Fabric rates applied to kinematic models: evaluating elliptical granular materials under simple shear tests via discrete element method

Abstract

This study aims to identify a simple and accurate fabric rate to represent an angular velocity variable in a kinematic model of non-coaxial granular materials via discrete element method (DEM). The fabric tensor is a statistical quantity that represents vector directions (e.g., particle orientation, contact normal, contact force), the fabric anisotropy is an invariant of the fabric tensor which describes the vector direction anisotropy in an assembly, and the fabric inclination marks the principal direction of the fabric tensor—fabric rates are their respective time derivatives. Specimens with inherent anisotropy composed of elliptical particles were generated and tested using an upgraded two-dimensional (2D) DEM code, NS2D; naturally, it is appropriate to utilize a 2D DEM approach to investigate a 2D kinematic model. Strain-rate controlled constant-volume DEM monotonic and cyclic simple shear tests were conducted on two types of granular materials with particle aspect ratios of 1.4 and 1.7, and several fabric anisotropy rates and fabric inclination rates were considered based on a few fabric tensors: contact normal, contact force, and particle orientation. We then compared the theoretical rotation rates and measured fabric rates for a medium-dense specimen by DEM simple shear testing, and found that all the fabric anisotropy rates (and most fabric inclination rates) differed significantly from the theoretical values. Only the modified fabric inclination rate of particle orientation (FIRP) accurately reflected its theoretical rotation rate in the simple shear tests. Averaged micro-pure rotation rate (APR) was also applied to examine the rotation rates, as suggested by previous researchers, to explore the difference between APR as a statistical variable of time derivative of particle directions while FIRP is the time derivative of a statistical variable of particle directions.