Controlling Elastic Instabilities: From Complex Pattern Formation to Functionality

Exploiting elastic instability in thin films has proven a robust method for creating complex patterns and structures across a wide range of lengthscales. Even the simplest of systems, an elastic membrane with a lattice of pores, under stress, generates a plethora of complex patterns featuring long-range orientational order. Harnessing the underlying elastic instability allows for the rational design of materials with highly desirable properties: from a film with a switchable photonic bandgap to a material with a negative Poisson ratio. Within the framework of linear elasticity, we model the system as a lattice of interacting deformation elements, or ``dislocation dipoles,'' which captures the configuration and orientational order present in any conceivable deformation of the system. In addition, when we promote this system to a curved surface, a novel set of features, patterns and broken symmetries appears.