An evaluation of higher-order plasticity theories for predicting size effects and localisation

Conventional plasticity theories are unable to capture the observed increase in strength of metallic structures with diminishing size. They also give rise to ill-posed boundary value problems at the onset of material softening. In order to overcome both deficiencies, a range of higher-order plasticity theories have been formulated in the literature. The purpose of this paper is to compare existing higher-order theories for the prediction of a size effect and the handling of localisation effects. To this end, size effect predictions for foils in bending are compared with existing experimental data. Furthermore, a study of one-dimensional harmonic incremental solutions from a uniform reference state allows one to assess the nature of material localisation as predicted by these competing higher-order theories. These analyses show that only one of the theories considered—the Fleck–Hutchinson strain gradient plasticity theory based upon the Toupin–Mindlin strain gradient framework [Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. Adv. Appl. Mech. 33, 295–361]—allows one to describe both phenomena. The other theories show either nonphysical size effects or a pathologically localised post-peak response.