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Models and phenomena in fracture mechanics. (English) Zbl 1047.74001
Foundations of Engineering Mechanics. Berlin: Springer (ISBN 3-540-43767-3/hbk). xvii, 576 p. (2002).
This impressive book includes a comprehensive material concerning crack problems as well as dynamic extensions for cell lattices and phase transitions with associated fractural effects. Additional elements as Fourier transforms with related topics and wave propagation are also exposed. An important amount of solutions and models are due to the author which presents the development of aspects in which he was involved during the late sixties with different scientists.
The evolved ideas appear in a very explanatory manner in the first chapter. The author starts with the definition of cracks and associated concepts of release criteria and surface and failure energies together with the procedures for their determination (variational, convolutive, integral procedures). This is exemplified by shock waves, bodies moving on water, elastic foundations, fractures (zones, Irwin criterion, size effects, initiation, propagation and instability). The necessary mathematical support is Fourier and Laplace transforms, Wiener-Hopf technique, and discrete transforms.
The subsequent chapters are devoted to waves (sinusoidal and exponential) in different formulations. The effective solving procedures for linearly elastic crack problems are further presented with Kolosov-Muskhelishvili and Neuber-Papkowitch representations, and various applications are given as finite plane crack, tip singularities, stress intensity factors, dislocations, crack arrays and kinks, weight functions and Betti’s theorem. The nonlinear elastic model is considered in order to determine logarithmic singularities occuring at crack tips, and exact formulations for energy release are used to derive generalized integral formulations of practical interest.
The next step towards a more complete treatment of fractural events concerns viscoelastic calculus for stationary and collinear systems of cracks, for growing cracks and for void elastic cohesion zones. Natural continuation of these aspects consists in the elastic-plastic fracture theory for fixed cracks including Barenblatt-Dugdale model in plane stress, crack growth theory under cyclic loading, and dynamic fracture (Knopoff’s solution for elastic-plastic cracks). The dynamic fracture theory includes sub- and intersonic crack asymptotes and energy release, the factorization of fundamental solutions for transient and uniform crack propagation, intensity stress factors, plate bending and dissipation rates (closure, opening and multiple cracks are taken into account).
A more important role plays the square cell-lattice analysis which gives elastic macro- and micro-solutions for homogeneous materials, describes plane waves and viscoelastic waves in terms of Fourier transforms for unloaded lattice, and examines strings with the corresponding crack growth and local energy release. For triangular cells, macro- and micro-level solutions are obtained which describe dissipation, sub-, inter- and supersonic phenomena, and higher-order models. Finally, the author treats the dynamic amplification factors in fracture and phase transitions by using numerical simulations.
The book is of special interest for scientists elaborating on technical applications of the fracture theory.

74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74Rxx Fracture and damage
74A45 Theories of fracture and damage
74G70 Stress concentrations, singularities in solid mechanics
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics