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The deformation of brittle material is primarily accompanied bymicro-cracking and faulting. However, it has often been found that continuumfluid models, usually based on a non-Newtonian viscosity, are applicable. Toexplain this rheology, we use a fiber-bundle model, which is a model of damagemechanics. In our analyses, yield stress was introduced. Above this stress, wehypothesize that the fibers begin to fail and a failed fiber is replaced by anew fiber. This replacement is analogous to a micro-crack or an earthquake andits iteration is analogous to stick-slip motion. Below the yield stress, weassume that no fiber failure occurs, and the material behaves elastically. Weshow that deformation above yield stress under a constant strain rate for asufficient amount of time can be modeled as an equation similar to that usedfor non-Newtonian viscous flow. We expand our rheological model to treatviscoelasticity and consider a stress relaxation problem. The solution can beused to understand aftershock temporal decay following an earthquake. Ourresults provide justification for the use of a non-Newtonian viscous flow tomodel the continuum deformation of brittle materials.

A fiber-bundle model for the continuum deformation of brittle material