Effects of shear stability and residual stresses in computer glasses

Numerical investigations of disordered solids often involve employing a fixed simulation-box geometry and periodic boundary conditions, the latter are intended to minimize surface effects. One consequence of this methodological approach is that the resulting solids typically feature residual macroscopic stresses and could feature negative shear moduli, in which case they are deemed unstable to shear. In this work, we review and validate via numerical simulations the statistical theory that explains how the fraction of shear-unstable solids within an ensemble of solids created via the same protocol depends on the system size. We further demonstrate and rationalize how the fraction of disordered soft-sphere packings that are unstable to shear depends on their proximity to the unjamming point at which solidity is lost. Finally, we show that residual-stress-free structural glasses created in a fixed-box geometry have the same vibrational and elastic properties as glasses that do feature residual stresses. This result seemingly contradicts previous work that shows that residual-stress-free samples created using variable box shape feature different vibrational properties. These observations raise questions about the equivalence of constant-stress vs constant box-geometry ensembles in the thermodynamic limit, which are discussed together with future research directions.