Breakdown of two-phase random resistor networks

Journal Article · Wed Feb 01 00:00:00 EST 1995 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.51.3476· OSTI ID:6641906

Duxbury, P M ^[1]; Beale, P D ^[2]; Moukarzel, C ^[3]

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1. Department of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824-1116 (United States)
2. Department of Physics, University of Colorado, Boulder Colorado 80309 (United States)
3. Hoechstleistungsrechenzentrum, Forschungszentrum, D-52425 Juelich (Germany)

We describe the failure of two-component square- and cubic-lattice random resistor networks. The model behavior is dependent on the ratio of the conductances of the two components [ital g], the ratio of the (brittle) failure thresholds of the two components [ital i], the volume fraction [ital p], and the sample size [ital L]. For much of the parameter space, the average strength of the networks shows a rather weak size effect, and a scaling argument suggests that this size effect is logarithmic. As usual, near the percolation points, there can be algebraic scaling provided [ital i] and [ital g] are very large or small. Near the limits [ital p]=0 and [ital p]=1, there is a logarithmic ( dilute-limit'') singularity in average strength. The ability to absorb damage is very strongly dependent on the model parameters. When one phase is more conducting and weaker than the other, and the strong phase is connected, the damage is usually extensive. Basically most of the weak bonds fail prior to the failure of the whole network. In the other regions of parameter space, damage is not extensive, but it does sometimes scale in a nontrivial way with the sample size.

• DOE Contract Number: FG02-90ER45418
• OSTI ID: 6641906
• Journal Information: Physical Review, B: Condensed Matter; (United States), Vol. 51:6; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
RANDOMNESS
ELECTRIC CONDUCTIVITY
BREAKDOWN
CRITICAL CURRENT
CUBIC LATTICES
ELASTICITY
RESISTORS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
CURRENTS
ELECTRIC CURRENTS
ELECTRICAL EQUIPMENT
ELECTRICAL PROPERTIES
EQUIPMENT
MECHANICAL PROPERTIES
PHYSICAL PROPERTIES
TENSILE PROPERTIES
665000* - Physics of Condensed Matter- (1992-)