An approach to determining the thicknesses of shear bands with an echelon‐crack structure

Abstract

In this paper, the internal structure of shear band is investigated, and a model of the shear band with an echelon crack structure is developed. The model assumes the shear band to be composed of two conjugate sets of echelon cracks, such that the smaller echelon cracks are embedded in the space of the larger ones. The additional strain induced by the echelon cracks and the anisotropic development of the compliance tensor in the shear band zone are analyzed. The critical crack density at the onset of shear band is obtained by applying the bifurcation condition. Deviating from previous approaches, the new procedure evaluates the thickness of shear band based on the geometrical characteristics of echelon crack arrays and the failure probability of grain boundaries in the longitudinal direction at the onset of shear band. Parametric analysis shows that grain size, internal friction angle, dilation angle, and failure probability of grain boundaries are the dominant factors that account for the shear band thickness. The calculated results are consistent with the experimental data available in the literature. The model soundly explains that the measurements of the shear band thickness are generally scattered, ranging from 4 to 30 (or even more) times the grain size.

Micropolar hypoplasticity for persistent shear band in heterogeneous granular materials

“…An interesting conclusion from these figures is that the persistent shear band is not a band in the beginning, but rather, a thick zone of progressively increasing deformation. As the sample is vertically compressed, the deformation gradually concentrates within a narrow zone (see [13,61,62]), and only when the sample is compressed enough does the true geometric character of the persistent shear band emerge. Next we address the issue of time stepping, which is critical for the accuracy of an explicit time integration.…”