A plastic flow theory for amorphous materials

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.