Tomohiro Tachi’s research while affiliated with The University of Tokyo and other places

Auxetic kirigami patterns have been used for fabricating given target surfaces from flat sheets. In particular, bistable kirigami patterns are useful as they keep the structure stable at the target shapes. In this paper, we propose a family of new bistable kirigami patterns that potentially resolves the limitation of existing bistable kirigami, which are (1) the small range of the scale factor that limits the target surface and (2) the asynchronous deployment with multiple locally stable states other than the target surface. The proposed patterns are obtained by adding bistability-inducing bar elements to star tiling kirigami patterns. The experiments show the improvement of synchronization of our structure. We propose an optimization-based computational design method to obtain curved surfaces by arranging the kirigami patterns and the bar elements such that each unit expands to the given scale factor. We applied this method to several surfaces and validated the physical prototypes.

Origami Metamaterials In article number 2107998, Glaucio H. Paulino and co‐workers create a class of metamaterials derived from a reconfigurable origami pattern with triclinic symmetry, leading to reversible auxeticity. When the tristable unit cells are tessellated, phenomena that resemble linear and point defects emerge as a result of geometric frustration, which can be reprogrammed at desired locations. The resulting tessellations and metamaterials display tunable anisotropy and have potential applications to wave propagation control and in microrobots.

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, we present a triclinic metamaterial system of minimal symmetry, which is originated 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's effect. Such effect, associated to reversible auxeticity in the changing triclinic frame, is observed experimentally, and predicted theoretically by elegant math 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 resembles 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 were hitherto non‐existent, leading to triclinic metamaterials with tunable anisotropy for potential applications such as wave propagation control and compliant micro‐robots. This article is protected by copyright. All rights reserved

Folded surfaces of origami tessellations have attracted much attention because they sometimes exhibit non-trivial behaviors. It is known that cylindrical folded surfaces of waterbomb tessellation called waterbomb tube can transform into wave-like surfaces, which is a unique phenomenon not observed on other tessellations. However, the theoretical reason why wave-like surfaces arise has been unclear. In this paper, we provide a kinematic model of waterbomb tube by parameterizing the geometry of a module of waterbomb tessellation and derive a recurrence relation between the modules. Through the visualization of the configurations of waterbomb tubes under the proposed kinematic model, we classify solutions into three classes: cylinder solution, wave-like solution, and finite solution. We investigate how the behavior of waterbomb tube changes when the crease-pattern is changed by applying the knowledge of stability. Furthermore, we give proof of the existence of a wave-like solution around one of the cylinder solutions.

Folded surfaces of origami tessellations have attracted much attention because they sometimes exhibit non-trivial behaviors. It is known that cylindrical folded surfaces of waterbomb tessellation called waterbomb tube can transform into wave-like surfaces, which is a unique phenomenon not observed on other tessellations. However, the theoretical reason why wave-like surfaces arise has been unclear. In this paper, we provide a kinematic model of waterbomb tube by parameterizing the geometry of a module of waterbomb tessellation and derive a recurrence relation between the modules. Through the visualization of the configurations of waterbomb tubes under the proposed kinematic model, we classify solutions into three classes: cylinder solution, wave-like solution, and finite solution. Furthermore, we give proof of the existence of a wave-like solution around one of the cylinder solutions by applying the knowledge of the discrete dynamical system to the recurrence relation.