The Prediction of Mechanical Properties of Graphene by Molecular Mechanics and Structural Mechanics Method

Based on molecular mechanics and the stick-spiral model, this paper first presents the analytical analysis of the effective in-plane mechanical properties of both zigzag and armchair monolayer graphene sheets. We find that the equivalent in-plane elastic constants of monolayer graphene sheets are the same in the two principal directions of graphene. The effective in-plane mechanical properties of graphene are then evaluated numerically using an improved molecular structural mechanics (MSM) model, in which the flexible connections are used to characterize the bond angle variations of graphene. Furthermore, the effective bending rigidity of the beam representing a C-C bond in this improved MSM model is determined from the energy equivalence over the basic cell of graphene and the force constants given by molecular mechanics. A rigidly connected frame model with the bending stiffness of the equivalent beams for C-C bonds different from the existing structural mechanics model is also used to evaluate the mechanical properties of graphene. The flexibly connected frame model gives very good results of Youngs modulus and Poisson ratio of monolayer graphene sheet. The new rigidly connected frame model presented here also gives improved results than the existing rigidly connected frame model of graphene.

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“…We find that the Young's modulus and Poisson ratio of zigzag graphene are the same with armchair graphene [8] .…”

Section: Analytical Solutionmentioning

confidence: 74%

Equivalent Mechanical Properties of Graphene Predicted by an Improved Molecular Structural Mechanics Model

Cheng

Shi

2014

KEM

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“…The numerical values of these stiffness constants, k r , k u , k , for the carbon-carbon bond are derived from Cheng and Shi 16 Comparison of the above relations for the three methods, classical molecular mechanics, flexural method, and MCS-MM method, shows that the MCS-MM method in this paper predicts the elastic and shear modulus of the beam more than the other two methods. For the beam diameter, this prediction is the opposite.…”

Section: Modification Of MM Considering the Mcs Theorymentioning

confidence: 97%

“…Some researchers tried to modify molecular mechanics methods for estimating the accurate values of mechanical properties of nanostructures. Cheng and Shi 16 investigated the mechanical properties of graphene using a new version of molecular mechanics. They described relationships between force constants and molecular mechanical parameters.…”

Section: Introductionmentioning

confidence: 99%

A novel upgraded molecular mechanics framework with considering the length scale parameter and its advantages in analyzing the behavior of nanostructures

Sha’bani

Ahmadi

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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A novel upgraded molecular mechanics framework has been developed by improving the flexural and torsional behavior in bonds between atoms based on modified couple stress theory (MCS-MM). The MCS-MM approach drives a considerable advancement in predicting the mechanical behavior of nanostructures. Due to applying the modified couple stress theory in the beam energy equations, the length scale parameter is added to the equations. The presented method provides a better prediction for the elastic and geometric properties of the equivalent beams in the atomic structure. In order to show the efficiency of this upgraded proposed model, various aspects of graphene sheets were considered, such as energy deviation, mechanical properties, buckling behavior, and crack opening displacement (COD). The results confirm the efficiency and accuracy of the model and are consistent with molecular dynamics modeling. The MCS MM method leads to a significant improvement in strain energy deviation. It predicts the elastic properties and mechanical behavior of graphene sheets more accurately. The MCS-MM method can be replaced with previous ones as an appropriate approach.

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The molecular mechanics study on mechanical properties of graphene and graphite

Chang

Chen

2014

Appl. Phys. A

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The Prediction of Mechanical Properties of Graphene by Molecular Mechanics and Structural Mechanics Method

Cited by 5 publications

References 7 publications

Equivalent Mechanical Properties of Graphene Predicted by an Improved Molecular Structural Mechanics Model

Equivalent Mechanical Properties of Graphene Predicted by an Improved Molecular Structural Mechanics Model

A novel upgraded molecular mechanics framework with considering the length scale parameter and its advantages in analyzing the behavior of nanostructures

The molecular mechanics study on mechanical properties of graphene and graphite

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