Strain gradient plasticity: the flow rule of Fleck and Hutchinson violates thermodynamics ?

^aDepartment of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA

^bDepartment of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

We discuss the physical nature of flow
rules for rate-independent (gradient) plasticity laid down by Aifantis
and by Fleck and Hutchinson. As a central result we show that:

•
the flow rule of Fleck and Hutchinson is incompatible with
thermodynamics unless its nonlocal term is dropped. If the underlying
theory is augmented by a general defect energy dependent on γ^p and γ^p, then compatibility with thermodynamics requires that its flow rule reduce to that of Aifantis.

We
establish this result (and others) within a general framework obtained
by combining a virtual-power principle of Fleck and Hutchinson with the
first two laws of thermodynamics—balance of energy and the
Clausius–Duhem inequality—under isothermal conditions.

Keywords: Constitutive behavior; Viscoplasticity; Strain-gradient plasticity; Prinicipla of virtual power; Thermodynamics