A higher-gradient non-local model for slow granular flows, and its predictions for selected complex flows

A variety of non-local plasticity models have been proposed for dense, slow granular flows, motivated by several experimental observations, such as the occurrence of thin shear layers adjacent to moving boundaries, and the apparent creep in regions far from the shear layers. While some models have a clear mechanical basis, others are based on analologies to other physical systems whos relevance to granular flows is unconvincing. A rational basis for arriving at a simple non-local plasticity model that accurately captures the observed experiemntal features is therefore of interest. Here we present a non-local model that is based on the simple idea of volume averaging over rapidly-varying quantities. We show that it overcomes many of the shortcomings of the previously proposed models. In addition to capturing regions of sharp velocity gradients, the model also incorporates the accompanying reduction in density within such regions. The predictions of the model for some selected flow geometries that yield complex two or three dimensional flows will be presented, and comparisons will be made with experiments.