Abstract

Thin nematic elastomer sheets can be programmed, via the nematic director field embedded into them, to take different shapes in different environments. Recent experiments from various groups demonstrate excellent control over the director field, thus opening a door for achieving accurate and versatile designs of shape-shifting surfaces. At the crux of any effort to implement this design mechanism lies the inverse design problem—given an arbitrary surface geometry, constructing the director field that would induce it. In this talk I describe several aspects of this inverse problem. I present a numerical algorithm for finding global approximate solutions for any 2D geometry. I also show that many exact solutions always exist locally and can be readily integrated, and classify the set of all director fields that deform into an arbitrary given geometry. These results allow optimizing the resultant director fields for different purposes, e.g. maximizing the domain of a global solution, increasing its robustness, reducing residual stresses, or controlling the entire shape-shifting path.