An equivalent continuum-atomistic algorithm is proposed for carbon-based structures such as nano-scale graphene platelets (NGPs) and carbon nanotubes (CNTs) individually or as stiffeners with polymers. This equivalent continuum-atomistic model will account for the nonlocal effect at the atomistic level and will be a highly accurate mean to determine the bulk properties of graphene-structured materials from its atomistic parameters. In the model, the equivalent continuum and atomic domains are analyzed by finite elements and molecular dynamics finite element-based where atoms stand as nodes in discretized form. Micromechanics idea of representative volume elements (RVE) will be used to determine averaged homogenized properties. In the procedure, a unit hexagonal cell will be the RVE. A minimum volume of material containing this RVE and the neighboring hexagonal cells will be chosen. The size of this volume should cover all the atoms, which have bonded, and nonbonded interaction with the atoms of the RVE unit cell. This minimum volume will be subjected to several load cases. Determination of the response of the RVE hexagonal unit cell contained within the minimum volume, and its potential energy density under the defined load cases, will lead to the determination of mechanical parameters of an equivalent, continuum geometrical shape. For a single layer NGP the thickness of the hexagonal continuum plate is assumed to be 0.34 nm, while in three-dimension and multilayered the actual thickness of layers can be implemented. Under identical loading on the minimum volumes, identical potential (strain) energies for both models will be assumed. Through this equivalence a linkage between the molecular force field constants and the structural elements stiffness properties will be established.
An Equivalent Continuum-Atomistic Characterization Model for Nanographitic Materials
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Karami, G. "An Equivalent Continuum-Atomistic Characterization Model for Nanographitic Materials." Proceedings of the ASME 2005 International Mechanical Engineering Congress and Exposition. Aerospace. Orlando, Florida, USA. November 5–11, 2005. pp. 471-478. ASME. https://doi.org/10.1115/IMECE2005-81858
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