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.

Geometric Mechanics of Origami Patterns Exhibiting Poisson's Ratio Switch by Breaking Mountain and Valley Assignment.

Exploring the configurational space of specific origami patterns [e.g., Miura-ori (flat surface with parallelogram crease patterns), eggbox] has led to notable advances in science and technology. To augment the origami design space, we present a pattern, named "Morph," which combines the features of its parent patterns. We introduce a four-vertex origami cell that morphs continuously between a Miura mode and an eggbox mode, forming an homotopy class of configurations. This is achieved by changing the mountain and valley assignment of one of the creases, leading to a smooth switch through a wide range of negative and positive Poisson's ratios. We present elegant analytical expressions of Poisson's ratios for both in-plane stretching and out-of-plane bending and find that they are equal in magnitude and opposite in sign. Further, we show that by combining compatible unit cells in each of the aforementioned modes through kinematic bifurcation, we can create hybrid origami patterns that display unique properties, such as topological mode locking and tunable switching of Poisson's ratio.