If full on attack, the process I teach is Musubi - Tsukuri - Kuzushi - Release. In the process of Musubi (connection and flow), my positioning and angles (part of Tsukuri) allow for the Kuzushi (my definition is allowing someone to lose their balance) to take place, then one just releases what ever anchor Nage is giving them and they fall.

If the attack is more "sophisticated" meaning not over-extended etc., the process becomes Connect - Blend - Track - Lead - Resolve. This can take a little more time, because Nage must process the interaction such that through tracking Uke's movement, speed etc., Uke "tells" nage exactly where the Avenue of Release (as I think of it) is as the interaction unfolds, and thus Kuzushi etc. happens.

Loss of structural integrity is a little more subtle, in a sense, in that Uke doesn't necessarily perceive why the loss is happening, he just experiences falling down, or more often, collapsing down or inward....