  A core-softened model of a glass forming fluid is numerically studied in the
limit of very low temperatures. The model shows two qualitatively different
behaviors depending on the strength of the attraction between particles. For no
or low attraction, the changes of density as a function of pressure are smooth,
although hysteretic due to mechanical metastabilities. For larger attraction,
sudden changes of density upon compressing and decompressing occur. This global
mechanical instability is correlated to the existence of a thermodynamic
first-order amorphous-amorphous transition. The two different behaviors
obtained correspond qualitatively to the different phenomenology observed in
silica and water.
