  Using numerical simulations, we study the failure of an amorphous solid under
quasi-static expansion starting from a homogeneous high-density state. During
the volume expansion, we demonstrate the existence of instabilities manifesting
via saddle-node bifurcation in which a minimum meets a saddle. During all such
events, the smallest eigenvalue of the Hessian matrix vanishes as a square-root
singularity. The plastic instabilities are manifested via sudden jumps in
pressure and energy, with the largest event happening when a cavity appears,
leading to the yielding of the material. We show that during cavitation and
prior to complete fracture, the statistics of pressure or energy jumps
corresponding to the plastic events show sub-extensive finite-size scaling,
similar to the case of simple shear but with different exponents. Thus,
overall, our study reveals universality in the fundamental characteristics
during mechanical failure in amorphous solids under any quasi-static
deformation protocol.
