Thermodynamics applied to gradient theories involving the accumulated plastic strain : The theories of Aifantis and Fleck and Hutchinson and their generalization

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.