Shear Band Formation in Granular Media as a Variational Problem

Abstract

Strain in sheared dense granular material is often localized in a narrow region called the shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The nontrivial shape of the shear band was measured as the function of the cell geometry. First, we present a geometric argument for narrow shear bands that 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 that are detached from the free surface and are entirely covered in the bulk.

Fragmentation and shear band formation by slow compression of brittle porous media

“…The spontaneous emergence of the shear band and its position, orientation, and structure are all important characteristics of the compressive failure of heterogeneous, disordered, or amorphous materials [1][2][3][4][5]25]. Since localization is preceded by random microcracking, the algorithmic determination of the position of the shear band is rather complex in DEM simulations.…”

“…They can also occur by locally brittle failure in disordered granular media such as concrete, ice, rock, and some ceramics, where the microscopic failure mechanism involves tensile or shear fracture [4,5]. In particular, natural faults and localized shear bands in brittle porous media often contain a loose aggregate of fragments known as a "fault gouge."…”

Hydrodynamic modeling of granular flows in a modified Couette cell

“…However a theoretical framework is still lacking to understand them. A modified Couette configuration has recently brought the possibility of observing wide shear bands in granular media [5] and allows to more deeply test recent theories [6,7]. In this configuration sketched in Fig.…”

“…This is consistent with the fact that our model reduces to a simple Coulomb friction law (a Drucker-Prager criterion) for I→0. In Unger et al's model [6], a constant friction law produces sharp shear bands. Concerning the closed shape, the widths have roughly the same behavior, but for low rotation rate we observe a slight departure from the power law.…”

“…In this regime, a differential rotation (called precession in the following) appears: the central upper part rotates more slowly than the bottom [9,10]. A theoretical model, which is based on a principle of minimization of the Coulomb friction dissipation, predicts infinitely sharp shear band and a hysteretic transition between open and closed regimes [6]. Török et al recently introduce a random disorder, they find a smooth transition and wide shear bands with corrects scaling laws when averaging over an ensemble of sharp bands [11].…”