## The Fiber Bundle Model: Modeling Failure in MaterialsGathering 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. |

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### Contents

2 | 224 |

Contents | xiii |

Appendix | 1 |

Average Properties | 11 |

B 2 | 19 |

Fluctuation Effects | 27 |

1 | 49 |

Local and Intermediate Load Sharing | 63 |

The Characteristic Function 214 | 71 |

Recursive Breaking Dynamics | 115 |

Predicting Failure | 137 |

Fiber Bundle Model in Material Science 169 | 169 |

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### Common terms and phrases

assume asymptotic avalanche size distribution average force backward condition behavior Beno Gutenberg Brownian motion bundle strength burst distribution Chapter corresponding critical point crossover distribution of fiber distribution of index elastic constant elongation energy emission equal-load-sharing fiber bundle equal-load-sharing model equation exponent failed fibers failure process fiber bundle model fiber fails fiber strength distribution fibers have failed finite fixed point fluctuations follows force per fiber fracture function fuse model Gumbel Hemmer Hence inclusive bursts intact fibers iteration KGaA largest hole load curve local-load-sharing model Måløy matrix number of bursts number of fibers number of intact parameter Phys physics power law probability distribution random number random walk redistribution samples Section shown in Figure simulation results statistics step surviving fibers threshold distribution P(x threshold values total number uniform distribution uniform threshold distribution unit interval Waloddi Weibull Weibull distribution Wiley-VCH Verlag 𝜀 𝜅 𝜎 𝜎c