Shear band formation in granular media as a variational problem

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.