Certain transitions of soft matter systems, such as jamming, rigidity percolation, and the glass transition, rely on a mechanical transition from fluid-like to solid-like behavior. This tends to be ill-defined in a significant portion of the soft matter literature. Precisely, the development of rigidity is defined as the ability of a material to elastically support a finite shear stress. The manner in which materials develop rigidity is a deep and well-studied topic, with roots going as far back as Maxwell and de Gennes.
Future versions of this page should incorporate Maxwell's criterion relating rigidity in a central force network to isostaticity and the coordination number; ideas from rigidity percolation, including the important fact that connectivity percolation may not be sufficient for rigidity percolation in a central force network (e.g. if bonds can support stretching but not bending); etc.