Methods of fracture mechanics: Solid matter physics
type: Item
instance of: scholarly article
title: Methods of fracture mechanics: Solid matter physics
zbMATH Open document ID: 0908.73002
published in: Solid Mechanics and Its Applications
publication date: 1998-06-14T00:00:00Z
review text: 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 tr…
Mathematics Subject Classification ID: 74-02
Mathematics Subject Classification ID: 74R99
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74M25
Mathematics Subject Classification ID: 82D20
zbMATH DE Number: 1164864
zbMATH Keywords: Wiener-Hopf method
zbMATH Keywords: Noble-Jones technique
zbMATH Keywords: iterative methods
zbMATH Keywords: surface energy
zbMATH Keywords: self-similar singular solutions
zbMATH Keywords: crack tip
zbMATH Keywords: thermal fluctuation theory of fracture
zbMATH Keywords: microstack nucleation
zbMATH Keywords: theory of functions of complex variable
zbMATH Keywords: Mellin transform method
zbMATH Keywords: sintering
zbMATH Keywords: method of invariant integrals
zbMATH Keywords: nanofracture mechanics
zbMATH Keywords: dislocation emission
zbMATH Keywords: crack growth
zbMATH Keywords: dislocation nucleation
zbMATH Keywords: minimization methods
zbMATH Keywords: relativistic effects of high-intensity electron beams
zbMATH Keywords: method of driving forces
zbMATH Keywords: fractals
author: Genady P. Cherepanov
reviewed by: M. Cengiz Dökmeci
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1164864