Mechanical Response of a Creased Sheet

Abstract

We investigate the mechanics of thin sheets decorated by non-interacting creases. The system considered here consists in parallel folds connected by elastic panels. We show that the mechanical response of the creased structure is twofold, depending both on the bending deformation of the panels and the hinge-like intrinsic response of the crease. We show that a characteristic length scale, defined by the ratio of bending to hinge energies, governs whether the structure's response consists in angle opening or panel bending when a small load is applied. The existence of this length scale is a building block for future works on origami mechanics.

Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials

“…The model is made scalable and incorporates thickness (t = 0.01), Young's modulus (E = 10 6 ), Poisson's ratio (ν = 1=4), and density (ρ = 1) of the material (32). A parameter, R FP = 1=10, relates fold line bending to panel bending stiffness and can vary greatly, depending on the materials, the fabrication technique, and the actuation process (33)(34)(35)(36). Using a sensitivity analysis in SI Text, section S3 and Fig.…”

Geometry and design of origami bellows with tunable response

“…[5] demonstrates how face bending can generate a pathway for an origami mechanism to follow while transitioning through a geometrically forbidden configuration to a lower energy state, while in Ref. [10] a straightforward technique to measure the competition between crease and plate bending is demonstrated.…”

“…In particular, they fail for structures folded out of materials with nonzero elasticity, as both the faces and the creases have innate elastic energy. Indeed, creases have a preferred angle of repose [10], which can either stabilize a particular configuration or drive it far from its rigid-face equilibrium. Moreover, creases and faces tend to bend on different energy scales, and the competition of these effects leads to dramatically different behavior than what geometric models might predict.…”

Vibrant times for mechanical metamaterials

“…[68] Effectively, one can think of the creases as torsional Hooke's springs. [69] Temperature-responsive polymergels instead of paper are yet another option. [70] Paper is an inextensible constituent material, yet the metamaterials made thereof can effectively be highly flexible.…”