Cafiero, Raffaele and Caldarelli, Guido and Gabrielli, Andrea
*Damage and cracking in thin mud layers.*
Journal of Physics A: Mathematical and Theoretical, 33 (45).
pp. 8013-8028.
ISSN 1751-8113
(2000)

## Abstract

We present a detailed study of a two-dimensional lattice model introduced to describe mud cracking in the limit of extremely thin layers. In this model to each bond in the lattice is assigned a (quenched) random breaking threshold. Fractures proceed by selecting the `weakest' part of the material (i.e. the smallest value of the threshold). A local damage rule is also implemented, by using two different types of weakening of the neighbouring sites, corresponding to different physical situations. We present the results of numerical simulations on this model. We also derive some analytical results through a probabilistic approach known as run time statistics. In particular, we find that the total time to divide the sample scales with the square power L2 of the linear size L of the lattice. This result is not straightforward since the percolating cluster has a non-trivial fractal dimension. Furthermore, we present here a formula for the mean weakening of the whole sample during the evolution.

Item Type: | Article |
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Identification Number: | 10.1088/0305-4470/33/45/301 |

Uncontrolled Keywords: | PACS: 05.50.+q Lattice theory and statistics (Ising, Potts, etc.); 81.40.Np Fatigue, corrosion fatigue, embrittlement, cracking, fracture, and failure; 62.20.M- Structural failure of materials |

Subjects: | Q Science > QC Physics |

Research Area: | Economics and Institutional Change |

Depositing User: | Ms T. Iannizzi |

Date Deposited: | 23 Feb 2012 11:15 |

Last Modified: | 20 Nov 2013 14:01 |

URI: | http://eprints.imtlucca.it/id/eprint/1159 |

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