Multi-stable structures have gathered extensive interest because they can provide a broad spectrum of adaptive functions for many engineering systems. Especially, origami sheets with a translational periodicity can be stacked and assembled to form a multi-stable cellular solid, which has emerged as a promising platform to design functional structures. This paper investigates the multi-stability characteristics of a non-rigid stacked Miura-origami mechanism consisting of Miura-ori sheets and accordion-shaped connecting sheets, focusing on the elemental unit cell. A nonlinear mechanical model based on the barhinge approach is established to quantitatively study the unit cell’s multi-stability with intentionally relaxed rigid-folding conditions. Results show that only two stable states are achievable in the unit cell with enforced rigid-folding kinematics. However, if one relaxes the rigid-folding conditions and allows the facet to deform (i.e. non-rigid folding), four stable states are reachable in the unit cell if the crease torsional stiffness of the connecting sheets becomes sufficiently larger than that of the Miura-ori sheets, or the stress-free folding angle deviates away from 0°. A close examination of the potential energy composition of the non-rigid unit cell provides a detailed principle underpinning the multi-stability. By showing the benefits of exploiting facet compliance, this study can become the building blocks for origami-based structures and material systems with a wider variety of novel functionalities.
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Triclinic Metamaterials by Tristable Origami with Reprogrammable Frustration
Geometrical‐frustration‐induced anisotropy and inhomogeneity are explored to achieve unique properties of metamaterials that set them apart from conventional materials. According to Neumann's principle, to achieve anisotropic responses, the material unit cell should possess less symmetry. Based on such guidelines, a triclinic metamaterial system of minimal symmetry is presented, which originates from a Trimorph origami pattern with a simple and insightful geometry: a basic unit cell with four tilted panels and four corresponding creases. The intrinsic geometry of the Trimorph origami, with its changing tilting angles, dictates a folding motion that varies the primitive vectors of the unit cell, couples the shear and normal strains of its extrinsic bulk, and leads to an unusual Poisson effect. Such an effect, associated with reversible auxeticity in the changing triclinic frame, is observed experimentally, and predicted theoretically by elegant mathematical formulae. The nonlinearities of the folding motions allow the unit cell to display three robust stable states, connected through snapping instabilities. When the tristable unit cells are tessellated, phenomena that resemble linear and point defects emerge as a result of geometric frustration. The frustration is reprogrammable into distinct stable and inhomogeneous states by arbitrarily selecting the location of a single or multiple point defects. The Trimorph origami demonstrates the possibility of creating origami metamaterials with symmetries that are hitherto nonexistent, leading to triclinic metamaterials with tunable anisotropy for potential applications such as wave propagation control and compliant microrobots.
more » « less- NSF-PAR ID:
- 10377284
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Advanced Materials
- Volume:
- 34
- Issue:
- 43
- ISSN:
- 0935-9648
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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