  Sulci are surface folds commonly seen in strained soft elastomers and form
via a strongly subsubcriticalcritical, yet scale-free instability. Treating the
threshold for nonlinear instability as a nonlinear critical point, we explain
the nature of sulcus patterns in terms of the scale and translation symmetries
which are broken by the formation of an isolated, small sulcus. Our
perturbative theory and simulations show that sulcus formation in a thick,
compressed slab can arise either as a supercritical or as a weakly subcritical
bifurcation relative to this nonlinear critical point, depending on the
boundary conditions. An infinite number of competing, equilibrium patterns
simultaneously emerge at this critical point, but the one selected has the
lowest energy. We give a simple, physical explanation for the formation of
these sulcification patterns using an analogy to a solid-solid phase transition
with a finite energy of transformation.
