Calculation of the incremental stress-strain relation of a polygonal packing

The constitutive relation of the quasi-static deformation on two dimensional packed samples of polygons is calculated using molecular dynamic simulations. The stress values at which the system remains stable are bounded by a failure surface, that shows a power law dependence on the pressure. Below the failure surface, non linear elasticity and plastic deformation are obtained, which are evaluated in the framework of the incremental linear theory. The results shows that the stiffness tensor can be directly related to the micro-contact rearrangements. The plasticity obeys a non-associated flow rule, with a plastic limit surface that does not agree with the failure surface.Comment: 11 pages, 20 figur

On the use of graphics processing units (GPUs) for molecular dynamics simulation of spherical particles

General-purpose computation on Graphics Processing Units (GPU) on personal computers has recently become an attractive alternative to parallel computing on clusters and supercomputers. We present the GPU-implementation of an accurate molecular dynamics algorithm for a system of spheres. The new hybrid CPU-GPU implementation takes into account all the degrees of freedom, including the quaternion representation of 3D rotations. For additional versatility, the contact interaction between particles is defined using a force law of enhanced generality, which accounts for the elastic and dissipative interactions, and the hard-sphere interaction parameters are translated to the soft-sphere parameter set. We prove that the algorithm complies with the statistical mechanical laws by examining the homogeneous cooling of a granular gas with rotation. The results are in excellent agreement with well established mean-field theories for low-density hard sphere systems. This GPU technique dramatically reduces user waiting time, compared with a traditional CPU implementation

Effect of rolling on dissipation in fault gouges

Sliding and rolling are two outstanding deformation modes in granular media. The first one induces frictional dissipation whereas the latter one involves deformation with negligible resistance. Using numerical simulations on two-dimensional shear cells, we investigate the effect of the grain rotation on the energy dissipation and the strength of granular materials under quasistatic shear deformation. Rolling and sliding are quantified in terms of the so-called Cosserat rotations. The observed spontaneous formation of vorticity cells and clusters of rotating bearings may provide an explanation for the long standing heat flow paradox of earthquake dynamics

Non-spherical granular flows down inclined chutes

In this work, we numerically examine the steady-state granular flow of 3D non-spherical particles down an inclined plane. We use a hybrid CPU/GPU implementation of the discrete element method of nonspherical elongated particles. Thus, a systematic study of the system response is performed varying the particle aspect ratio and the plane inclination. Similarly to the case of spheres, we observe three well-defined regimes: arresting flows, steady uniform flows and accelerating flows. Both steady and dynamic macroscopic fields are derived from microscopic data, by time-averaging and spatial smoothing (coarse-graining), including density, velocity, as well as the kinetic and contact stress tensors. The internal morphology of the flow was quantified exploring the solid fraction profiles and the particle orientation distribution. Furthermore, the system¿s characteristic time and length scales are investigated in detail. Our aim is to achieve a continuum mechanical description of granular flows composed of non-spherical particles based on the micromechanical details. Thus, to evaluate the influence of particle shape on the constitutive response in granular of those systems. However, to meet the proceeding¿s page restrictions here we will only discuss the dependence of some terms of the continuum averaged equations on the coarse-graining scale, specifically the case of the kinetic part of the stress tensor

Bottlenecks in granular flow: When does an obstacle increase the flowrate in an hourglass?

Bottlenecks occur in a wide range of applications from pedestrian and traffic flow to mineral and food processing. We examine granular flow across a bottleneck using particle-based simulations. Contrary to expectations we find that the flowrate across a bottleneck actually increases if an opti- mized obstacle is placed before it. The dependency of flowrate on obstacle diameter is derived using a phenomenological velocity-density relationship that peaks at a critical density. This relationship is in stark contrast to models of traffic flow, as the mean velocity does not depend only on density but attains hysteresis due to interaction of particles with the obstacle.Comment: Submitted to Phys. Rev. Let

The anisotropy of granular materials

The effect of the anisotropy on the elastoplastic response of two dimensional packed samples of polygons is investigated here, using molecular dynamics simulation. We show a correlation between fabric coefficients, characterizing the anisotropy of the granular skeleton, and the anisotropy of the elastic response. We also study the anisotropy induced by shearing on the subnetwork of the sliding contacts. This anisotropy provides an explanation to some features of the plastic deformation of granular media.Comment: Submitted to PR