Statistical properties of fractures in damaged materials

Details Statistical properties of fractures in damaged materials Statistical properties of fractures in damaged materials

1999-01-12

arxiv.org/abs/cond-mat/9901107v1

Physics

Condensed Matter

5 pages, 4 figures, to be published in Europhysics Letters

Scientific paper

10.1209/epl/i1999-00124-7

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 L^2 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.

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