Determination of Elastic Properties of Hexagonal Sheets by Atomistic Finite Element Method
MQ Le and DT Nguyen, JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, 12, 566-574 (2015).
An atomistic finite element method (AFEM), which considers atoms and atomic displacements as nodes and nodal displacements, respectively, is developed based on harmonic force fields. It is demonstrated that the potential energy of an atomic structure at small strains is expressed as second-order polynomials of atomic displacements. Element stiffness matrices are thus explicitly established in terms of atomic coordinates and harmonic force field parameters. The same formalism of the conventional finite element method is used to assemble the global stiffness matrix and to capture relations between atomic displacement and forces. The proposed AFEM are applied to determine elastic properties of graphene, boron nitride (BN), silicon carbide (SiC), and boron antimonide (BSb) monolayer sheets. Using the same force field parameters, deviations between Young's and shear moduli obtained by AFEM and those by molecular dynamics simulations appear within 5%. By comparing simulation results with available data in the literature for these 4 sheets, it may be concluded that the proposed AFEM is a simple and fast technique to analyze accurately elastic properties of nanostructured materials.
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