2014/10/26 by Nakul Bende, Nakul P. Bende, Arthur A. Evans +5 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Advanced Sensor and Energy Harvesting Materials #Artificial intelligence #Biomimetics #Computer science #Deformation (meteorology) #Engineering #Folding (DSP implementation) #Geometry #Hummingbird #Materials science #Mathematics #Mechanical engineering #Mechanism (biology) #Microfluidics #Modular Robots and Swarm Intelligence #Motion (physics) #Nanotechnology #Physics #cond-mat.soft
paper · pdf · doi:10.1073/pnas.1509228112
arxiv created 2014/10/26 · openalex publication_date 2015/08/20 · arxiv updated 2018/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains to wrinkled membranes and programmable metamaterials. While the well-known rules and mechanisms behind folding a flat surface have been used to create deployable structures and shape transformable materials, folding of curved shells is still not fundamentally understood. Shells naturally deform by simultaneously bending and stretching, and while this coupling gives them great stability for engineering applications, it makes folding a surface of arbitrary curvature a nontrivial task. Here we discuss the geometry of folding a creased shell, and demonstrate theoretically the conditions under which it may fold smoothly. When these conditions are violated we show, using experiments and simulations, that shells undergo rapid snapping motion to fold from one stable configuration to another. Although material asymmetry is a proven mechanism for creating this bifurcation of stability, for the case of a creased shell, the inherent geometry itself serves as a barrier to folding. We discuss here how two fundamental geometric concepts, creases and curvature, combine to allow rapid transitions from one stable state to another. Independent of material system and length scale, the design rule that we introduce here explains how to generate snapping transitions in arbitrary surfaces, thus facilitating the creation of programmable multistable materials with fast actuation capabilities.