Proceedings of the IASS-SLTE 2014 Symposium “Shells, Membranes and Spatial Structures: Footprints” 15 to 19 September 2014, Brasilia, Brazil Reyolando M.L.R.F. BRASIL and Ruy M.O. PAULETTI (eds.) Copyright © 2014 by the authors. Published by the International Association for Shell and Spatial Structures (IASS) with permission. 1 Digital modelling of deployable structures based on curved-line folding Aline VERGAUWEN * , Niels DE TEMMERMAN a , Lars DE LAET b * Doctoral researcher, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, Belgium, Aline.Vergauwen@vub.ac.be a Professor, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, Belgium, Niels.De.Temmerman@vub.ac.be b Professor, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, Belgium, Lars.De.Laet@vub.ac.be Abstract Curved-line folding is the act of folding a flat sheet of material along a curved crease pattern in order to create a 3D shape, using the combination of folding (plastic deformation) and bending (elastic deformation). Most applications of curved-line folding only make use of the end state of the folding process: a static solution obtained through folding along a curved crease pattern. However, the elastic deformations that occur when a flat sheet is forced into a curved shape can produce an interesting transformation process. When one surface area is bent, the forces and moments are transmitted through the curved creases to the adjacent surface areas, which results in a folding motion. As a result, this kind of transformation process could be used for the development of a new type of deployable structure, finding its application in the context of kinetic shading systems. The aim of this paper is to give an overview of how this transformation process can be modelled and analysed in a digital environment. Existing methods as well as some new approaches are discussed and evaluated. A distinction is made between pure geometrical modelling methods and simulations with finite elements software. It can be concluded that the existing tools for geometrical modelling of the folding process of deployable structures based on curved-line folding are sufficient to quickly check the deployment of different curved-line folding patterns and can find their application in the early design stage. However, for a more profound analysis, which takes into account material properties and forces, a calculation with finite elements is required. Keywords: Curved-line folding, curved-crease folding, deployable structures, pliable structures, digital modelling. 1 Introduction When a very thin material (like paper) is folded along a curved crease, a 3D shape is obtained by folding (plastic deformation) as well as bending (elastic deformation) of the sheet. This principle is called curved-line folding and has been discovered by students from the Bauhaus in the late 1920’s, as explained in Demaine et al. [1]. Until now, most applications of curved-line folding in architecture only make use of the end state of the folding process. Starting from a flat sheet of material three-dimensional shapes with a geometrical stiffness are obtained, finding applications in sculptures, façade components, furniture etc. Accordingly, the plastic deformation present at the fold lines is permanent and the artefact cannot return to its initial state. However, the authors of this paper believe that curved-line folding can also be used for the design of deployable structures, by use of the elastic deformations that occur when a flat sheet is forced into a curved shape. As one surface area is bent, the forces and moments are transmitted through the curved creases to the adjacent surface areas, which then results in a folding motion. Figure 1 shows how the elastic deformation of the paper model’s central area, generated by pushing the ends towards the centre, forces the adjacent areas to fold inwards. In Schleicher et al. [2] this phenomenon is referred to as bending-active kinetics and shows great potential for application in the design of adaptive façade shading systems. This paper gives an overview of existing methods and tools to simulate the folding process of curved-line folding patterns in a digital environment. Besides tools that allow digital modelling based on the geometry alone, the authors also present a method using FEM simulation software. This method allows the designer to consider real material properties, actuation forces and boundary conditions when designing a deployable structure based on curved-line folding.