Durable bistable auxetics made of rigid solids
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Ahmad Rafsanjani John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Damiano Pasinia) Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada (Received 30 July 2017; accepted 3 October 2017)
Bistable Auxetic Metamaterials (BAMs) are a class of monolithic perforated periodic structures with negative Poisson’s ratio. Under tension, a BAM can expand and reach a second state of equilibrium through a globally large shape transformation that is ensured by the flexibility of its elastomeric base material. However, if made from a rigid polymer, or metal, BAM ceases to function due to the inevitable rupture of its ligaments. The goal of this work is to extend the unique functionality of the original kirigami architecture of BAM to a rigid solid base material. We use experiments and numerical simulations to assess performance, bistability, and durability of rigid BAMs at 10,000 cycles. Geometric maps are presented to elucidate the role of the main descriptors of the BAM architecture. The proposed design enables the realization of BAM from a large palette of materials, including elastic-perfectly plastic materials and potentially brittle materials.
I. INTRODUCTION
Metamaterials are designer matters with unusual properties that are governed by their underlying architecture rather than their chemical composition. Firstly introduced in the field of electromagnetic materials,1 the concept quickly extended to mechanical systems.2 Since then, a great interest in the mechanics of materials arena has emerged due to the exotic and tunable properties that mechanical metamaterials can offer, such as negative modulus and mass density, vanishing shear modulus, and programmable properties among many others.3–8 The Poisson’s ratio, m, the ratio between the transverse and longitudinal strain in the direction of an applied stretch, is a property of interest here; for isotropic 3D materials, m can vary between 1 and 1/2,9 whereas for 2D materials 1 , m , 1; for auxetics, it is negative. Compared to solids with positive m, auxetic materials offer enhanced shear moduli, indentation resistance, and fracture toughness,10,11 thus providing mechanical gains in a large range of applications, such as medical stents and skin grafts,12,13 porous dampers and acoustic foams,14 as well as gas turbines.15,16 Several efforts have been recently devoted toward the creation of auxetic layers obtained by perforating monolithic sheets with Contributing Editor: Katia Bertoldi a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2017.417
uniformly,17 randomly,18 as well as hierarchically13 distributed incision patterns. In three-dimensions, auxetic materials have also been obtained from re-entrant origami-based Tachi-Miura polyhedrons19 and origami tubes.20 Other works on auxetic materials exploit elastic instability to modulate the pattern switch and trigger distinct shape transformations. These include square planar lat
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