Abstract
The fiber bundle model is essentially an array of elements that break when sufficient load is applied on them. With a local loading mechanism, this can serve as a model for a one-dimensional interface separating the broken and unbroken parts of a solid in mode-I fracture. The interface can propagate through the system depending on the loading rate and disorder present in the failure thresholds of the fibers. In the presence of a quasi-static drive, the intermittent dynamics of the interface mimic front propagation in disordered media. Such situations appear in diverse physical systems such as mode-I crack propagation, domain wall dynamics in magnets, charge density waves, contact lines in wetting etc. We study the effect of the range of interaction, i.e. the neighborhood of the interface affected following a local perturbation, on the statistics of the intermittent dynamics of the front. There exists a crossover from local to global behavior as the range of interaction grows and a continuously varying ‘universality’ in the intermediate range. This means that the interaction range is a relevant parameter of any resulting physics. This is particularly relevant in view of the fact that there is a scatter in the experimental observations of the exponents, in even idealized experiments on fracture fronts, and also a possibility in changing the interaction range in real samples.
Highlights
The fiber bundle model, introduced in Ref. [1], is a useful approach for modeling catastrophic failures in disordered solids from a microscopic point of view [2, 3]
We study the effect of the range of interaction, i.e. the neighborhood of the interface affected following a local perturbation, on the statistics of the intermittent dynamics of the front
It aims at using the minimal ingredients that capture the universal statistical features associated with phenomena [4, 5, 6] such as: the breaking of disordered samples like wood [7], glass [8], polymeric foam [9], and paper [10]; roughness of fracture fronts in peeling experiments with PDMS samples [11, 12, 13]; and precursor events in the catastrophic collapse of cliffs [14], landslides [15] etc
Summary
The fiber bundle model, introduced in Ref. [1], is a useful approach for modeling catastrophic failures in disordered solids from a microscopic point of view [2, 3]. It aims at using the minimal ingredients that capture the universal statistical features associated with phenomena [4, 5, 6] such as: the breaking of disordered samples like wood [7], glass [8], polymeric foam [9], and paper [10]; roughness of fracture fronts in peeling experiments with PDMS samples [11, 12, 13]; and precursor events in the catastrophic collapse of cliffs [14], landslides [15] etc It considers a set of elements having finite failure thresholds drawn from a probability distribution as a simple model for a disordered solid. Statistics that are qualitatively similar to experiments [23] are observed only in the mean-field limit
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