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Amorphous solids, such as glasses, have complex responses to deformations,with significant consequences in material design and applications. In thisrespect two intertwined aspects are important: stability and reversibility. Itis crucial to understand on the one hand how a glass may become unstable due toincreased plasticity under shear deformations; on the other hand, to whatextent the response is reversible, meaning how much a system is able to recoverthe original configuration once the perturbation is released. Here we focus onassemblies of hard spheres as the simplest model of amorphous solids such ascolloidal glasses and granular matter. We prepare glass states quenched fromequilibrium supercooled liquid states, which are obtained by using the swapMonte Carlo algorithm and correspond to a wide range of structural relaxationtime scales. We exhaustively map out their stability and reversibility undervolume and shear strains, using extensive numerical simulations. The region onthe volume-shear strain phase diagram where the original glass state remainssolid is bounded by the shear-yielding and the shear-jamming lines which meetat a yielding-jamming crossover point. This solid phase can be further dividedinto two sub-phases: the stable glass phase where the system deforms purelyelastically and is totally reversible, and the marginal glass phase where itexperiences stochastic plastic deformations at mesoscopic scales and ispartially irreversible. The details of the stability-reversibility map dependstrongly on the quality of annealing of the glass. This study provides aunified framework for understanding elasticity, plasticity, yielding andjamming in amorphous solids.

A stability-reversibility map unifies elasticity, plasticity, yielding and jamming in hard sphere glasses