Encoding Gaussian curvature in glassy and elastomeric liquid crystal polymer networks

Considerable recent attention has been given to the study of shape formation using modern responsive materials that can be preprogrammed to undergo spatially inhomogeneous local deformations. In particular, nematic liquid crystal polymer networks offer exciting possibilities in this context. In this paper, we discuss the generation of Gaussian curvature in thin nematic sheets using smooth in-plane director fields patterned across the surface. We highlight specific patterns which encode constant Gaussian curvature of prescribed sign and magnitude and present experimental results which appear to support the theoretical predictions. Specifically, we provide experimental evidence for the realization of positive and negative Gaussian curvature in glassy and elastomeric liquid crystal polymer networks through the stimulation of smoothly varying in-plane director fields.