  Motivated by recent experiments studying the creep and breakup of a protein
gel under stress, we introduce a simple mesoscopic model for the irreversible
failure of gels and fibrous materials, and demonstrate it to capture much of
the phenomenology seen experimentally. This includes a primary creep regime in
which the shear rate decreases as a power law over several decades of time, a
secondary crossover regime in which the shear rate attains a minimum, and a
tertiary regime in which the shear rate increases dramatically up to a finite
time singularity, signifying irreversible material failure. The model also
captures a linear Monkman-Grant scaling of the failure time with the earlier
time at which the shear rate attained its minimum, and a Basquin-like power law
scaling of the failure time with imposed stress, as seen experimentally. The
model furthermore predicts a slow accumulation of low levels of material damage
during primary creep, followed by the growth of fractures leading to sudden
material failure, as seen experimentally.
