  We introduce two versions of a renormalization group scheme for the equal
load sharing fiber bundle model. The renormalization group is based on
formulating the fiber bundle model in the language of damage mechanics. A
central concept is the work performed on the fiber bundle to produce a given
damage. The renormalization group conserves this work. In the first version of
the renormalization group, we take advantage of ordering the strength of the
individual fibers. This procedure, which is the simpler one, gives EXACT
results -but cannot be generalized to other fiber bundle models such as the
local load sharing one. The second renormalization group scheme based on the
physical location of the individual fibers may be generalized to other fiber
bundle models.
