On leaves, flowers, and sea slugs

Leaves, flowers, fins, wings, and marine invertebrates are examples of the ubiquity of non-Euclidean plates (NEP), i.e. prestrained thin elastic objects whose intrinsic geometry does not allow for a stress-free embedding into 3-space. When the intrinsic geometry is hyperbolic, these objects often display intricate, hierarchical, “multi-scale” undulations and buckling patterns around their edges. I will discuss recent advances in the mathematics and mechanics of hyperbolic NEP, emphasizing the connections between the math and the ‘extreme’ mechanical properties of hyperbolic NEP that might explain their ubiquity in natural objects.