Phase transition in fiber bundle models with recursive dynamics

Abstract

We study the phase transition in a class of fiber bundle models in which the fiber strengths are distributed randomly within a finite interval and global load sharing is assumed. The dynamics is expressed as recursion relations for the redistribution of the applied stress and the evolution of the surviving fraction of fibers. We show that an irreversible phase transition of second-order occurs, from a phase of partial failure to a phase of total failure, when the initial applied stress just exceeds a critical value. The phase transition is characterised by static and dynamic critical properties. We calculate exactly the critical value of the initial stress for three models of this kind, each with a different distribution of fiber strengths. We derive the exact expressions for the order parameter, the susceptibility to changes in the initial applied sress and the critical relaxation of the surviving fraction of fibers for all the three models. The static and dynamic critical exponents obtained from these expressions are found to be universal.

15 pages (REVTeX4); 7 figures (eps); title and abstract modified; paragraph of discussion added before section VI; three new references included; to appear in Phys. Rev. E (2003)

References in corpus (3)

• Bursts in a fiber bundle model with continuous damage
• Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model
• Time dependence of breakdown in a global fiber-bundle model with continuous damage

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