  The squeezing of soft solids, the constrained growth of biological tissues,
and the swelling of soft elastic solids such as gels can generate large
compressive stresses at their surfaces. This causes the otherwise smooth
surface of such a solid to becomes unstable when its stress exceeds a critical
value. Previous analyses of the surface instability have assumed
two-dimensional plane-strain conditions, but in experiments isotropic stresses
often lead to complex three-dimensional sulcification patterns. Here we show
how such diverse morphologies arise by numerically modeling the lateral
compression of a rigidly clamped elastic layer. For incompressible solids,
close to the instability threshold, sulci appear as I-shaped lines aligned
orthogonally with their neighbors; at higher compressions they are Y-shaped and
prefer a hexagonal arrangement. In contrast, highly compressible solids when
squeezed show only one sulcified phase characterized by a hexagonal sulcus
network.
