  Amorphous solids, such as glasses, have complex responses to deformations,
with significant consequences in material design and applications. In this
respect two intertwined aspects are important: stability and reversibility. It
is crucial to understand on the one hand how a glass may become unstable due to
increased plasticity under shear deformations; on the other hand, to what
extent the response is reversible, meaning how much a system is able to recover
the original configuration once the perturbation is released. Here we focus on
assemblies of hard spheres as the simplest model of amorphous solids such as
colloidal glasses and granular matter. We prepare glass states quenched from
equilibrium supercooled liquid states, which are obtained by using the swap
Monte Carlo algorithm and correspond to a wide range of structural relaxation
time scales. We exhaustively map out their stability and reversibility under
volume and shear strains, using extensive numerical simulations. The region on
the volume-shear strain phase diagram where the original glass state remains
solid is bounded by the shear-yielding and the shear-jamming lines which meet
at a yielding-jamming crossover point. This solid phase can be further divided
into two sub-phases: the stable glass phase where the system deforms purely
elastically and is totally reversible, and the marginal glass phase where it
experiences stochastic plastic deformations at mesoscopic scales and is
partially irreversible. The details of the stability-reversibility map depend
strongly on the quality of annealing of the glass. This study provides a
unified framework for understanding elasticity, plasticity, yielding and
jamming in amorphous solids.
