The Fiber Bundle Model

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.

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

• By (author) Alex Hansen
• By (author) Per Christian Hemmer
• By (author) Srutarshi Pradhan