## Abstract

The fiber bundle model is widely used in probabilistic modeling of various phenomena across different engineering fields, from network analysis to earthquake statistics. In structural strength analysis, this model is an essential part of extreme value statistics that governs the left tail of the cumulative probability density function of strength. Based on previous nano-mechanical arguments, the cumulative probability distribution function of strength of each fiber constituting the bundle is assumed to exhibit a power-law left tail. Each fiber (or element) of the bundle is supposed to be subjected to the same relative displacement (parallel coupling). The constitutive equations describing various fibers are assumed to be related by a radial affinity while no restrictions are placed on their particular form. It is demonstrated that, even under these most general assumptions, the power-law left tail is preserved in the bundle and the tail exponent of the bundle is the sum of the exponents of the power-law tails of all the fibers. The results have significant implications for the statistical modeling of strength of quasibrittle structures.

Original language | English (US) |
---|---|

Pages (from-to) | 1-7 |

Number of pages | 7 |

Journal | Probabilistic Engineering Mechanics |

Volume | 36 |

DOIs | |

State | Published - Apr 2014 |

### Funding

Support under NSF grant CMMI-1153494 and ARO grant W911NF--0-1-0043, both to Northwestern University, is gratefully acknowledged.

## Keywords

- Extreme value statistics
- Fiber bundle model
- Fracture mechanics
- Quasibrittle structures
- Random strength
- Structural safety

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Civil and Structural Engineering
- Nuclear Energy and Engineering
- Condensed Matter Physics
- Aerospace Engineering
- Ocean Engineering
- Mechanical Engineering