2000/04/17 by Raffaele Cafiero, Guido Caldarelli, Cafiero, Raffaele +3
Engineering · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Geotechnical Engineering and Soil Mechanics #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0004281
10 pages, 7 figures (9 postscript files), RevTeX
arxiv created 2000/04/17 · openalex publication_date 2000/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a detailed study of a two-dimensional minimal lattice model for the description of mud cracking in the limit of extremely thin layers. In this model each bond of the lattice is assigned to a (quenched) breaking threshold. Fractures proceed through the selection of the part of the material with the smallest breaking threshold. A local damaging rule is also implemented, by using two different types of weakening of the neighboring sites, corresponding to different physical situations. Some analytical results are derived through a probabilistic approach known as Run Time Statistics. In particular, we find that the total time to break down the sample grows with the dimension L of the lattice as L2 even though the percolating cluster has a non trivial fractal dimension. Furthermore, a formula for the mean weakening in time of the whole sample is obtained.