Discrete element modelling of material non‐coaxiality in simple shear flows

Abstract

SUMMARYWe investigate the quasi-static simple shear flow of a two-dimensional assembly of cohesionless particles using discrete element method (DEM) simulations. We focus on the unsteady flow regime where the solid would experience significant evolution of stresses, mobilised shear strength and dilation. We construct the DEM model using a discretised-wall confined granular cell where the apparent boundary is allowed to dilate or contract synchronously with the confined solid. A rather uniform simple shear field is achieved across the whole assembly, which benefits rheological studies in generalising constitutive laws for continuum methods. We examine two aspects of the simple shear behaviour: macroscopic stress and strain rate evolution, particularly the noncoaxiality between the principal directions of the two; and micromechanics such as evolution of fabric. For an initially anisotropic specimen sheared under constant normal pressure, the direction of principal stress rotates towards that of the principal strain rate, gradually reducing the degree of non-coaxiality from about 45°to fluctuating around 0°. The rate in approaching coaxiality is slower in samples with larger initial porosity, stress ratio and mean stress. Generally, a faster rate in approaching coaxiality in simple shear is observed in a more dilatant sample, which often shows a larger degree of mobilised fabric anisotropy, suggesting the possible important role of instantaneous internal friction angle. The evolution of principal fabric direction resembles that of the principal stress direction.

Macro deformation and micro structure of 3D granular assemblies subjected to rotation of principal stress axes

“…Calvetti et al [20] presented the evolution of material anisotropy under complex loading condition including principal axes rotations based on laboratory tests on wooden roller stacks. Numerically, discrete element method (DEM) [21] has been used in numerous studies on material responses to biaxial/triaxial shearing and direct/simple tests [22][23][24][25][26]. Responses of two dimensional granular materials to rotation of principal stress axes have been investigated [27,28].…”

Study of the interaction between dry granular flows and rigid barriers with an SPH model

“…It is easy to verify that | s | = p sin ϕ c r i t , which is often referred to as the Drucker‐Prager yield criterion . Studies show that the stress tensor and strain rate tensor are coaxial at the critical state in simple shear flows and transient flows . With such a coaxial assumption, the following equation is used to calculate the deviatoric stress tensor.…”

Rapid dry granular flows down an incline: a constitutive theory with an independent kinematic internal length

“…The shear flow corresponds to the critical state, defined as the state in which _ q ¼ 0 and Z ¼ 0 [25,59]. Since in the critical state f d is set to be unity, incorporating this definition into (46) gives rise to…”