Thesis: Concentrated Gauss Curvature in Shape-Programmed Shells


In this thesis we will design new patterns of deformation in shape-programmed sheets, pushing forward the paradigm of `metric mechanics’, in which active shells respond to stimuli by undergoing large spontaneous deformations. Our focus will be on novel ways to program Gauss curvature, motivated by its deep mechanical consequences - principally it imparts strength, since Gauss-curved shells cannot be flattened without expensive stretch. Concentrated Gauss curvature will be of particular interest, offering qualitatively new mechanics, and interesting theoretical challenges. Specifically we will explore the Gauss curvature encoded in deformation patterns containing topological defects, holes, and seams - all features where Gauss curvature is generically concentrated. Finally we will address the load-bearing and lifting capacity of shape-programmed cones, which have become a classic example, and whose strength ultimately stems from their Gauss-curved tips. This will reveal many surprises, including new thin-limit results for buckling of conical shells, exhibiting unexpected scalings and holding broad implications within and beyond shape programming.

University of Cambridge