A continuum-atomistic multi-scale technique for nonlinear behavior of nano-materials

AR Khoei and AR Sameti and YN Kazerooni, INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 148, 191-208 (2018).

DOI: 10.1016/j.ijmecsci.2018.08.012

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.

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