zbMATH — the first resource for mathematics

Introduction to continuum damage mechanics. (English) Zbl 0596.73091
Mechanics of Elastic Stability, 10. Dordrecht/Boston/Lancaster: Martinus Nijhoff Publishers, a member of the Kluwer Academic Publishers Group. X, 135 p. Dfl. 125.00; $ 39.50; £34.75 (1986).
This book is probably the first one on the subject of continuum damage mechanics (CDM), which is a branch of fracture mechanics and unifies earlier and recent developments concerning the damage phenomenon mostly in metals.
The book contains the basic principles of CDM, which permit to formulate, in terms of mechanics, a variety of damage and fracture phenomena, related to creep, large plastic deformation, fatigue and to the influence of the environment. It also contains several applications, which provide a better insight in the theory, as well as information on the scarcely available experimental data in this field.
Although the length of the book is limited, it covers the subject to a large extent. This has been achieved by a compact and clear mathematical representation of the theory without superfluous mathematical formalisms. Moreover, the reader is gradually and progressively introduced to complicated matters by treating, at the beginning simple uniaxial problems followed by the more general multiaxial problems. Thus, the book is accessible to engineers and scientists, engaged to the design of structures.
The whole text is divided into six chapters. The first chapter is an introduction to the basic aspects and to the equations governing the damage phenomenon. In the second chapter, which has a quite great extent, problems of creep and fracture under uniaxial stress are treated. The time spent for a ductile or brittle fracture is calculated in the case of a uniform stress field, while the non-uniform stress field (bending) is confronted with the concept of the moving front of fracture. This chapter contains also a number of examples.
In the third chapter the previous subjects are extended to multiaxial stress problems. The generalisation of the theory is accompanied with several interesting applications, e.g. the fracture of tubes under internal pressure and the brittle fracture of a thin soft interlayer. In the fourth chapter the problem of crack growth under creep conditions is treatd, a dissipative criterion of fracture is formulated and an approximate model of crack growth is given. The last two chapters, which are quite short, are devoted to a damage model for ductile fracture and to fatigue damage, respectively. Finally, the book includes forty five references some of which are in Russian.
The book, written by an experienced scientist of this field of mechanics, embraces all the basic ingredients of a complete and authoritative treatise in this modern field of the mechanics of continuum damage.
Reviewer: P.S.Theocaris

74R99 Fracture and damage
74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74C99 Plastic materials, materials of stress-rate and internal-variable type
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)