  We develop a critical-state model of fused silica plasticity on the basis of
data mined from molecular dynamics (MD) calculations. The MD data is suggestive
of an irreversible densification transition in volumetric compression resulting
in permanent, or plastic, densification upon unloading. The MD data also
reveals an evolution towards a critical state of constant volume under
pressure-shear deformation. The trend towards constant volume is from above,
when the glass is overconsolidated, or from below, when it is
underconsolidated. We show that these characteristic behaviors are
well-captured by a critical state model of plasticity, where the densification
law for glass takes the place of the classical consolidation law of granular
media and the locus of constant volume states denotes the critical-state line.
A salient feature of the critical-state line of fused silica, as identified
from the MD data, that renders its yield behavior anomalous is that it is
strongly non-convex, owing to the existence of two well-differentiated phases
at low and high pressures. We argue that this strong non-convexity of yield
explains the patterning that is observed in molecular dynamics calculations of
amorphous solids deforming in shear. We employ an explicit and exact rank-2
envelope construction to upscale the microscopic critical-state model to the
macroscale. Remarkably, owing to the equilibrium constraint the resulting
effective macroscopic behavior is still characterized by a non-convex
critical-state line. Despite this lack of convexity, the effective macroscopic
model is stable against microstructure formation and defines well-posed
boundary-value problems.
