Curvature Design of Programmable Textile

We propose an inverse curvature design method for programmable textiles, i.e., self-morphing structures that combine a pre-stretched fabric and elastic rods in a planar state. Specifically, we target a class of structures consisting of a quadrangular grid with all rods interconnected to create a periodically corrugated shape, which offers surface programmability and resilience of the structure. The shape of such a structure is the result of a complex nonlinear equilibrium. We bypass the costly inverse computation of such equilibrium by decomposing the computation of macroscopic shrinkage behavior solved geometrically and microscopic material behavior modeled through experiments. We first investigate the behavior of programmable textiles through experiments, subsequently construct a geometric model to represent the deformation, and then propose a three-step inverse design method. The design method first calculates a conformal mapping of the target shape onto a planar region. Then, we determine an optimized grid layout for arranging rods satisfying geometric constraints on this planar region. Finally, the cross-sectional shapes of the rods at each part are computed based on experimental results. Thanks to our geometric model, there are smaller geometric constraints than the number of variables for determining the grid layouts. This design flexibility allows the grid layout to incorporate smooth boundary conditions and user preferences on the grid shapes. We demonstrate the validity and potential of our approach through design examples and comparisons with the target shape.