Extreme Mechanics Letters 38 (2020) 100748 Contents lists available at ScienceDirect Extreme Mechanics Letters journal homepage: www.elsevier.com/locate/eml Poisson’s ratio of two-dimensional hexagonal crystals: A mechanics model study Chunbo Zhang a , Ning Wei b , Enlai Gao a,∗ , Qingping Sun c ,∗ a Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China b Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, Jiangnan University, 214122 Wuxi, China c Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Hong Kong, China article info Article history: Received 18 January 2020 Received in revised form 11 March 2020 Accepted 20 April 2020 Available online 25 April 2020 Keywords: Poisson’s ratio 2D hexagonal crystals Regulation strategies Limits abstract The Poisson’s ratio of two-dimensional hexagonal crystals has been widely studied due to its funda- mental and fantastic nature. However, the issue involved in the regulation strategy and in the bounds of Poisson’s ratio of two-dimensional hexagonal crystals has not been addressed. In this work, we predict that the Poisson’s ratio of two-dimensional hexagonal crystals can be controlled by modifying the structural interaction therein, where the lower bound and upper bound are −1/3 and +1, respectively. Furthermore, molecular simulations verify these predictions. Finally, the underlying mechanism is revealed as the interplay between two deformation modes (i.e., bond stretching and angle changing). This work provides an universal regulation strategy to tune the Poisson’s ratio of two-dimensional hexagonal crystals, and determines fundamental limits on the Poisson’s ratio of two-dimensional hexagonal crystals. © 2020 Elsevier Ltd. All rights reserved. 1. Introduction Poisson’s ratio, as one of the most fundamental parameters to measure the deformation of materials, has attracted consid- erable interests [1,2]. Poisson’s ratio not only affects the elastic behaviors of materials, but also closely relates to the material properties beyond elasticity, such as vibration absorption [3], indentation resistance [4], and toughness [5]. Therefore, a large number of strategies including modifying the internal factors, such as the geometry, topology, or anisotropy, and applying ex- ternal fields, such as temperature, pressure, or electric field, that could control the sign and magnitude of Poisson’s ratio have been proposed [1,2,6]. The limits on the Poisson’s ratio of conven- tional three-dimensional (3D) isotropic materials are well known as −1< ν < 1/2 that results from the requirement of elastic stability. As the compressibility increases, the Poisson’s ratio of 3D isotropic materials decreases from 1/2 to −1. To be specific, for highly incompressible rubber, ν ≈ 0.5; for slightly compress- ible metals, polymers and ceramics, 0.25 < ν < 0.35; for more compressible network structures, ν can be negative; for highly compressible fluids, ν can even approach −1[1]. In addition to isotropic materials, Ting et al. predicted that the Poisson’s ratio for anisotropic materials has no bounds [7]. These studies on the regulation strategies and the bounds of the Poisson’s ratio are of ∗ Corresponding authors. E-mail addresses: enlaigao@whu.edu.cn (E. Gao), meqpsun@ust.hk (Q. Sun). fundamental importance for guiding the design, fabrication, and applications of 3D materials having diverse Poisson’s ratios. Recently two-dimensional (2D) materials have received much attention because of their extraordinary properties resulting from the reduced dimensions [8–14]. Most of 2D materials possess hexagonal lattice [15] and thus are named as two-dimensional hexagonal crystals (2DHCs), in which the well-known examples are graphene and hexagonal boron nitride (h-BN). The in-plane elastic behavior of 2DHCs is known as elastic isotropy resulting from their six-fold rotational symmetry [16]. Thus it calls for only two independent elastic constants to measure the elastic deformation, in which the Poisson’s ratio is a commonly used one. Many studies have been conducted to investigate the Poisson’s ratios of 2DHCs, and thus diverse Poisson’s behaviors have been observed in 2D materials by tailoring their structures, such as introducing ripples, hydrogenation, or free edges [17–21]. Grima et al. demonstrated that graphene can be modified to exhibit a negative Poisson’s ratio by introducing defects, which was ex- plained by a ‘crumpled paper’ model [17]. Subsequently, it was further shown that graphene can exhibit a large magnitude of negative Poisson’s ratio by distributing defects in a specific ar- rangement [19]. Wan et al. found that the Poisson’s ratio of monolayer graphene oxide can be controlled from positive to neg- ative values by modifying its oxidation degree [21]. Furthermore, Jiang et al. found that graphene can exhibit negative Poisson’s ra- tio in a certain stage of the strain–stress curve resulting from the interplay of atom interactions [22]. The Poisson’s ratios, especially negative Poisson’s ratios of 2DHCs have been widely studied, https://doi.org/10.1016/j.eml.2020.100748 2352-4316/© 2020 Elsevier Ltd. All rights reserved.