Plastic instabilities in Amorphous Solids

Abstract: In this colloquium I will review recent progress in
understanding the mechanical responses
of amorphous solids to external strains. Fundamental plastic
instabilities appear as saddle-node bifurcations
which result in eigenvalues of the system's Hessian matrix hitting
zero, leading to either local or highly
correlated non affine irreversible re-arrangements of particle
positions. The theory results in a consistent
statistical mechanics of plasticity in amorphous solids, including
ab-initio predictions of the yield-stress
and of important rheological laws.