Responsive nematic solid shells: Topology, compatibility, and shape

Nematic solids, both glassy and elastomeric, with defects in the director field can attain stress-free Gaussian curvature from an initially flat state. In this letter we show how the intrinsic curvature and/or the global topology of the initial reference state interacts with the curvature arising from the spontaneously strained nematic director field. In particular, locally compatible mechanical deformations due to the director can be globally incompatible in certain topologies