Overview
- The first book that focuses on the mathematical and numerical analyses of crack path prediction
- Contributes to a better understanding of crack path stability and resulting cracking formation in brittle solids
- Includes accurate prediction methods for the life and path of fatigue crack propagation, as well as possible crack arrest after unexpected brittle crack initiation
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematics for Industry (MFI, volume 2)
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Table of contents (11 chapters)
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Front Matter
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Elasticity
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Front Matter
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Fracture
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Front Matter
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Design
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Front Matter
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Back Matter
Keywords
About this book
This book is about the pattern formation and the evolution of crack propagation in engineering materials and structures, bridging mathematical analyses of cracks based on singular integral equations, to computational simulation of engineering design. The first two parts of this book focus on elasticity and fracture and provide the basis for discussions on fracture morphology and its numerical simulation, which may lead to a simulation-based fracture control in engineering structures. Several design concepts are discussed for the prevention of fatigue and fracture in engineering structures, including safe-life design, fail-safe design, damage tolerant design.
After starting with basic elasticity and fracture theories in parts one and two, this book focuses on the fracture morphology that develops due to the propagation of brittle cracks or fatigue cracks.
In part three, the mathematical analysis of a curved crack is precisely described, based on the perturbation method. The stability theory of interactive cracks propagating in brittle solids may help readers to understand the formation of a fractal-like cracking patterns in brittle solids, while the stability theory of crack paths helps to identify the straight versus sharply curved or sometimes wavy crack paths observed in brittle solids.
In part four, the numerical simulation method of a system of multiple cracks is introduced by means of the finite element method, which may be used for the better implementation of fracture control in engineering structures.
This book is part of a series on “Mathematics for Industry” and will appeal to structural engineers seeking to understand the basic backgrounds of analyses, but also to mathematicians with an interest in how such mathematical solutions are evaluated in industrial applications.
Authors and Affiliations
Bibliographic Information
Book Title: Mathematical and Computational Analyses of Cracking Formation
Book Subtitle: Fracture Morphology and Its Evolution in Engineering Materials and Structures
Authors: Yoichi Sumi
Series Title: Mathematics for Industry
DOI: https://doi.org/10.1007/978-4-431-54935-2
Publisher: Springer Tokyo
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Japan KK 2014
Hardcover ISBN: 978-4-431-54934-5Published: 01 July 2014
Softcover ISBN: 978-4-431-56385-3Published: 23 August 2016
eBook ISBN: 978-4-431-54935-2Published: 11 June 2014
Series ISSN: 2198-350X
Series E-ISSN: 2198-3518
Edition Number: 1
Number of Pages: XII, 282
Number of Illustrations: 156 b/w illustrations, 12 illustrations in colour
Topics: Solid Mechanics, Characterization and Evaluation of Materials, Classical Mechanics, Mathematical and Computational Engineering, Mathematical Modeling and Industrial Mathematics, Solid Mechanics