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

R.A.B. Engelen, N.A. Fleck, R.H.J. Peerlings, M.G.D. Geers

Research output: Contribution to journalArticleAcademicpeer-review

79 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1857-1877
JournalInternational Journal of Solids and Structures
Issue number7-8
Publication statusPublished - 2006


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