Methods of fracture mechanics: Solid matter physics
This is one of few books that is specifically concerned with some applications of the mathematical methods of fracture mechanics in solid matter physics. The topic of this book is valuable for researchers and important from a technological point of view. The book consists of eight chapters and is organized as follows. Chapter 1 is addressed to define, calculate and measure the surface energy of a solid. Some new examples of the derivation of self-similar singular solutions to some nonlinear partial differential equations of hyperbolic and elliptic type are given. Chapter 2 considers the classical fracture mechanics based on the crack tip study with the thermal fluctuation theory of fracture. In chapter 3 the author treats some basic mechanisms of microstack nucleation in polycrystalline and amorphous materials. The methods of the theory of functions of a complex variable, the Mellin transform method and the Wiener-Hopf and Noble-Jones techniques are used in some examples. In Chapter 4, an interdisciplinary approach to the physics of sintering is presented and the governing equations of sintering are formulated. The method of invariant integrals due to the author is presented in chapter 5 as an alternative approach to classical theories of mathematical physics. Chapter 6 which is the main chapter of the book is devoted to the application of nanofracture mechanics to the dislocation emission and crack growth in a cubic lattice of atoms. The authors reports here the results of mathematical modelling of dislocation generation vs subcritical crack growth. Also, the chapter involves the method of thermofluctuation theory of fracture for analysis of dislocation nucleation, the analytic methods of the theory of functions of a complex variable, the method of singularity driving forces, the analysis of solid matter states, and some numerical methods including the iterative and minimization methods. In Chapter 7, the relativistic effects of high-intensity electron beams are treated, and the method of invariant integrals, the method of singular solutions and the method of driving forces are reported. In the final chapter 8, following some preliminaries for practical fracture geometry, the methods of the theory of fractals are applied to fracture phenomena. The book which is written in a clear and precise style provides a comprehensive and unified treatment of the methods of fracture mechanics. Besides, it is rich in research topics in solid and fracture mechanics and in physics. The book is useful for courses on computational fracture mechanics, and it is of a real interest for graduate students and researchers working in various areas of fracture mechanics.
relativistic effects of high-intensity electron beams
scientific article; zbMATH DE number 1164864