Evolution of burst distribution in fiber bundle model

TL;DR

This paper investigates how burst size distributions evolve in a fiber bundle model with equal load sharing, revealing that the power-law exponent remains constant across bundle sizes and varies with loading steps, supported by theoretical and numerical analysis.

Contribution

It introduces a probability-theoretic approach to analyze burst distributions and their evolution in fiber bundle models under load, highlighting the invariance of the distribution exponent with bundle size.

Findings

The burst distribution exponent s does not depend on bundle size.

The exponent s varies with loading step, showing regions of constancy and transition.

Numerical simulations up to N=10^10 confirm the theoretical predictions.

Abstract

We consider a fiber bundle model with a equal load sharing and uniformly distributed breakdown thresholds. A unified probability-theoretic approach was used to describe bundle under continuous and discrete load increase. It was shown that the ratio of distribution D(d) of avalanches of sizes d to the number of bundle load steps exactly corresponds to burst probability of size d. Evolution of s - power law distribution exponent of D(d) was studied as a function of loading step and bundle size. It was shown that s does not depend on bundle size. In the numerical experiment, dependence s on loading step was obtained with fiber bundle size up to N=10^10. The regions of s values constancy and the transition region were found. A distribution of fiber bursts on each loading step was recovered in the numerical simulations. It was shown that a change in the type of this distribution is the reason for evolution of s values in the range of -3 - -5/2.