Constraint and size effects in confined layer plasticity

Mitsutoshi Kuroda*, Viggo Tvergaard, Alan Needleman

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


Plane strain finite element analyses are used to model the experiments of Mu et al. (2014, 2016) for a thin metal layer confined between elastic solids. The thin metal layer undergoes elastic–plastic deformations, here modeled by strain gradient plasticity, while the rest of the solid deforms only elastically. Plane strain is assumed and finite strains are accounted for. The microscopic boundary condition at the band interface is initially taken to be zero plastic strain increment, but plastic straining at the interface is allowed when the plastic strain gradient at the interface has exceeded a critical value. When the narrow metal band is inclined 45° relative to the direction of compression of the solid, simple shear develops in the band and predictions are rather similar to those of a one-dimensional analysis for an infinite band. For a band at 90° the elastic parts give significant constraint on plastic flow, the stress fields are non-uniform along the band and the average nominal compressive stress shows strong sensitivity to the layer thickness and to the width of the specimen. Remarkably good qualitative, and in some cases quantitative, agreement is found with the experimental observations of Mu et al. (2014, 2016). Considering also other band angles, both the average nominal shear and compressive stress show variations with the angle.
Original languageEnglish
Article number104328
JournalJournal of the Mechanics and Physics of Solids
Number of pages15
Publication statusPublished - 2021


  • Strain gradient plasticity
  • Plastic constraint
  • Size effects
  • Microscopic boundary conditions


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