TY  - JOUR
N2  - 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.
JF  - Journal of Physics A: Mathematical and Theoretical
SN  - 1751-8113
Y1  - 2000/09//
AV  - none
TI  - Damage and cracking in thin mud layers
ID  - eprints1159
IS  - 45
UR  - http://dx.doi.org/10.1088/0305-4470/33/45/301
KW  - PACS: 05.50.+q Lattice theory and statistics (Ising
KW  -  Potts
KW  -  etc.); 81.40.Np Fatigue
KW  -  corrosion fatigue
KW  -  embrittlement
KW  -  cracking
KW  -  fracture
KW  -  and failure; 62.20.M- Structural failure of materials

VL  - 33
EP  - 8028
PB  - Institute of Physics
SP  - 8013
A1  - Cafiero, Raffaele
A1  - Caldarelli, Guido
A1  - Gabrielli, Andrea
ER  -