Metallic glasses and other amorphous solids fail by the severe localization of strain into "shear bands" which typically precede failure. I will discuss the methodology we use to model this problem on the atomic scale, molecular dynamics simulation. Using these simulations, we infer a set of partial differential equations that model the behavior of the atomic system in terms of a "disorder temperature" that describes the structural degrees of freedom in the glass. The suppositions of this theory can then be tested quantitatively against the atomistic model. To capture the localized deformation it is natural to extend these equations to include a length scale related to the transition between the plastically and elastically deforming regions. The resulting equation is similar in many ways to the Fisher-Kolmogorov equation, which also arises in the modeling on solidification fronts and other propagating interfaces. The solutions of this equation and the consequences for the physical problem will be discussed.
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