Stress distribution in static two dimensional granular model media in the absence of friction

TL;DR

This study uses simplified 2D granular simulations without friction to analyze stress distribution, contact networks, and arching effects, revealing how boundary conditions and polydispersity influence stress fluctuations and distributions.

Contribution

It demonstrates that a frictionless, linear spring-dashpot model can reproduce key stress phenomena in granular media, connecting arching and stress fluctuations to contact network structure.

Findings

Observation of stress dip under the pile center due to arching

Polydispersity induces stress network with strong fluctuations

Probability distribution of bottom stress aligns with theoretical predictions

Abstract

We present simulations of static model sandpiles in two dimensions (2D) and focus on the stress distribution in such arrays made of discrete particles. We use the simplest possible model, i.e. spherical particles with a linear spring and a linear dashpot active on contact and without any frictional forces. Our model is able to reproduce several recent theoretical predictions. For different boundary conditions we examine the contact network and the stresses in the array and at the bottom of the pile. In some cases we observe a dip, i.e. the relative minimum in pressure, under the center of the pile. We connect the dip to arching, and we relate arching to the structure of the contact network. Finally, we find that small polydispersity is sufficient to cause a so called stress-network, i.e. strong fluctuations in stress. From those data we determine the probability distribution for the vertical stress at the bottom and relate it to theoretical and other numerical work.