Many bodies in nature that undergo inhomogeneous growth/shrinkage become "pre-strained"; that is, they are stressed even in the absence of external forces. Many such bodies, such as leaves or supramolecular assemblies, are also thin—shell-like, rod-like or ribbon-like—and exhibit interesting energy-driven patterns.

Pre-strained bodies are typically modeled by having an intrinsic non-flat metric, giving rise to "non-Euclidean elasticity". In this talk I will describe this model, and then focus on thin bodies and the relations between their intrinsic curvature and their elastic behavior; if time permits, I will explain how these are related to phase transitions in shapes of non-Euclidean ribbons.