The Fiber Bundle Model

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.

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