  Shear bands are narrow zones of intense shear observed during plastic
deformations of metals at high strain rates. Because they often precede
rupture, their study attracted attention as a mechanism of material failure.
Here, we aim to reveal the onset of localization into shear bands using a
simple model developed from viscoplasticity. We exploit the properties of scale
invariance of the model to construct a family of self-similar focusing
solutions that capture the nonlinear mechanism of shear band formation. The key
step is to de-singularize a reduced system of singular ordinary differential
equations and reduce the problem into the construction of a heteroclinic orbit
for an autonomous system of three first-order equations. The associated
dynamical system has fast and slow time scales, forming a singularly perturbed
problem. The geometric singular perturbation theory is applied to this problem
to achieve an invariant surface. The flow on the invariant surface is analyzed
via the Poincar\'{e}-Bendixson theorem to construct a heteroclinic orbit.
