TRACKING OF SHEAR BANDS .1. THE ONE-DIMENSIONAL CASE

We develop a model for the dynamics of a fully developed shear band th at allows effective computation across several length scales, From a m acroscopic point of view, a shear band is a discontinuity in tangentia l velocity that supports a shear stress, Numerical simulation of the f ull system of governing equations reveals that the internal structure of the band consists of a quasistatic core surrounded by a thermal lay er, We show that the shear band can be modeled as a composite structur e whose evolution is governed by an integral equation, coupled to the external flow through jump conditions, We establish the accuracy of th e model equations by numerical experiments.