eprintid: 1159
rev_number: 6
eprint_status: archive
userid: 6
dir: disk0/00/00/11/59
datestamp: 2012-02-23 11:15:18
lastmod: 2013-11-20 14:01:16
status_changed: 2012-02-23 11:15:18
type: article
metadata_visibility: show
creators_name: Cafiero, Raffaele
creators_name: Caldarelli, Guido
creators_name: Gabrielli, Andrea
creators_id: 
creators_id: guido.caldarelli@imtlucca.it
creators_id: 
title: Damage and cracking in thin mud layers
ispublished: pub
subjects: QC
divisions: EIC
full_text_status: none
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

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.
date: 2000-09
date_type: published
publication: Journal of Physics A: Mathematical and Theoretical
volume: 33
number: 45
publisher: Institute of Physics
pagerange: 8013-8028
id_number: 10.1088/0305-4470/33/45/301
refereed: TRUE
issn: 1751-8113
official_url: http://dx.doi.org/10.1088/0305-4470/33/45/301
related_url_url: http://arxiv.org/abs/cond-mat/0004281
citation:   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)