Deployment and surface accuracy of regularly creased membranes

Abstract

Creases are highly localized regions ubiquitous across different length scales in low-dimensional natural and engineering systems. Their presence strongly influences the mechanical response and surface accuracy of creased membrane materials and structures. In this paper, we study the deployment of folded sheets composed of an arbitrary number of non-interacting and parallel creases. We develop a mathematical formulation that describes the nonlinear mechanics of systematically creased membranes composed of a single or multiple folds, and predicts their surface accuracy during unfolding. The proposed solution shows the contribution of membrane bending and crease energies during deployment, and reveals the presence of two dimensionless parameters that govern the unfolding behaviour. Sensitivity analyses are also performed to assess the influence of the crease geometry and constitutive behaviour. The analytical predictions are validated through finite element analyses and deployment tests performed on thin films with one, two and three fold lines, where imaging techniques are employed to quantify deformation. The excellent agreement between theoretical and experimental results testifies that the developed formulation represents a precise tool to assess the tensioning of creased membranes, with applications ranging from origami metamaterials to lightweight space structures where precise shape control is paramount.