Tracking of shear bands I. The one-dimensional case

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