Issue |
Europhys. Lett.
Volume 57, Number 6, March 2002
|
|
---|---|---|
Page(s) | 831 - 837 | |
Section | Condensed matter: structure, mechanical and thermal properties | |
DOI | https://doi.org/10.1209/epl/i2002-00586-5 | |
Published online | 01 August 2002 |
The random fuse network as a dipolar magnet
1
CEA, Service de Physique de la Matière Condensée BP12, 91680
Bruyères-le-Châtel, France
2
Department of Physics, Harvard University - Cambridge,
MA 02138, USA
3
CEA, Service de Physique Théorique - 91191 Gif-sur-Yvette,
Cedex, France
Received:
29
October
2001
Accepted:
9
January
2002
We introduce an approximate mapping between the random fuse network (RFN) and a random field dipolar Ising model (RFDIM). The state of the network damage is associated with a metastable spin configuration. A mean-field treatment, numerical solutions, and heuristic arguments support the broad validity of the approximation and yield a generic phase diagram. At low disorder, the growth of a single unstable “crack” leads to an abrupt global failure. Beyond a critical disorder, the conducting network sustains significant damage before the coalescence of cracks results in global failure.
PACS: 62.20.Mk – Fatigue, brittleness, fracture, and cracks / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems
© EDP Sciences, 2002
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