Interdisciplinary Applied Mathematics

Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation

Authors: Yosibash, Zohar

  • Many solved example problems  
  • Explicit mathematical expressions
  • Solutions to selected exercises in the book
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About this book

This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction  solutions in the neighborhood of singular points in two-dimensional domains, and  singular edges and vertices in three-dimensional domains. These are presented in an  engineering terminology for practical usage. The author treats the mathematical   formulations from an engineering viewpoint and presents high-order finite-element  methods for the computation of singular solutions in isotropic and anisotropic materials,  and multi-material interfaces.  The proper interpretation of the results in engineering practice  is advocated, so that the computed data can be correlated to experimental observations.

 

The book is divided into fourteen chapters, each containing several sections.

Most of it (the first nine Chapters) addresses two-dimensional domains, where

only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis.  Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein.

 

Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along  singular edges are presented and demonstrated by several example  problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with  some remarks on open questions.

This well illustrated book will appeal to both applied  mathematicians and engineers working in the field of fracture mechanics and  singularities.

About the authors

Zohar Yosibash is a Professor of Mechanical Engineering at Ben-Gurion University of the Negev in Beer-Sheva, Israel

Reviews

From the reviews:

“The main goal of the book is to provide a unified approach to the analysis of singular points, both analytical and numerical, and the subsequent use of the computed data in engineering practice for predicting and eventually preserving failures in structural mechanics. The book is divided into 14 chapters, each containing several sections. … The book is written as much as possible self-contained.” (Ján Sládek, Zentralblatt MATH, Vol. 1244, 2012)


Table of contents (20 chapters)

  • Introduction

    Yosibash, Zohar

    Pages 1-25

  • An Introduction to the p- and hp-Versions of the Finite Element Method

    Yosibash, Zohar

    Pages 27-45

  • Eigenpair Computation for Two-Dimensional Heat Conduction Singularities

    Yosibash, Zohar

    Pages 47-72

  • GFIFs Computation for Two-Dimensional Heat Conduction Problems

    Yosibash, Zohar

    Pages 73-95

  • Eigenpairs for Two-Dimensional Elasticity

    Yosibash, Zohar

    Pages 97-132

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-1-4614-1508-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-1-4614-1507-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-1-4899-9510-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation
Authors
Series Title
Interdisciplinary Applied Mathematics
Series Volume
37
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LCC
eBook ISBN
978-1-4614-1508-4
DOI
10.1007/978-1-4614-1508-4
Hardcover ISBN
978-1-4614-1507-7
Softcover ISBN
978-1-4899-9510-0
Series ISSN
0939-6047
Edition Number
1
Number of Pages
XXII, 462
Topics