A continuum-atomistic multi-scale technique for nonlinear behavior of nano-materials. (November 2018)

• Record Type: Journal Article
• Authors: Khoei, A.R.; Sameti, A. Rezaei; Kazerooni, Y. Nikravesh
• Is Part Of: International journal of mechanical sciences. Volume 148(2018)
• Page Start: 191
• Page End: 208
• Publication Date: 2018-11
• Subjects: Hierarchical multi-scale -- Atomistic RVE -- Nonlinear FEM -- Inter-scale consistency; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2018.08.012
• Languages: English
• ISSNs: 0020-7403

Abstract

Highlights: A hierarchical RVE-based continuum-atomistic multi-scale procedure is developed. The inter-scale kinematic and energetic consistency principals are exploited. The kinematic compatibility is applied by the atomistic periodic boundary conditions. The energetic consistency is satisfied by the Hill-Mandel periodic boundary conditions. Coarse-scale is modeled using the stress tensor and tangent modulus computed from atomistic RVE. Abstract: In this paper, a hierarchical RVE-based continuum-atomistic multi-scale procedure is developed to model the nonlinear behavior of nano-materials. The atomistic RVE is accomplished in consonance with the underlying atomistic structure, and the inter-scale consistency principals, i.e. kinematic and energetic consistency principals, are exploited. To ensure the kinematic compatibility between the fine- and coarse-scales, the implementation of periodic boundary conditions is elucidated for the fully atomistic method. The material properties of coarse-scale are modeled with the nonlinear finite element method, in which the stress tensor and tangent modulus are computed using the Hill-Mandel principal through the atomistic RVE. In order to clearly represent the mechanical behavior of the fine-scale, the stress-strain curves of the atomistic RVE undergoing distinct type of deformation modes are delineated. These results are then assessed to obtain the proper fine-scale parameters for the multi-scale analysis. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. Graphical abstract: Schematically representation of the hierarchical atomistic-continuum multi-scale procedure.