Abstract

Much of shape formation at a variety of length scales in nature, ranging from the cell walls of plants and bacteria to macrostructures such as growing plant leaves, is governed by local deformations driven by differential growth or a non-uniform response to external stimuli. The increasing availability of modern responsive materials in which spatially inhomogeneous expansions and contractions can be precisely programmed and controlled via external stimuli such as uniform heat or illumination offers the promise of replicating the complex shape transitions observed in nature. This has contributed to a growing interest in the modelling of shape transitions of thin elastic structures that arise primarily due to non-uniform local deformations resulting from the material’s internal structure. In this talk I will present a differential geometric framework for the analysis of such shape transformations and will discuss the application of the theory to nematic liquid crystalline solids. A number of original results will be introduced.