Digital modelling of deployable structures based on curved-line folding

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.