Numerical implementation and validation of a consistently homogenized higher order plasticity model

Abstract

SummaryA homogenization theory was developed earlier that starts with a meso‐scale gradient plasticity model at the bottom and recovers a macroscopically continuous micromorphic model at the top. Through the scale transition framework, the granular mechanics are smeared consistently over a single grain such that the fine scale properties, microstructural length scale (l), and grain size (L) manifest themselves naturally in the homogenized relations, a point of departure from many continuous higher order theories that assume the constitutive relations a priori. This paper elaborates on the numerical implementation of the homogenized model and benchmark its performance through a plane indentation example against detailed numerical simulations. For the two limiting cases of microfree and microhard condition at grain boundaries, the excellent predictive capability of the homogenized model is demonstrated for a range of l/L ratios, at a significantly lower computational cost. It is furthermore highlighted that a more realistic response at grain boundaries can be achieved easily in the homogenized model, by changing the interfacial resistance parameter. In contrast, a non‐trivial numerical treatment is required at the grain boundaries with meso‐scale models. Finally, the homogenized model is shown to perform well even in the absence of a strong scale separation between meso and macro. Copyright © 2015 John Wiley & Sons, Ltd.