Mean-field theory of localization in a fuse model

Renaud Toussaint (1) , Alex Hansen (2)

1 IPGS - Institut de physique du globe de Strasbourg
2 Physics NTNU - Department of Physics [Trondheim]

We propose a mean-field theory for the localization of damage in a quasistatic fuse model on a cylinder. Depending on the quenched disorder distribution of the fuse thresholds, we show analytically that the system can either stay in a percolation regime up to breakdown, or start at some imposed current, to localize starting from the smallest scale (lattice spacing), or instead go to a diffuse localization regime where damage starts to concentrate in bands of width scaling as the width of the system, but remains diffuse at smaller scales. Depending on the nature of the quenched disorder on the fuse thresholds, we derive analytically the phase diagram of the system separating these regimes and the current levels for the onset of these possible localizations. We compare these predictions to numerical results.

Mots clés: damage model; fracture; fuse network

Domaines: Mécanique statistique [cond-mat.stat-mech]; Science des matériaux [cond-mat.mtrl-sci]; Mécanique des solides [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Géophysique [physics.geo-ph]

Renaud Toussaint, Alex Hansen. Mean-field theory of localization in a fuse model. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2006, 73 (4), pp.046103. ⟨10.1103/PhysRevE.73.046103⟩. ⟨hal-00107354⟩