Geometry for evolving topographies of light-responsive plastic sheets

Abstract

Recently, topography change by illumination of pre-stretched, flat sheets covered in ink of optical density varying in-plane has been demonstrated by (Mailen et al, 2019 Smart Mater. Struct. 48 107587). They reduce an analysis of the problem to one of metric change in the sheets in the thin limit, that is, to a question of geometry. We present the explicit form of the contraction field needed to produce the bowls these authors were interested in, using a method that can also yield the contraction field for more general desired, circularly-symmetric topography development. We give as examples the fields required for developing paraboloids and catenoids.