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The random fiber bundle (RFB) model, with the strength of the fibersdistributed uniformly within a finite interval, is studied under the assumptionof global load sharing among all unbroken fibers of the bundle. At any fixedvalue of the applied stress (load per fiber initially present in the bundle),the fraction of fibers that remain unbroken at successive time steps is shownto follow simple recurrence relations. The model is found to have stable fixedpoint for applied stress in the range 0 and 1; beyond which total failure ofthe bundle takes place discontinuously. The dynamic critical behavior near thisfailure point has been studied for this model analysing the recurrencerelations. We also investigated the finite size scaling behavior. At thecritical point one finds strict power law decay (with time t) of the fractionof unbroken fibers. The avalanche size distribution for this mean-fielddynamics of failure has been studied. The elastic response of the RFB model hasalso been studied analytically for a specific probability distribution of fiberstrengths, where the bundle shows plastic behavior before complete failure,following an initial linear response.Comment: 13 pages, 5 figures, extensively revised and accepted for publication  in Phys. Rev.

Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model