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

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The simplifications arising in elasticity theory from consideration of resultant boundary conditions instead of mathematically exact pointwise conditions have been the key to widespread application of the subject. Thus, for example, theories for strength of materials, plates, and shells rely on such relaxed boundary conditions for their development. The justification of this approximation is usually based on some form of the celebrated Saint-Venant’s principle. A comprehensive survey of contemporary research concerning Saint-Venant’s principle (covering primarily the period 1965–1981) was given by Horgan and Knowles (1983). Since that time, several developments have taken place demonstrating continued interest in understanding the ramifications of Saint-Venant’s principle from both a physical and mathematical point of view. In this article we review these developments, thus providing an update on contributions to this fundamental engineering principle.

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Cavitation phenomena in nonlinearly elastic solids have been the subject of extensive investigation in recent years. The impetus for much of these theoretical developments has been supplied by pioneering work of Ball in 1982. Ball investigated a class of bifurcation problems for the equations of nonlinear elasticity which model the appearance of a cavity in the interior of an apparently solid homogensous isotropic elastic sphere or cylinder once a critical external tensile load is attained. This model may also be interpreted in terms of the sudden rapid growth of a pre-existing microvoid. In this paper, we briefly summarize some of the main results obtained to date on radially symmetric cavitation, using the bifurcation model. The paper is a review and a comprehensive list of references is given to original work where details of the analyses may be found.

Certain aspects of the mechanical response of arterial walls can be described using nonlinear elasticity theory. Uniaxial tests on vascular walls reveal nonlinear stress-strain behavior, with higher extensibility in the low stretch range and progressively lower extensibility with increasing stretch. This phenomenon is well known in the framework of rubber-like materials where it is called a strain-hardening or strain-stiffening effect. Constitutive models of incompressible hyperelasticity that take this into account include power-law models and limiting chain extensibility models. Our purpose in this paper is to bring to the attention of the biomechanics community some essential features of one such model of the latter type due to Gent. This model is compared with isotropic versions of biomechanical constitutive models by Takamizawa-Hayashi and Fung; the latter is a limiting version of a power-law material. Two particular problems are considered for which experimental data on arterial wall deformations are available. The first concerns small oscillations superposed on a large static stretch of a vertical string of arterial tissue. It is shown that the exponential model of Fung and the Gent model match well with the experimental data. The second problem is the extension of an internally pressurized circular cylindrical tube. It is shown that an inversion phenomenon observed experimentally for the human iliac artery can be described within a membrane theory by the Gent model whereas this cannot be described using the exponential model. The foregoing considerations are carried out for isotropic elastic materials in the absence of residual stress. Extensions to include anisotropy are also indicated.

In this paper, we carry out an explicit analysis of a bifurcation problem for a solid circular cylinder composed of a particular compressible nonlinearly elastic material. This problem is concerned with the bifurcation of a solid body into a configuration involving an internal cavity. A discussion of its physical interpretation is then carried out. In particular, it is shown that this model may be used to describe the nucleation of a void from a pre-existing micro-void.

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