7R14. Models and Phenomena in Fracture Mechanics. Foundations of Engineering Mechanics. - LI Slepyan (Dept of Solid Mech, Mat, and Syst, Tel Aviv Univ, Ramat Aviv, 69978, Israel). Springer-Verlag, Berlin. 2002. 576 pp. ISBN 3-540-43767-3. $229.00.

Reviewed by AS Grandt (Sch of Aeronaut and Astronaut, Purdue Univ, 1282 Grisson Hall, W Lafayette IN 47907-1282).

The author’s objective for this 14-chapter volume is to provide a broad overview of various models of cracks, material behavior, and crack growth that characterize the general fracture process. He discusses, for example, how crack tip stresses may be modeled by singular stress fields or by finite stresses in cohesive zone models. Material behavior is represented by linear and nonlinear elastic, viscoelastic, elastic-plastic, and porous material descriptions, as well as by elastic and viscoelastic lattice models. The ultimate goal of all these approaches is to determine how a crack grows under certain conditions or whether it remains stable.

Chapter 1 reviews fundamental fracture mechanics concepts and presents several methods for determining the energy released by crack growth. The author characterizes Chapters 2 and 3 as “auxiliary material” that leads to a better understanding of fracture mechanics phenomena (eg, Fourier transforms and various aspects of wave propagation). Chapter 4 describes a one-dimensional view of crack growth, while Chapter 5 gives two- and three-dimensional treatment of static cracks in linear elastic bodies. Nonlinear elastic bodies are then discussed in Chapter 6, followed by viscoelastic fracture in Chapter 7, elastic-plastic fracture in Chapter 8, and dynamic fracture in Chapter 9.

Chapter 10 deals with crack growth in plate bending where one must take into account the possibility for crack surfaces to come into contact. Chapters 11–14 conclude the text with discrete models for dynamic and quasi-static fracture and phase transition. First, square-cell elastic and viscoelastic lattices are discussed in Chapter 11, followed by triangular cell elastic lattices in Chapter 12. Two-phase models of phase transition are then presented in Chapter 13, concluding with dynamic aspects of fracture and phase transformation in Chapter 14.

The author has researched fracture mechanics problems since the late 1960s and has obtained vast experience with the key technical issues. He has had the opportunity to meet and interact with many other important investigators involved in related research topics. Indeed, one of the book’s key attributes is the wide-ranging background and mathematical rigor that the author brings to the fracture mechanics arena. The book’s 576 pages present a total of 142 figures, 274 references, and over 2300 equations. Models and Phenomena in Fracture Mechanics will be of main interest to researchers, with a strong fracture mechanics background, who desire a rigorous description of many different approaches to modeling the fracture process. The text also will serve as a guide to the vast literature on these topics.