A method for developing the equivalent continuum model of a single layer graphene sheet

2008 ◽  
Vol 516 (21) ◽  
pp. 7636-7640 ◽  
Author(s):  
Ali Hemmasizadeh ◽  
Mojtaba Mahzoon ◽  
Ehsan Hadi ◽  
Rasoul Khandan
Keyword(s):  
Graphene Sheet ◽  
Continuum Model ◽  
Single Layer ◽  
Single Layer Graphene ◽  
Layer Graphene ◽  
Equivalent Continuum Model ◽  
Equivalent Continuum

A Semi-Analytical Method for Developing the Equivalent Continuum Model of a Single Layer Graphene Sheet

2008 ◽  
Author(s):  
Ali Hemmasizadeh ◽  
Mojtaba Mahzoon ◽  
Vahid Yavari ◽  
Rasoul Khandan
Keyword(s):  
Molecular Dynamics ◽  
Graphene Sheet ◽  
Analytical Method ◽  
Continuum Model ◽  
Single Layer ◽  
Continuum Theory ◽  
Single Layer Graphene ◽  
Nano Indentation ◽  
Equivalent Continuum Model ◽  
Equivalent Continuum

A semi-analytical method is presented to develop the equivalent continuum model for a single-layered graphene sheet. This method integrates molecular dynamics method as an exact numerical solution with theory of shell as an analytical method. The force-depth results obtained from molecular dynamics (MD) simulation of nano-indentation of a single graphene sheet are compared with the formulation for large deflection of circular plates loaded at the centre. As a result, the effective Young’s modulus and mechanical thickness of the sheet wall are independently obtained. The validity of this new approach is verified by comparing finite element modeling of nano-indentation of a single graphene sheet with molecular dynamics results available in the literature. Presented results demonstrate that the proposed method could provide a valuable tool for studying the mechanical behavior of single-layered graphene sheets, as well as efficiency of continuum theory in nano-structured material.

scholarly journals Geometrical Dimensional Effect on Natural Frequency of Single Layer Graphene in Armchair Configuration

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Harshad Patel
Keyword(s):  
Graphene Sheet ◽  
Plate Theory ◽  
Single Layer ◽  
Free Edge ◽  
Single Layer Graphene ◽  
Geometrical Parameters ◽  
Classical Plate Theory ◽  
Element Analysis ◽  
Nanomechanical Resonator ◽  
Layer Graphene

Graphene has remarkable strength, such as yield strength and elasticconstant. The dynamic behaviour of graphene sheet is affected bygeometrical variation in atomic arrangement. This paper introducedgraphene with armchair atomic structure for estimating fundamental naturalfrequencies. The presented analysis can be useful for the possible highfrequency nanomechanical resonator systems. The analytical formulation,based on classical plate theory and continuum solid modelling based finiteelement method have been performed for estimation of fundamental naturalfrequencies of single layer graphene sheet (SGLS) with different boundaryconditions. The free edge and clamped edge boundary conditions have beenconsidered. For simplifying analytical formulations, Blevins approach fordynamic solution has been adopted and for validating analytical results.The finite element analysis of SLGS has been performed using ANSYSsoftware. The effect of variation in geometrical parameters in terms ofwidth and length of SLGS has been analysed for realization of ultra-highfrequency based nanomechanical resonator systems

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