Continuous Damage Fiber Bundle Model for Strongly Disordered Materials
arXiv:0706.1554 · doi:10.1103/PhysRevE.77.046102
Abstract
We present an extension of the continuous damage fiber bundle model to describe the gradual degradation of highly heterogeneous materials under an increasing external load. Breaking of a fiber in the model is preceded by a sequence of partial failure events occurring at random threshold values. In order to capture the subsequent propagation and arrest of cracks, furthermore, the disorder of the number of degradation steps of material constituents, the failure thresholds of single fibers are sorted into ascending order and their total number is a Poissonian distributed random variable over the fibers. Analytical and numerical calculations showed that the failure process of the system is governed by extreme value statistics, which has a substantial effect on the macroscopic constitutive behaviour and on the microscopic bursting activity as well.
10 pages, 13 figures
References in corpus (15)
- Statistical Models of Fracture
- Tri-critical behavior in rupture induced by disorder
- Burst avalanches in solvable models of fibrous materials
- Damage in Fiber Bundle Models
- Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure
- Bursts in a fiber bundle model with continuous damage
- Effective toughness of heterogeneous brittle materials
- Failure time and microcrack nucleation
- Local load sharing fiber bundles with a lower cutoff of strength disorder
- Crossover behavior in failure avalanches
- Thermodynamics of fiber bundles
- Planar cracks in the fuse model
- Time dependence of breakdown in a global fiber-bundle model with continuous damage
- Effect of discontinuity in threshold distribution on the critical behaviour of a random fiber bundle
- Exact numerical solution for a time-dependent fiber-bundle model with continuous damage