A plastic flow theory for amorphous materials

TL;DR

This paper develops a dynamical Lagrangian model for plastic flow in amorphous materials, extending fluid and solid theories, and demonstrates its application to simple deformation scenarios.

Contribution

It introduces a novel set of dynamical equations for amorphous plasticity, extending existing models to include a Lagrangian framework and connecting to the Maxwell model.

Findings

Necking occurs naturally in the model, not as an instability.

The model reproduces known behaviors of plastic deformation.

Special conditions can suppress necking phenomena.

Abstract

Starting from known kinematic picture for plasticity, we derive a set of dynamical equations describing plastic flow in a Lagrangian formulation. Our derivation is a natural and a straightforward extension of simple fluids, elastic and viscous solids theories. These equations contain the Maxwell model as a special limit. We discuss some results of plasticity which can be described by this set of equations. 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.