  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.
