Volume 45, Number 1, January I 1999
|Page(s)||13 - 19|
|Published online||01 September 2002|
Statistical properties of fractures in damaged materials
Dipartimento di Fisica, Università degli Studi “Tor Vergata”, v.le della Ricerca Scientifica, 1, 00133 Roma, Italy
2 INFM, Sezione di Roma 1, and Dipartimento di Fisica, Università di Roma I “La Sapienza” - P.le A. Moro 2, 00185 Roma, Italy
3 Max-Planck Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
4 Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, CB3 0HE Cambridge, UK
Accepted: 8 November 1999
We introduce a model for the dynamics of mud cracking in the limit of of extremely thin layers. In this model the growth of fracture proceeds by selecting the part of the material with the smallest (quenched) breaking threshold. In addition, weakening affects the area of the sample neighbour to the crack. Due to the simplicity of the model, it is possible to derive some analytical results. 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, we obtain a formula for the mean weakening with time of the whole sample.
PACS: 05.20.-y – Statistical mechanics / 61.43.Hv – Fractals; macroscopic aggregates (including diffusion-limited aggregates) / 62.20.Mk – Fatigue, brittleness, fracture and cracks
© EDP Sciences, 1999
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