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Modeling the Nonlinear Behavior of Nano-Materials Via Hierarchical RVE-based Multi-Scale Method

Nikravesh Kazerooni, Yousef | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50517 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. In this paper, a hierarchical RVE-based continuum-atomistic multiscale framework is established on the basis of the nonlinear finite element method and molecular dynamics simulation in order to model the geometric and material nonlinearities of deformable solids. In this framework, the coarse scale material properties required for nonlinear finite element method are directly exploited via fine scale atomistic simulation of atomic RVEs designated for each coarse scale integration point and required boundary conditions for atomic RVE simulation are achieved from the coarse scale kinematical response. In order to ensure the kinematical and energetic consistency between the two scales, the fine-scale atomistic simulation is accomplished in the presence of the periodic constraint. Taking the advantage of fine-scale atomistic simulation provides an opportunity to precisely capture sophisticated coarse scale constitutive relation merely based on the valuable information extracted from interatomic interactions and therefore obviates the necessity of employing any phenomenological constitutive models. Since the atomic RVE represents underlying atomistic configuration in a finite vicinity of coarse scale points, the proposed method has the capability to deal with the materials possessing heterogeneous fine-scale configuration such as defect, dislocation, grain boundary and etc. In order to gain a deeper understanding of the fine-scale behavior, the stress-strain curves of a stress-free atomic RVE undergoing two deformational modes are plotted for different values of three fine-scale parameters including atomistic simulation velocity, boundary layer percentage of the atomic RVE and number of atoms within the RVE. The results of the stress-strain curves are then assessed to opt proper fine-scale parameters for multiscale framework calibration. Finally, several numerical examples are presented to illustrate capability and versatility of the proposed framework
  9. Keywords:
  10. Representative Volume Element ; Finite Element Method ; Molecular Dynamics ; Multiscale Finite Volume Method ; Nonlinear Behavior ; Nano-Scale Modeling

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