Unilateral interparticle interactions have an effect on the elastic response
of granular materials due to the opening and closing of contacts during
quasi-static shear deformations. A simplified model is presented, for which
constitutive relations can be derived. For biaxial deformations the elastic
behavior in this model involves three independent elastic moduli: bulk, shear,
and anisotropy modulus. The bulk and the shear modulus, when scaled by the
contact density, are independent of the deformation. However, the magnitude of
the anisotropy modulus is proportional to the ratio between shear and
volumetric strain. Sufficiently far from the jamming transition, when
corrections due to non-affine motion become weak, the theoretical predictions
are qualitatively in agreement with simulation results.Comment: 6 pages, 5 figure