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Published March 2020 | Published
Journal Article Open

Size Scaling of Plastic Deformation in Simple Shear: Fractional Strain-Gradient Plasticity and Boundary Effects in Conventional Strain-Gradient Plasticity


A recently developed model based on fractional derivatives of plastic strain is compared with conventional strain-gradient plasticity (SGP) models. Specifically, the experimental data and observed model discrepancies in the study by Mu et al. (2016, "Dependence of Confined Plastic Flow of Polycrystalline Cu Thin Films on Microstructure," MRS Com. Res. Let. 20, pp. 1–6) are considered by solving the constrained simple shear problem. Solutions are presented both for a conventional SGP model and a model extension introducing an energetic interface. The interface allows us to relax the Dirichlet boundary condition usually assumed to prevail when solving this problem with the SGP model. We show that the particular form of a relaxed boundary condition does not change the underlying size scaling of the yield stress and consequently does not resolve the scaling issue. Furthermore, we show that the fractional strain-gradient plasticity model predicts a yield stress with a scaling exponent that is equal to the fractional order of differentiation.

Additional Information

© 2020 by ASME. Received: November 4, 2019; Revised: December 18, 2019; Accepted: December 18, 2019; Published: January 3, 2020; Published Online: January 14, 2020. Paper No: JAM-19-1556. C.F.O.D. gratefully acknowledges financial support from Vetenskapsrådet (VR E0566901) and the VINN Excellence Center Hero-m funded by Vinnova. M.O. is grateful for the support of the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 1060 "The mathematics of emergent effects" at the Hausdorff Center for Mathematics of the University of Bonn, Germany.

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