  Cavitation and sulcification of soft elastomers are two examples of
thresholdless, nonlinear instabilities that evade detection by linearization. I
show that the onset of such instabilities can be understood as a kind of phase
coexistence between multiple scale-invariant states, and I constructively
enumerate the possible scale-invariant states of incompressible rubber in two
dimensions. Whereas true phases (like the affine deformations of rubber) are
homogeneous, the alternatives are inhomogeneous. In terms of the thermodynamics
of solids, both classes of states must generally be given equal consideration.

Soft Condensed Matter;Materials Science;Statistical Mechanics;Analysis of PDEs