Stress anisotropy in quasistatically sheared granular packings*

We seek to understand the development of shear and normal stress
anisotropies in frictionless granular packings undergoing athermal
quasistatic simple and pure shear. We focus on packings of bidisperse
disks and circulo-polygons in two spatial dimensions that interact via
purely repulsive contact forces. In previous studies, we showed that
jammed disk packings form geometric families, for which the packing
fraction varies approximately quadratically with strain with positive
curvature, for packings that share the same interparticle contact
network. We find that packings of circulo-polygons also form
geometric families during shear, but they can be either concave up or
down. We derive and confirm relations for the shear and normal stress
anisotropies in terms of the derivative of the packing fraction with
respect to strain for packings of disks and circulo-polygons. We show
that disk and circulo-polygons packings develop a nonzero shear stress
(with a zero normal stress anisotropy) in the large-system limit when
undergoing quasistatic simple shear. In contrast, static disk and
circulo-polygon packings possess a nonzero normal stress anisotropy
(with a zero shear stress) in the large-system limit when undergoing
quasistatic pure shear.