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

Abstract: 
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.