Solid behavior of anisotropic rigid frictionless bead assemblies

TL;DR

This study uses numerical simulations to analyze the structure and mechanical behavior of frictionless bead assemblies, revealing finite deviator stress, fabric and force anisotropies, and a nearly singular elastic moduli tensor.

Contribution

It demonstrates that anisotropic, frictionless bead assemblies sustain finite deviator stress without dilatancy and characterizes their anisotropies and elastic properties in the quasistatic limit.

Findings

Assemblies sustain finite deviator stress without dilatancy.

Fabric and force anisotropies are characterized by one parameter each.

Elastic moduli tensor is nearly singular and uniaxial.

Abstract

We investigate the structure and mechanical behavior of assemblies of frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by numerical simulation. Three different loading paths are explored: triaxial compression, triaxial extension and simple shear. Generalizing recent results [1], we show that the material, despite rather strong finite sample size effects, is able to sustain a finite deviator stress in the macroscopic limit, along all three paths, without dilatancy. The shape of the yield surface is adequately described by a Lade-Duncan (rather than Mohr-Coulomb) criterion. While scalar state variables keep the same values as in isotropic systems, fabric and force anisotropies are each characterized by one parameter and are in one-to-one correspondence with principal stress ratio along all three loading paths.The anisotropy of the pair correlation function extends to a distance between bead surfaces on the order of 10% of the diameter. The tensor of elastic moduli is shown to possess a nearly singular, uniaxial structure related to stress anisotropy. Possible stress-strain relations in monotonic loading paths are also discussed.