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**Dynamic fracture mechanics.**
*(English)*
Zbl 0712.73072

Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge etc.: Cambridge University Press. xvii, 563 p. £40.00/hbk, $ 59.50/hbk, £24.95/pbk, $37.95/pbk (1990).

The author of this book is well known for his contribution in the area of mathematical analysis of plane cracks in elastic media. Most of the discussions are based on the problems involving plane cracks in homogeneous isotropic elastic media, where all three fracture modes are included. There are three basic classes of problems considered in the analytical developments of linear elastic fracture mechanics (LEFM). For some problems, it is assumed that the cracks remain stationary under loading while in the second class of problems, the speed of propagation of the crack is assumed to be a known constant. In the last and most complicated class of problems, the crack speed is not known a priori and needs to be determined for a given loading using some fracture criterion. One of the most pioneering concept in fracture mechanics is the Griffith’s energy criterion for elemental crack advancement under a given loading, which is basically an energy balance concept. This was later modified by Irwin for more general applications.

This book covers all of these areas beginning with the mathematical elasticity background needed for the development of LEFM. Other associated mathematical theories like Wiener-Hopf techniques, Rayleigh- Ritz methods and asymptotic theories needed for the solution of crack problems are also explained in detail. Path independent energy integrals and their applications are included in Chapter 5. Crack growth at nonuniform speeds using critical stress intensity fracture criterion has been discussed in detail in Chapter 7. The last chapter of this book is devoted to the discussion of the effect of plasticity and rate effects on the crack propagation in otherwise elastic media.

This book contains a wealth of references related to the study of analytical treatment of plane cracks in elastic media. It is well written and mostly complete for basic understanding of the phenomena associated with the mathematical theory of cracks. Some of the most modern problems in fracture mechanics, e.g., fracture of prefractured materials, effect of dissimilar material interfaces on crack propagation, crack bifurcations, nonplanar fracture of fresh materials and catastrophic linkage of cracks are not included in this treatise.

This book covers all of these areas beginning with the mathematical elasticity background needed for the development of LEFM. Other associated mathematical theories like Wiener-Hopf techniques, Rayleigh- Ritz methods and asymptotic theories needed for the solution of crack problems are also explained in detail. Path independent energy integrals and their applications are included in Chapter 5. Crack growth at nonuniform speeds using critical stress intensity fracture criterion has been discussed in detail in Chapter 7. The last chapter of this book is devoted to the discussion of the effect of plasticity and rate effects on the crack propagation in otherwise elastic media.

This book contains a wealth of references related to the study of analytical treatment of plane cracks in elastic media. It is well written and mostly complete for basic understanding of the phenomena associated with the mathematical theory of cracks. Some of the most modern problems in fracture mechanics, e.g., fracture of prefractured materials, effect of dissimilar material interfaces on crack propagation, crack bifurcations, nonplanar fracture of fresh materials and catastrophic linkage of cracks are not included in this treatise.

Reviewer: A.Chatterjee

### MSC:

74R99 | Fracture and damage |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |