A Method to Determine the Geometry-Dependent Bending Stiffness of Multilayer Graphene Sheets

2020 ◽  
Vol 88 (1) ◽  
Author(s):  
Xiaojie Ma ◽  
Luqi Liu ◽  
Zhong Zhang ◽  
Yueguang Wei
Keyword(s):  
Graphene Sheet ◽  
Cylindrical Surface ◽  
Complex Geometry ◽  
Lattice Structure ◽  
Stress Transfer ◽  
Quantitative Agreement ◽  
Bending Stiffness ◽  
Graphene Sheets ◽  
Multilayer Graphene ◽  
Trilayer Graphene

Abstract We consider how the bending stiffness of a multilayer graphene sheet relies on its bending geometry, including the in-plane length L and the curvature κ. We use an interlayer shear model to characterize the periodic interlayer tractions due to the lattice structure. The bending stiffness for the sheet bent along a cylindrical surface is extracted via an energetic consideration. Our discussion mainly focuses on trilayer sheets, particularly the complex geometry-dependency of their interlayer stress transfer behavior and the overall bending stiffness. We find that L and κ dominate the bending stiffness, respectively, in different stable regions. These results show good quantitative agreement with recent experiments where the stiffness was found to be a non-monotonic function of the bending angle (i.e., Lκ). Besides, for a given in-plane length, the trilayer graphene in the flat state (κ → 0) is found to have the maximum bending stiffness. According to our analytical solution to the flat state, the bending stiffness of trilayer graphene sheet can vary by two orders of magnitude. Furthermore, once multilayer graphene sheets are bent along a cylindrical surface with small curvature, the sheets perform similar characteristics. Though the discussion mainly focuses on the trilayer graphene, the theoretical framework presented here can be readily extended for various van der Waals materials beyond graphene of arbitrary layer numbers.

Free Vibration of Single Layer Graphene Sheets: Lattice Structure Versus Continuum Plate Theories

2011 ◽  
Vol 2 (3) ◽  
Author(s):  
S. Arghavan ◽  
A. V. Singh
Keyword(s):  
Graphene Sheet ◽  
Lattice Structure ◽  
Plate Theory ◽  
Single Layer ◽  
Torsional Stiffness ◽  
Single Layer Graphene ◽  
Mode Shapes ◽  
Graphene Sheets ◽  
Layer Graphene ◽  
Young’S Moduli

Prospect of applications of graphene sheets in composites and other advanced materials have drawn attention from a broad spectrum of research fields. This paper deals with the methods to find mechanical properties of such nanoscale structures. First, the lattice structure method with the Poisson’s ratio of 0.16 and the thickness of 3.4 Å is used to obtain the Young’s moduli for the in-plane and out-of-plane deformation states. This method has the accuracy of molecular dynamics simulations and efficiency of the finite element method. The graphene sheet is modeled as a plane grid of carbon atoms taken as the nodal points, each of which carries the mass of the carbon atom and is assigned as a six degrees of freedom. The covalent bond between two adjacent carbon atoms is treated as an extremely stiff frame element with all three axial, bending, and torsional stiffness components. Subsequently, the computed Young’s moduli, approximately 0.11 TPa for bending and 1.04 TPa for the in-plane condition, are used for studying the vibrational behaviors of graphene sheets by the continuum plate theory. The natural frequencies and corresponding mode shapes of various shaped single layer graphene sheet ), such as rectangular, skewed, and circular, are computed by the two methods which are found to yield very close results. Results of the well-established continuum plate theory are very consistent with the lattice structure method, which is based on accurate interatomic forces.

Elastic properties of graphene-reinforced aluminum nanocomposite: Effects of temperature, stacked, and perforated graphene

2020 ◽  
Vol 234 (9) ◽  
pp. 1218-1227
Author(s):  
Ashish Kumar Srivastava ◽  
Vimal Kumar Pathak
Keyword(s):  
Graphene Sheet ◽  
Graphene Sheets ◽  
Marginal Effect ◽  
Multilayer Graphene ◽  
Plane Shear ◽  
Shear Moduli ◽  
Temperature Changes ◽  
Stiffness Properties ◽  
Out Of Plane ◽  
Dynamics Simulations

In this article, the elastic and shear moduli of the graphene sheet-reinforced aluminum nanocomposite have been investigated by molecular dynamics simulations. Different models have been simulated to study the effect of multilayer graphene sheet, perforation of GS, and temperature on the elastic and shear moduli of resulting nanocomposite. The simulation results show that the elastic and shear moduli of graphene sheet-reinforced aluminum are sensitive to the temperature changes, multilayer, and perforated graphene sheets. The temperature and perforation of graphene sheets exert adverse effects on the elastic and shear moduli of graphene sheet-reinforced aluminum nanocomposites. However, the multilayer graphene sheet leads to favorable effects on the stiffness properties of the nanocomposite. It is also observed that there is only a marginal effect of the chirality of graphene sheet on the out-of-plane shear moduli of the nanocomposite.

Meso-origami: Folding multilayer graphene sheets

2009 ◽  
Vol 95 (12) ◽  
pp. 123121 ◽  
Author(s):  
Steven Cranford ◽  
Dipanjan Sen ◽  
Markus J. Buehler
Keyword(s):  
Graphene Sheets ◽  
Multilayer Graphene

Bending stiffness of circular multilayer van der Waals material sheets

2022 ◽  
pp. 1-36
Author(s):  
Xiaojie Ma ◽  
Luqi Liu ◽  
Zhong Zhang ◽  
Yueguang Wei
Keyword(s):  
Lattice Structure ◽  
Van Der Waals ◽  
Bending Stiffness ◽  
Quantitative Prediction ◽  
Young’S Moduli ◽  
Different Types ◽  
Interlayer Shear Strength ◽  
Isometric Deformations ◽  
Good Agreement ◽  
Sinusoidal Function

Abstract We study the bending stiffness of symmetrically bent circular multilayer van der Waals (vdW) material sheets, which corresponds to the non-isometric configuration in bulge tests. Frenkel sinusoidal function is employed to describe the periodic interlayer tractions due to the lattice structure nature and the bending stiffness of sheets is theoretically extracted via an energetic consideration. Our quantitative prediction shows good agreement with recent experimental results, where the bending stiffness of different types of sheets with the comparable thickness could follow a trend opposite to their Young's moduli. Based on our model, we propose that this trend may experience a transition as the thickness decreases. Apart from the apparent effects of Young's modulus and interlayer shear strength, the interlayer distance is also found to have an important impact on the bending stiffness. In addition, according to our analysis on the size effect, the bending stiffness of such symmetrically bent circular sheets can steadily own a relatively large value, in contrast to the cases of isometric deformations.

scholarly journals Nanocomposite Materials of Alternately StackedC60Monolayer and Graphene

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
Makoto Ishikawa ◽  
Shu Kamiya ◽  
Shoji Yoshimoto ◽  
Masaru Suzuki ◽  
Daisuke Kuwahara ◽  
...  
Keyword(s):  
Electrical Properties ◽  
Graphene Sheet ◽  
Preparation Method ◽  
Nanocomposite Materials ◽  
Graphene Sheets ◽  
The Novel ◽  
Graphite Intercalation

We synthesized the novel nanocomposite consisting alternately of a stacked single graphene sheet and aC60monolayer by using the graphite intercalation technique in which alkylamine molecules help intercalate largeC60molecules into the graphite. Moreover, it is found that the intercalatedC60molecules can rotate in between single graphene sheets by usingC13NMR measurements. This preparation method provides a general way for intercalating huge fullerene molecules into graphite, which will lead to promising materials with novel mechanical, physical, and electrical properties.

scholarly journals CASIMIR EFFECTS IN GRAPHENE SYSTEMS: UNEXPECTED POWER LAWS

2012 ◽  
Vol 14 ◽  
pp. 531-540 ◽  
Author(s):  
BO E. SERNELIUS
Keyword(s):  
Graphene Sheet ◽  
Power Law ◽  
Power Laws ◽  
Graphene Sheets ◽  
Zero Temperature ◽  
Actual Distance ◽  
Distance Dependence

We present calculations of the zero-temperature Casimir interaction between two freestanding graphene sheets as well as between a graphene sheet and a substrate. Results are given for undoped graphene and for a set of doping levels covering the range of experimentally accessible values. We describe different approaches that can be used to derive the interaction. We point out both the predicted power law for the interaction and the actual distance dependence.

Design Method for Lattice-Skin Structure Fabricated by Additive Manufacturing

2014 ◽  
Author(s):  
Yunlong Tang ◽  
Yaoyao Fiona Zhao
Keyword(s):  
Complex Geometry ◽  
Lattice Structure ◽  
Design Method ◽  
Mapping Function ◽  
Second Step ◽  
Parameter Distribution ◽  
Skin Structure ◽  
Traditional Design ◽  
Novel Design

Parts with complex geometry structure can be produced by AM without significant increase of fabrication time and cost. One application of AM technology is to fabricate customized lattice-skin structure which can enhance performance of products with less material and less weight. However, most of traditional design methods only focus on design at macro-level with solid structure. Thus, a design method which can generate customized lattice-skin structure for performance improvement and functionality integration is urgently needed. In this paper, a novel design method for lattice-skin structure is proposed. In this design method, FSs and FVs are firstly generated according to FRs. Then, initial design space is created by filling FVs and FSs with selected lattice topology and skin, respectively. In parallel to the second step, initial parameters of lattice-skin structure are calculated based on FRs. Finally, TO method is used to optimize parameter distribution of lattice structure with the help of mapping function between TO’s result and lattice parameters. The design method proposed in this paper is proven to be efficient with case study and provides an important foundation for wide adoption of AM technologies in industry.

Growth of ZnO nanorods on the surface and edges of a multilayer graphene sheet

2017 ◽  
Vol 139 ◽  
pp. 77-82 ◽  
Author(s):  
Faramarz Hossein-Babaei ◽  
Mehdi Akbari-Saatlu
Keyword(s):  
Graphene Sheet ◽  
Zno Nanorods ◽  
Multilayer Graphene
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