Similarity and Bifurcation in Unstable Viscoplastic Shear

Abstract

The linear stability of perturbed simple shear in a ductile plastic material which can strain-soften is analyzed on a finite time interval. An asymptotic study is made of the influence of two small dimensionless coefficients, which are shown to be connected by a similarity parameter. The first coefficient is a dimensionless group of parameters which can be interpreted as the ratio of the momentum flux to the plastic flow stress, while the second coefficient gives the scale of the viscous damping. A criterion is derived for the minimum strain rate where the early-time behavior changes from oscillatory to exponential.