Hansen / Hemmer / Pradhan The Fiber Bundle Model

Modeling Failure in Materials
1. Auflage 2015
ISBN: 978-3-527-67198-4
Verlag: Wiley-VCH
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 236 Seiten, E-Book

Reihe: Statistical Physics of Fracture and Breakdown

Gathering research from physics, mechanical engineering, and statistics in a single resource for the first time, this text presents the background to the model, its theoretical basis, and applications ranging from materials science to earth science.

The authors start by explaining why disorder is important for fracture and then go on to introduce the fiber bundle model, backed by various different applications. Appendices present the necessary mathematical, computational and statistical background required.

The structure of the book allows the reader to skip some material that is too specialized, making this topic accessible to the engineering, mechanics and materials science communities, in addition to providing further reading for graduate students in statistical physics.

Autoren/Hrsg.

Hansen, Alex

Hemmer, Per Christian

Pradhan, Srutarshi

Inhaltsverzeichnis

THE FIBER BUNDLE MODEL

Rivets Versus Welding

Fracture and Failure: A Short Summary

The Fiber Bundle Model in Statistics

The Fiber Bundle Model in Physics

The Fiber Bundle Model in Materials Science

Structure of the Book

 

AVERAGE PROPERTIES

Equal Load Sharing vs. Local Load Sharing

Strain-Controlled vs. Force-Controlled Experiments

The Critical Strength

Fiber Mixtures

Non-Hookean Forces

 

FLUCTUATION EFFECTS

Range of Force Fluctuations

The Maximum Bundle Strength

Avalanches

 

LOCAL AND INTERMEDIATE LOAD SHARING

The Local Load Sharing Model

Local Load Sharing in Two and More Dimensions

The Soft Membrane Model

Intermediate Load Sharing Models

Elastic Medium Anchoring

 

RECURSIVE BREAKING DYNAMICS

Recursion and Fixed Points

Recursive Dynamics Near the Critical Point

 

PREDICTING FAILURE

Crossover Phenomena

Variation of Average Burst Size

Failure Dynamics Under Force-Controlled Loading

Over-Loaded Situations

 

FIBER BUNDLE MODEL IN MATERIALS SCIENCE

Repeated Damage and Work Hardening

Creep Failure

Viscoelastic Creep

Fatigue Failure

Thermally Induced Failure

Noise-Induced Failure

Crushing: The Pillar Model

 

SNOW AVALANCHES AND LANDSLIDES

Snow Avalanches

Shallow Landslides

 

APPENDIX A: MATHEMATICAL TOOLBOX

Lagrange's Inversion Theorem

Some Theorems in Combinatorics

Biased Random Walks

An Asymmetrical Unbiased Random Walk

Brownian Motion as a Scaled Random Walk

 

APPENDIX B: STATISTICAL TOOLBOX

Stochastic Variables, Statistical Distributions

Order Statistics

The Joint Probability Distribution

 

APPENDIX C: COMPUTATIONAL TOOLBOX

Generating Random Numbers Following a Specified Probability Distribution

Fourier Acceleration

 

Index

Über Autor(innen)

Alex Hansen earned his Ph.D. from Cornell University in 1986. He was then Joliot-Curie fellow at the Ecole Normale Supérieure in Paris, followed by postdoctoral positions at the Universities of Cologne and Oslo. In 1992, Hansen became a CNRS scientist at the University of Rennes 1 in France. From 1994, he has been professor of physics at the Norwegian University of Science and Technology in Trondheim, Norway. Hansen is member of the Norwegian Academy of Science and Letters, the Royal Norwegian Society of Science and Letters and the

Norwegian Academy of Technical Sciences. He is Dr. honoris causa at the University of Rennes 1. Hansen chairs at present the Commission on Computational Physics of the International Union of Pure and Applied Physics, where he is also a vice president.

 

Per Christian Hemmer earned his doctorate from the Norwegian Institute of Technology in 1959. He was then NORDITA fellow in Copenhagen, followed by a postdoctoral position at The Rockefeller Institute, New York. In 1959 he was appointed professor of theoretical physics at the University of Trondheim, now the Norwegian University of Science and Technology. He has been dean of the faculty for general sciences at the university. Hemmer has been secretary of the Commission on Statistical Physics of the International Union of Pure and Applied Physics, as well as a vice president of the union. He is member of the Royal Norwegian Society of Science and Letters, the Norwegian Academy of Science and Letters, and the Norwegian Academy of Technical Sciences.

 

Srutarshi Pradhan completed his Ph.D. work at Saha Institute of Nuclear Physics, Kolkata, India in 2004 and earned his doctorate from Jadavpur University, Kolkata, India . He was then a postdoctoral fellow at the Norwegian University of Science and Technology for 4 years (2004-2007) with a fellowship from the Norwegian Research Council. In 2008 he was appointed as a research scientist at SINTEF Petroleum Research, Trondheim, Norway. Pradhan has been promoted to senior scientist position at SINTEF Petroleum Research in 2012.