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Dynamic fracture mechanics. Vol. 1. Stationary cracks. Transl. and rev. from the 1985 Russian ed. by Ram S. Wadhwa, Engl. ed. edited by Richard B. Hetnarski. (English) Zbl 0744.73037
New York etc.: Hemisphere Publishing Corp.. xxi, 322 p. (1989).
The mathematical theory of cracks in either a homogeneous isotropic or nonhomogeneous medium has a very rich literature. The domain of analysis is usually divided into the following groups that manifest some characteristics of the effects of cracks in an otherwise flawless medium. 1) Stationary planar and nonplanar cracks in an isotropic or anisotropic medium due to given static loading, 2) diffraction of harmonic waves due to planar or nonplanar cracks, 3) response of cracked media due to given transient loading, and 4) fully linear or nonlinear problem of a single or multiple crack propagation in a medium due to known transient loading.
This book by Parton and Boriskovsky is an excellent review of the problems described in 2) and 3) above. The book begins with a discussion of the classical theory of stress distribution in the presence of a crack and the most important concept of stress intensity factors, a measure of the stress elevation near the cracks tips. Chapter two discusses the problem of diffraction of harmonic waves due to finite and semi-infinite cracks in all three modes of fracture along with a discussion on periodic cracks. Chapter four includes the problem of transient, mechanical and thermal loading on known cracks. Besides the two-dimensional planar cracks, discussions on various methods to solve full three-dimensional planar cracks as well as two-dimensional nonplanar cracks with regular and irregular geometry are also included in this treatise. Due to the curvature of nonplanar cracks, a higher stress intensity factor arises and hence contributes to the ensuing instability of the stationary cracks. Even though the focus of most of the mathematical analysis involving cracks is on the determination of the stress intensity factors, numerical methods are essential for the calculation of the displacement and stress field anywhere in the medium. These numerical methods usually are discretization of the involved singular integro-differential equations which arise due to the displacement discontinuity across the cracks. A review of the available numerical methods including finite element techniques suitable for crack problems are included in Chapters three and five.
Even though this book is easy reading for people experienced in this area, some knowledge of the mathematical methods involving the integro- differential equations are needed for better understanding. This book is certainly an excellent addition to the growing number of books in the area of mathematical theory of cracks.

74R99 Fracture and damage
74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74G70 Stress concentrations, singularities in solid mechanics
74J20 Wave scattering in solid mechanics