Characterization of mesoscale instabilities in localized granular shear using digital image correlation

Abstract

Within shear bands in sands, deformation is largely non-affine, stemming primarily from buckling of well-known force chains and also from vortex-like structures. In the spirit of current trends toward multiscale modeling, understanding the links between these mesoscale deformational entities and corresponding macroscale response will form the basis for the next generation of sand behavioral models and may also aid in efforts to understand jamming-unjamming transitions in dense granular flows in general. Experimental methods to quantify and characterize such subscale kinematics, in particular in real sands, will play critical roles in these efforts. Digital Image Correlation (DIC) is a fast growing experimental technique to nondestructively measure surface displacements from digital images. Here, DIC has been employed to identify and characterize the development of vortex structures inside shear bands formed in dense sands during plane strain compression. A rigorous assessment of the DIC method has been performed, in particular for subscale behavioral characterization in unbonded granular solids, and guidelines are offered for accurate implementation. While DIC systematically overestimates shear band thickness, a methodology has been devised to compensate for this overestimation. Shear band thickness for four different uniform sands were found to range between 6 and 9 grain diameters, and for a well-graded sand between 8 and 9.5 grain diameters. These determinations agree with visual inspections of grain kinematics from the image data, as well as recent theoretical predictions.

Vortex formation and dissolution in sheared sands

“…The vortex centers correlate with the peaks in rotational strain seen previously by the authors [17,18]. At the conflux between adjacent vortices, the residual displacements are in opposition and induce local volumetric contraction [26]. Interestingly, we do not see evidence of "microbands" of slip between adjacent vortices, as were seen by Alonso-Marroquin et al [8] and Tordesillas et al [15] in simulations on circular particles.…”

“…To further improve mapping accuracy, subsets are allowed to deform to first order (note, the pixels themselves are not physically deforming; rather, the cubic-order continuous fit to the gray level intensities is deforming). Previous research [26] has shown that DIC analysis increments used here (0.1 % axial strain or about 3 % gross shear strain across the shear band) are sufficient to accommodate first order subset deformation. However, as will be seen below, correlated grain motion such as in vortex cells occurs over longer time/strain increments than afforded by the DIC analyses.…”

“…While a brief description of DIC is given below, more detail can be found in [24,25]. Other works by the authors [18,26], discuss considerations specific to DIC use in dense granular solids.…”

“…Here, subsets were sized 63 pixels (slightly smaller than Fig. 3): this encompasses the equivalent of about four-by-four sand grains, manifests unique gray level patterns for reliable mapping, and is slightly smaller than the shear band thickness to enable discernment of individual vortices confined to within the shear band [26]. Subsets were spaced center-to-center 13 pixels, or about 0.75 mm, yielding displacement data point spacing on the order of a sand grain.…”

“…This jamming induces local volumetric contraction [26], but also serves to arrest the vortices from further progress: in the following increment, 142-148, only one vortex remains. Further, regions of affine-like deformation have formed directly behind the jammed regions of previous increments.…”