Nakul Bende

Geometrically controlled snapping transitions in shells with curved creases

Significance Shape-programmable structures have recently used origami to reconfigure using a smooth folding motion, but are hampered by slow speeds and complicated material assembly. Inspired by natural systems like the leaves of Venus flytraps and hummingbird beaks, we use curved creases to imbue elastic shells with programmable fast “snapping” motion. This deformation between preprogrammed states can be tuned to be either continuously foldable or snap discontinuously. Our results provide a purely geometrical mechanism for designing multistable structures, thus circumventing the need for complex materials or fabrication methods in creating structures with fast dynamics. This technique will find application in designing structures over a wide range of length scales, including self-folding materials, tunable optics, and switchable frictional surfaces for microfluidics. 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.

Nonuniform growth and topological defects in the shaping of elastic sheets.

We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the growth-induced buckling of a thin elastic sheet are the same as those produced by the Volterra construction of topological defects in which edges of an intrinsically flat surface are identified. With this connection, we study the problem of choosing an optimal pattern of growth for a prescribed developable surface, finding a fundamental trade-off between optimal design and the accuracy of the resulting shape which can be quantified by the length along which an edge should be identified.

Programmable and reversible assembly of soft capillary multipoles

The capillary assembly of stimulus-responsive hydrogel particles with programmed multipolar interactions defined by their prescribed three-dimensional (3D) shapes is demonstrated. Low-energy bending deformations of the particles, driven by surface tension, modifies the interactions between particles, while their temperature-dependent swelling enables switchable assembly.