Surface Instabilities and Topological Phase Transitions in Soft Solids 
Evan Hohlfeld, UMass Amherst

Soft solids, such as hydrogels and elastomers, can develop intricate, reticulated folding patterns in their surfaces and interfaces when compressed. The formation and evolution of these patterns---which resemble the sulcus patterns on our brains---can be understood as a first order phase transition between a flat surface and a surface with many sharply creased folds, or sulci. The transition has well defined binodal and spinodal points as well as an energy of transformation; however,  a droplet of the new phase (a single sulcus) does not have a discernible phase boundary and so cannot be described with a local order parameter. Rather, the transition is topological in nature: the surface or interface folds to self-contact (expelling the softer elastomer without tearing in the case of an interface), eliminating the free surface or interface. I will explain how these peculiar phase transitions arise in a prototype model of a soft solid, the neo-Hookean model of rubber, and how patterns form and evolve as an unusual kind of phase separation. These interfacial phase transitions break from the Landau-Ginzburg picture because the polyconvex form of the neo-Hookean free energy forbids the formation of phase boundaries, but does not forbid phase transitions.