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

TL;DR

This paper introduces a fiber-bundle damage mechanics model to explain the continuum deformation of brittle materials, linking micro-cracking behavior to non-Newtonian fluid rheology and earthquake aftershock decay.

Contribution

It presents a novel fiber-bundle model incorporating yield stress and fiber replacement to unify brittle deformation with non-Newtonian flow behavior.

Findings

Deformation above yield stress can be modeled as non-Newtonian viscous flow.

The model explains aftershock decay through stress relaxation analysis.

Fiber failure and replacement mimic micro-cracking and seismic events.

Abstract

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.