  We introduce a model for yielding, inspired by fracture models and the
failure of a sheared granular medium in which the applied shear is resisted by
self-organized force chains. The force chains in the granular medium (GM) are
considered as a bundle of fibres of finite strength amongst which stress is
randomly redistributed after any other fibre breaks under excessive load. The
model provides an exponential distribution of the internal stress and a
log-normal shaped distribution of failure stress, in agreement with
experimental observations. The model displays critical behaviour which
approaches mean field as the number of random neighbours $k$ becomes large and
also displays a failure strength which remains finite in the limit of infinite
size. From comparison with different models it is argued that this is an effect
of uncorrelation. All these macroscopic properties appear statistically stable
with respect to the choice of the chains' initial strength distribution. The
investigated model is relevant for all systems in which some generic external
load or pressure is borne by a number of units, independent of one another
except when failure of a unit causes load transfer to some random choice of
neighbouring units.
