A simple model for size effects in constrained shear

Abstract

Simple shear of a ductile layer constrained between two rigid solids is analyzed using a conventional one dimensional strain gradient plasticity formulation. The aim of the analyses is to gain insight into the scaling relations and size effects seen in the experiments of Mu et al.(2014, 2016, 2017). Our analysis presumes that the deviation from previous predictions based on conventional strain gradient plasticity theory is not due to a defect in the theory but is due to a change in boundary condition that takes place when a sufficiently large plastic shear strain gradient develops at the layer boundaries. Predictions based on this presumption are qualitatively, and in some aspects, quantitatively consistent with a range of the observations.