Fig. 4. Generality of our model to nonconvex surfaces.
(A) A face guard with both positive and negative Gaussian curvatures. (B) Overlap cannot be avoided in a single patch of the unfolded net due to the existence of hyperbolic vertices. (C) Unfolding for the hyperbolic vertex leads to θh > 2π and a self-overlapped net, while unfolding for the ellipsoidal vertex results in θe < 2π and an overlap-free net. (D) Optimized plies for the faceguard with each ply comprising two patches. (E) Experimental snapshot of the consolidated face guard fabricated from Tensylon HSBD30A. Scale bar, 20 mm. (F) Experimental force-displacement curves for face guards with random design and optimized design with tabs. Shaded areas indicate the SD of the measurements. (G) Potential applications of our model in structures with different length scales, ranging from helmets and auto racing seats to automobiles and airplanes.