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

We analyze dissipative scale effects within a one-dimensional theory, developed in [L. Anand et al., J. Mech. Phys. Solids, 53 (2005), pp. 1789–1826], which describes plastic flow in a thin strip undergoing simple shear. We give a variational characterization of the yield (shear) stress—the threshold for the onset of plastic flow—and we use this characterization, together with results from [M. Amar et al., J. Math. Anal. Appl., 397 (2011), pp. 381–401], 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.