Dissipative scale effects in strain-gradient plasticity: the case of simple shear

TL;DR

This paper investigates how the thickness of a strip influences its yield stress in strain-gradient plasticity, confirming that thinner specimens exhibit higher strength due to dissipative scale effects.

Contribution

It provides a variational characterization of yield stress in a one-dimensional shear model and derives an explicit relation between yield stress and strip height.

Findings

Thinner strips have higher yield stress.

Explicit relation between strip height and yield stress.

Supports the strengthening effect in small-scale plasticity.

Abstract

We analyze dissipative scale effects within a one-dimensional theory, developed in [L. Anand et al. (2005) J. Mech. Phys. Solids 53], which describes plastic flow in a thin strip undergoing simple shear. We give a variational characterization of the {\emph{ yield (shear) stress}} --- the threshold for the inset of plastic flow --- and we use this characterization, together with results from [M. Amar et al. (2011) J. Math. Anal. Appl. 397], to obtain an explicit relation between the yield stress and the height of the strip. The relation we obtain confirms that thinner specimens are stronger, in the sense that they display higher yield stress.