Session: MR-04-02 Origami-Based Engineering Design

Paper Number: 67141

Start Time: August 18, 11:10 AM

67141 - Auxetic Structures Based on Rhombic Tiling 

Auxetic material using corner-connected kinematic tiles has been used to design deployable structures and applied to mechanical metamaterials and programmable surfaces. Although large families of kinematic tiling have been discovered so far, all existing works rely on the connectivity of the regular polygonal tiling. Because of the overconstraining nature of kinematic tiling, only periodic patterns with global symmetry have been explored.

The objective of this study is to extend the family of corner-connected kinematic tiling to the non-regular topology. We propose a new family of auxetic structures based on non-regular and aperiodic rhombic tiling inspired by the Tokyo 2020 Olympic Paralympic Emblems, "Harmonized Chequered Emblems." The underlying geometry of the emblems is a rhombic tiling of a dodecagon, i.e., the emblem's pattern is obtained by drawing the inscribed rectangle of each tiled rhombus by connecting the midpoints of rhombus edges. We convert emblem-like patterns on rhombic tilings into kinematic structures by regarding the rectangular figure as voids and the region between rectangles as rigid bodies. Due to the geometric properties of rhombic tiling, the structure forms a one-degree-of-freedom planar mechanism with a Poisson ratio of -1.

The large combinatorial family of design variations of base rhombic tiling provides variations of kinematic structures with non-regular topology. We implemented a parametric system in software, where the base rhombi are tiled on a plane. Furthermore, we show a kirigami-based method for fabricating the structure as a compliant mechanism, i.e., laser-cutting the material along the slit pattern in the contracted state.

We believe this connection between math and art potentially broadens the range of architected materials based on folding, kirigami, and tessellation. The future work is to know the mechanical property of non-regular auxetic tiling.

Presenting Author: Kanata Warisaya The University of Tokyo

Authors:

Kanata Warisaya University of Tokyo
Hiroaki Hamanaka Hyogo University of Teacher Education
Asao Tokolo TOKOLO.COM
Tomohiro Tachi University of Tokyo