Experimental study of shear band formation: Bifurcation and localization

Abstract

-We report the experimental observation of the bifurcation at the origin of localization of the deformation in a granular material submitted to uniaxial compression. We present a quantitative characterization of the heterogeneity in the strain field repartition allowing to evidence objectively the existence of a bifurcation initiating the shear bands formation process. We show that this bifurcation is supercritical and has no clear signature on the stress-strain curve. At the bifurcation, a symetry breaking occurs characterized by the emergence of a well-defined orientation corresponding to the Mohr-Coulomb angle. Yet, plasticity is still diffuse and the shear band extension is of the order of the sample width. While loading proceeds, the shear band narrows until it reaches, after the peak of the stress-strain curve, a stationary width.

Experimental study of shear bands formation in a granular material

“…The observed behavior is very reproducible (see References [12,17] and the movies in supplemental material of those references). Intermittent heterogeneities of the strain are observed from the very beginning of the loading [12][13][14].…”

“…Other methods allows to obtain complementary informations that confort the results presented here (see Ref. [17] for a full detailed study).…”

“…The evolution of this pattern as the loading proceeds is complex. Finally, from an axial deformation of about 6.5%, well defined stationary shear bands are observed [12,17] with an angle corresponding to the Mohr-Coulomb angle [19]. The angles measured directly on the maps are shown in insert Figure 3(a) and the Mohr-Coulomb values deduced independently from the loading curve are indicated on the graph.…”

“…We have developed different image analysis tools [17,20,21] in order to characterize quantitatively the process of formation of the shear band. We present here only the results obtained using projection analysis.…”

Protocol Dependence and State Variables in the Force-Moment Ensemble

“…2-3, we observe that as confining pressure increases, the distributions of both normal and deviatoric components broaden [6][7][8]11]. Note that the states prepared under the two different shear-loading protocols (A, B) were found to exhibit spontaneous symmetry breaking, resulting in a bias towards negative and positive deviatoric components, respectively [38]. Consequently, we treat these two protocols separately.…”