  We present an extension of the continuous damage fiber bundle model to
describe the gradual degradation of highly heterogeneous materials under an
increasing external load. Breaking of a fiber in the model is preceded by a
sequence of partial failure events occurring at random threshold values. In
order to capture the subsequent propagation and arrest of cracks, furthermore,
the disorder of the number of degradation steps of material constituents, the
failure thresholds of single fibers are sorted into ascending order and their
total number is a Poissonian distributed random variable over the fibers.
Analytical and numerical calculations showed that the failure process of the
system is governed by extreme value statistics, which has a substantial effect
on the macroscopic constitutive behaviour and on the microscopic bursting
activity as well.
