  We extend the standard fiber bundle model (FBM) with the local load sharing
in such a way that the conservation of the total load is relaxed when an
isolated fiber is broken. In this modified FBM in one dimension (1D), it is
revealed that the model exhibits a well-defined phase transition at a finite
nonzero value of the load, which is in contrast to the standard 1D FBM. The
modified FBM defined in the Watts-Strogatz network is also investigated, and
found is the existences of two distinct transitions: one discontinuous and the
other continuous. The effects of the long-range shortcuts are also discussed.
