Some forms and properties of models of strain-gradient plasticity

A fairly general formulation for rate-independent strain-gradient plasticity is studied. It includes the possibility of both energetic and dissipative higher-order stresses and a general effective plastic strain-rate E, which is convex and homogeneous of degree 1 in the plastic strain-rate and its gradient. The corresponding work-conjugate generalized stress is a convex function of the dissipative stress and higher-order stress and is homogeneous of degree 1 in these variables. The free energy depends on plastic strain and its gradient, as well as on elastic strain. The generalized yield stress depends on the history up to the present of the plastic strain and its gradient. This contrasts with most studies to date in which generalized yield stress is taken to depend only on E, the time-integral of E. The simple shear of a strip is studied within this framework. It is loaded so as to produce uniform Cauchy stress, which increases monotonically in time. Initially the boundaries are free of micro-traction but at a time T the boundaries are passivated. As in previous studies, an elastic gap is observed, before plastic flow resumes. In contrast to previous studies, this is now demonstrated to be governed entirely by the function E that defines the associated flow law. The hardening, either energetic or dissipative, regulates the plastic strain-rate, once this resumes. (C) 2018 Elsevier Ltd. All rights reserved.