Quantification of large and localized deformation in granular materials

https://doi.org/10.1016/j.ijsolstr.2012.03.006Get rights and content
Under an Elsevier user license
open archive

Abstract

Quantifying large deformation in granular assemblies using concepts originating from continuum mechanics is a challenging task because of (1) the discontinuous nature of granular displacement, which does not allow the definition of a continuum measure of deformation, and (2) the almost inevitable shear band localization. These problems exist in both real-world granular materials and their numerical idealizations using particle-based simulations. In this work a new method is developed in order to address these issues. Instead of creating a meshed equivalent continuum for quantifying small engineering strains, the new method performs independent random queries on the velocity gradient characteristics of arbitrary sub-domains in the assembly through the novel concept of overlapping reference triangles, thus, enabling rigorous handling of large deformations which are usually associated with localization. The proposed method is illustrated and validated by discrete element method (DEM) simulation of a biaxial compressive test, in which apparent shear banding takes place. The homogenized deformation quantifications based on the new method match the estimations from the imposed boundary conditions. The numerical examples are also applied to (1) quantifying the heterogeneous distribution of deformation over the specimen, (2) visualizing the nucleation process of shear bands, and (3) characterizing shear flow patterns in shear bands. An investigation on the effects of the reference triangle sizes yields some inspiring and practically significant results.

Highlights

► A new method for quantifying large and localized deformation in granular assemblies is developed. ► Velocity gradient and rate-of-deformation instead of small engineering strain are used as the basic quantities. ► Deformation rate characteristics of arbitrary domains can be individually queried. ► Statistical analysis of queried information can be conveniently performed. ► Application of the new method in studying the shear banding process is demonstrated.

Keywords

Granular material
Deformation
Strain
Shear band
Discrete element method
Velocity gradient
Rate of deformation

Cited by (0)