A core-softened model of a glass forming fluid is numerically studied in th
e limit of very low temperatures. The model shows two qualitatively differe
nt 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 lar
ger attraction, sudden changes of density upon compressing and decompressin
g occur. This global mechanical instability is correlated to the existence
of a thermodynamic first-order amorphous-amorphous transition. The two diff
erent behaviors obtained correspond qualitatively to the different phenomen
ology observed in silica and water.