Model of plasticity of amorphous materials

Starting from a classical Kröener-Rieder kinematic picture for plasticity, we derive a set of dynamical equations describing plastic flow in a Lagrangian formulation. Our derivation is a natural and straightforward extension of simple fluids, elastic, and viscous solids theories. These equations contain the Maxwell model as a special limit. This paper is inspired by the particularly important work of Langer and coworkers. We shall show that our equations bear some resemblance with the shear-transformation zones model developed by Langer and coworkers. We shall point out some important differences. We discuss some results of plasticity, which can be described by the present model. We exploit the model equations for the simple examples: straining of a slab and a rod. We find that necking manifests always itself (not as a result of instability), except if the very special constant-velocity stretching process is imposed.

Figure 1

A sketch of the geometry under consideration.