Solid behavior of anisotropic rigid frictionless bead assemblies

Pierre-Emmanuel Peyneau (1) , Jean-Noël Roux (1)

1 LMSGC - Laboratoire des matériaux et structures du génie civil

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.

Mots clés: matériau granulaire; critère de rupture; dilatance; élastoplasticité

Domaines: Science des matériaux [cond-mat.mtrl-sci]; Matière Molle [cond-mat.soft]

Pierre-Emmanuel Peyneau, Jean-Noël Roux. Solid behavior of anisotropic rigid frictionless bead assemblies. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 78 (4), pp.041307. ⟨10.1103/PhysRevE.78.041307⟩. ⟨hal-00297449v2⟩