Shear band formation in granular media as a variational problem

TL;DR

This paper models shear band formation in dense granular media as a variational problem, using energy dissipation principles to predict shear band shapes and behaviors in different geometries.

Contribution

It introduces a variational framework based on energy dissipation to describe shear band shapes and explores detached shear bands in granular materials.

Findings

Minimum dissipation principle accurately predicts shear band shape.

Geometric argument links surface position to bulk shape.

Detached shear bands can form entirely within the bulk.

Abstract

Strain in sheared dense granular material is often localized in a narrow region called shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The non-trivial shape of the shear band was measured as the function of the cell geometry. First we present a geometric argument for narrow shear bands which connects the function of their surface position with the shape in the bulk. Assuming a simple dissipation mechanism we show that the principle of minimum dissipation of energy provides a good description of the shape function. Furthermore, we discuss the possibility and behavior of shear bands which are detached from the free surface and are entirely covered in the bulk.