TY - JOUR
T1 - Analytical models for predicting the nonlinear stress-strain relationships and behaviors of two-dimensional carbon materials
AU - Xiong, Zixin
AU - Zhang, Teng
AU - Li, Xiaoyan
N1 - Funding Information:
X. L. gratefully acknowledges the financial support from the National Natural Science Foundation of China (Grant Nos. 91963117, 11921002, and 11720101002). All the simulations were performed on the TianHe-1 supercomputer at the National Supercomputer Center in Tianjin.
Publisher Copyright:
© 2021 by ASME
PY - 2021/8
Y1 - 2021/8
N2 - Due to having a single atom layer, two-dimensional (2D) materials represented by graphene monolayers exhibit unique and excellent mechanical properties, such as ultrahigh moduli and strengths. A large number of experiments and atomistic simulations have demonstrated nonlinear stress-strain responses. However, there is no theoretical model that analytically describes the relationships between nonlinear mechanical properties and interatomic interaction parameters of 2D materials. Here, we developed a nonlinear stick-spiral model for four typical 2D materials (including graphene, γ-graphyne, β-graphyne, and hexagonal boron nitride) based on a molecular mechanics model. By using the perturbation method, we derived a series of analytical expressions for nonlinear stress-strain relationships and elastic constants of these 2D materials under uniaxial tension along the zigzag and armchair directions. Our analytic models indicated that both Young's moduli and Poisson's ratios of these 2D materials are isotropic and dominate the linear elastic deformation, while their third-order moduli are orientation-dependent and essentially characterize the nonlinear stress-strain responses. The nonlinear stress-strain relationships, elastic constants, and atomic behaviors (such as bond elongation and bond angle variation during deformation) predicted from our analytical models are in good agreement with those from atomistic simulations and previous experiments. Our analytical models further demonstrated that the mechanical properties and behaviors of 2D materials are linked with their bonding and atomic structures (from a quantitative perspective) and are mainly determined by stiffnesses for bond stretching, angle variation, and bond lengths. Our current study provides an effective and accurate analytical approach for investigating the nonlinear behaviors of 2D materials.
AB - Due to having a single atom layer, two-dimensional (2D) materials represented by graphene monolayers exhibit unique and excellent mechanical properties, such as ultrahigh moduli and strengths. A large number of experiments and atomistic simulations have demonstrated nonlinear stress-strain responses. However, there is no theoretical model that analytically describes the relationships between nonlinear mechanical properties and interatomic interaction parameters of 2D materials. Here, we developed a nonlinear stick-spiral model for four typical 2D materials (including graphene, γ-graphyne, β-graphyne, and hexagonal boron nitride) based on a molecular mechanics model. By using the perturbation method, we derived a series of analytical expressions for nonlinear stress-strain relationships and elastic constants of these 2D materials under uniaxial tension along the zigzag and armchair directions. Our analytic models indicated that both Young's moduli and Poisson's ratios of these 2D materials are isotropic and dominate the linear elastic deformation, while their third-order moduli are orientation-dependent and essentially characterize the nonlinear stress-strain responses. The nonlinear stress-strain relationships, elastic constants, and atomic behaviors (such as bond elongation and bond angle variation during deformation) predicted from our analytical models are in good agreement with those from atomistic simulations and previous experiments. Our analytical models further demonstrated that the mechanical properties and behaviors of 2D materials are linked with their bonding and atomic structures (from a quantitative perspective) and are mainly determined by stiffnesses for bond stretching, angle variation, and bond lengths. Our current study provides an effective and accurate analytical approach for investigating the nonlinear behaviors of 2D materials.
KW - 2D materials
KW - Constitutive modeling of materials
KW - Elastic constants
KW - Molecular mechanics model
KW - Nonlinear analytical model
KW - Nonlinear stress-strain relationship
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U2 - 10.1115/1.4050689
DO - 10.1115/1.4050689
M3 - Article
AN - SCOPUS:85107697867
SN - 0021-8936
VL - 88
JO - Journal of Applied Mechanics, Transactions ASME
JF - Journal of Applied Mechanics, Transactions ASME
IS - 8
M1 - 081005-1
ER -