Microscopic theory of two-step yielding in attractive colloids

Attractive colloids display two distinct amorphous solid phases: the attractive glass, due to particle bonding, and the repulsive glass, due to the hard core repulsion. By means of a microscopic mean field approach, we analyze their response to a quasi-static shear strain. We find that the presence of two distinct interaction length scales may result in a sharp two-step yielding process, which can be associated with a hysteretic stress response, or with a reversible but non-monotonic stress-strain curve. We derive a generic phase diagram characterized by two distinct yielding lines, an inverse yielding, and a critical point separating the hysteretic and reversible regimes. Our results should be applicable to a large class of glassy materials characterized by two distinct interaction length scales.