Coexistence of Scale-Invariant States in Incompressible Elastomers

Abstract

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.

5 pages, 1 figure + 9 pages of supplementary material

References in corpus (4)

• Unfolding the Sulcus
• Surface sulci in squeezed soft solids
• Shocks near Jamming
• Scale and Nature of Sulcification Patterns

Cited by in corpus (1)

• A general criterion for solid instability and its application to creases