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SUMMARYThis paper presents a gradient plasticity formulation developed in a strongly non-local format and applicable to ductile failure for ÿnite strain plasticity. The obtained formulation is an extension of a framework proposed by Simo (Computer Methods in Applied Mechanics and Engineering 1988; 66:199) into the softening and localization regime. The presented model inherits the well-established regularization properties of its strongly non-local enrichment and leads to an implicit computational scheme with a consistent tangent operator. Numerical examples are given which illustrate the strongly non-local character of the formulation, the in uence of the type of intrinsic length scale considered, as well as several topics on plastic failure initiation and evolution into the geometrically non-linear regime.

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 ToupinMindlin strain gradient framework . 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.

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