  We study random fiber bundle model (RFBM) with different threshold strength
distributions and load sharing rules. A mixed RFBM within global load sharing
scheme is introduced which consists of weak and strong fibers with uniform
distribution of threshold strength of fibers having a discontinuity. The
dependence of the critical stress of the above model on the measure of the
discontinuity of the distribution is extensively studied. A similar RFBM with
two types of fibers belonging to two different Weibull distribution of
threshold strength is also studied. The variation of the critical stress of a
one dimensional RFBM with the number of fibers is obtained for strictly uniform
distribution and local load sharing using an exact method which assumes
one-sided load transfer. The critical behaviour of RFBM with fibers placed on a
random graph having co-ordination number 3 is investigated numerically for
uniformly distributed threshold strength of fibers subjected to local load
sharing rule, and mean field critical behaviour is established.
