  The deformation of brittle material is primarily accompanied by
micro-cracking and faulting. However, it has often been found that continuum
fluid models, usually based on a non-Newtonian viscosity, are applicable. To
explain this rheology, we use a fiber-bundle model, which is a model of damage
mechanics. In our analyses, yield stress was introduced. Above this stress, we
hypothesize that the fibers begin to fail and a failed fiber is replaced by a
new fiber. This replacement is analogous to a micro-crack or an earthquake and
its iteration is analogous to stick-slip motion. Below the yield stress, we
assume that no fiber failure occurs, and the material behaves elastically. We
show that deformation above yield stress under a constant strain rate for a
sufficient amount of time can be modeled as an equation similar to that used
for non-Newtonian viscous flow. We expand our rheological model to treat
viscoelasticity and consider a stress relaxation problem. The solution can be
used to understand aftershock temporal decay following an earthquake. Our
results provide justification for the use of a non-Newtonian viscous flow to
model the continuum deformation of brittle materials.
