  The random fiber bundle (RFB) model, with the strength of the fibers
distributed uniformly within a finite interval, is studied under the assumption
of global load sharing among all unbroken fibers of the bundle. At any fixed
value of the applied stress (load per fiber initially present in the bundle),
the fraction of fibers that remain unbroken at successive time steps is shown
to follow simple recurrence relations. The model is found to have stable fixed
point for applied stress in the range 0 and 1; beyond which total failure of
the bundle takes place discontinuously. The dynamic critical behavior near this
failure point has been studied for this model analysing the recurrence
relations. We also investigated the finite size scaling behavior. At the
critical point one finds strict power law decay (with time t) of the fraction
of unbroken fibers. The avalanche size distribution for this mean-field
dynamics of failure has been studied. The elastic response of the RFB model has
also been studied analytically for a specific probability distribution of fiber
strengths, where the bundle shows plastic behavior before complete failure,
following an initial linear response.
