rigid sphere on a viscoelastic half-space so that the contact radius a(t) increases monotonically to a maximum and then decreases to zero monotonically. The contact problem in which a(t) increases for the second time and decreases again does not seem to have been studied; nor has the contact problem in which a(t) is nonzero initially and decreases monotonically been studied. In this paper, a method is introduced so that the contact problem can be solved for arbitrary a(t). The rigid indenter is assumed to be smooth and axisymmetric but otherwise arbitrary. The viscoelastic solutions are expressed in terms of the associated elastic solutions. A means for measuring the viscoelastic Poisson’s ratio is suggested.

No abstract

No abstract