Self-organized criticality in a fibre-bundle-type model

Abstract

The dynamics of a fibre-bundle type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to the elements broken during avalanches. When an avalanche ends, failed elements are regenerated with strengths taken from a probability distribution. For a large enough N and certain restrictions on the distribution of individual strengths, the system reaches a self-organized critical state where the spectrum of avalanche sizes is a power law with an exponent τ ≃ 1.5.

Fractures in complex fluids: the case of transient networks

“…Recently, Mora [Mora (2011)] has proposed a model, the Self healing and activated bond rupture nucleation model (SH-ABR model), which aims to describe fracture nucleation in transient networks considering both activated bond rupture and cross-links re-formation to overcome the intrinsic limitation of the ABR model. It is based on the fiber bundle model, usually used to study fracture in heterogeneous materials [Coleman (1958); Moreno et al (1999); Kun et al (2000); Ciliberto et al (2001); Pradhan et al (2010)]: a set of fibers (or bonds) is located on a supporting lattice and a random stress threshold is assigned to its elements. The set is loaded and a bond breaks when its load exceeds a threshold value.…”

Hydromechanical triggering of landslides: From progressive local failures to mass release

“…However, as a bundle approaches its global failure (i.e., the entire bundle breaks) the power law exponent converges to a value of −3/2 [ Pradhan et al , 2006] reflecting transition in which large events become more frequent. In contrast with the BTW and OFC models presented in previous subsections, a marginally stable critical state (fulfilling conditions of SOC systems) is not possible for FBM unless fibers can “heal” after failure [ Moreno et al , 1999]. The FBM formalism provides unique modeling capabilities that not only accommodate gradual loss of mechanical strength prior to abrupt failure, but also capture discrete mechanical events that may be measured independently by acoustic or electrical sensors [ Amitrano et al , 2005] and thus provide a means for noninvasive monitoring of system mechanical state.…”

Damage in fiber bundle models

“…The very successful micromechanical models of fiber reinforced composites are improved variants of FBM taking into account stress localization (local load transfer) [19,20,21,24], the effect of matrix material between fibers [20,21,22,23,29,30,31], and possible non-linear behavior of fibers [16]. Previous studies of FBM addressed the macroscopic constitutive behavior, the reliability and size scaling of the global material strength, and the avalanches of fiber breaks preceding ultimate failure [10,11,32,33,34,35,36].…”