Finite strain analysis of nonuniform deformation inside shear bands in sands

Abstract

SUMMARYA methodology has been developed to extend the incremental (Eulerian) Digital Image Correlation (DIC) technique to enable a Lagrangian-based large-strain analysis framework to examine the nature of strain and kinematic nonuniformity within shear bands in sands. Plane strain compression tests are performed on dense sands in an apparatus that promotes unconstrained persistent shear band formation. DIC is used to capture incremental, grain-scale displacements in and around shear bands. The performance of the developed accumulation algorithm is validated by comparing accumulated displacements with two sources of reference measurements. A comparison between large and infinitesimal rotation is performed, demonstrating the nature of straining within shear bands in sands and the necessity of using a finite strain formulation to characterize ensuing behavior. Volumetric strain variation along the shear band is analyzed throughout macroscopic postpeak deformation. During softening, volumetric activity within the shear band is purely dilative. During the global critical state, the shear band material is seen on the average to deform at zero volumetric strain; however, locally, the sand is seen to exhibit significant nonzero volumetric strain, putting into question the current definition of critical state. At the softening-critical state transition, a spatially periodic pattern of alternating contraction and dilation along the shear band is evidenced, and a preliminary evaluation indicates that the periodicity appears to be a physical phenomenon dictated only in part by median grain size.

Vortex formation and dissolution in sheared sands

“…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. To monitor displacements over longer strain increments, incremental DIC analyses are accumulated using the methodology described by Chupin et al [27]. DIC displacement measurement accuracy for our apparatus, materials and analysis increments is around ±0.002 mm.…”

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

“…From the rich DIC displacement fields, the local deformation gradient, F, is computed. Local volume changes (assumed to be reflective of in-plane area changes) are then quantified in terms of the Jacobian, J, of F. Macro-rotations, X, that correspond to rigid body rotations are obtained from the polar decomposition of F. Precise formulations for these quantities are described in detail in Chupin et al [9].…”

“…Thus, to evaluate behavior over wider strain increments, the incremental, Eulerian-based DIC results were accumulated in a Lagrangian frame [9]. Then, the deformation gradients were computed over the accumulated displacement field, and strain and kinematic measures subsequently determined.…”

“…Based on these findings, we recommend limiting strain increments for DIC analysis of no more than 4-5% gross shear band shear strain. To analyze kinematic behavior over larger strain increments, the incremental DIC analyses were accumulated [9].…”

Relationship between vortex structures and shear localization in 3D granular specimens based on combined DEM and Helmholtz–Hodge decomposition

“…The vortex structures were directly related to the occurrence of spontaneous shear localization in the granular specimen. The numerical results of vortex structures and local volume changes along a granular shear zone were qualitatively compared with the experimental outcomes of plane strain compression on sand by Abedi et al [11] and Chupin et al [30].…”