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

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:
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• 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 γpγp and ∇γp∇γp, 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.