Rigidity

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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 resist stretching but not bending); supporting a stress may not a higher degree of connectivity

- Connection between ergodicity breaking and rigidity; could be the case that the threshold for ergodicity breaking is earlier than the threshold for mechanical rigidity, which is quite counterintuitive!