Abstract
We present a domain-reduction approach for the simulation of one-dimensional nanocrystalline structures. In this approach, the domain of interest is partitioned into coarse and fine scale regions and the coupling between the two is implemented through a bridging-scale interfacial boundary condition. The atomistic simulation is used in the fine scale region, while the discrete Fourier transform is applied to the coarse scale region to yield a compact Green’s function formulation that represents the effects of the coarse scale domain upon the fine/coarse scale interface. This approach facilitates the simulations for the fine scale, without the requirement to simulate the entire coarse scale domain. After the illustration in a simple 1D problem and comparison with analytical solutions, the proposed method is then implemented for carbon nanotube structures. The robustness of the proposed multiscale method is demonstrated after comparison and verification of our results with benchmark results from fully atomistic simulations.
Highlights
Recent developments in synthesis of one-dimensional nanostructures such as nanowires and nanotubes have provided an exciting new venue for developing light weight, high strength structural components
Many of the multiscale methods developed have been based on coupling atomistic simulation method with continuum simulation techniques such as the Finite Element Methods (FEM)
The FEM nodes typically coincide with the positions of the atoms in the handshake region
Summary
Recent developments in synthesis of one-dimensional nanostructures such as nanowires and nanotubes have provided an exciting new venue for developing light weight, high strength structural components. The goal is to determine the set of boundary conditions defined on f such that application of the displacement and traction through Eqs.(7)-(8) would lead to the same solution for the atomic degree of freedom as in the original boundary value problem statement in Eqs.(3)-(5). This implementation results in a reduction to an equivalent problem defined on a relatively smaller fine scale domain as compared with the original problem. The rest of the paper is organized as follows: Section 2 outlines the formulation of the proposed domain-reduction approach based on the use of bridging-scale interfacial boundary condition. Forth, we refer to the K -matrices as the kernel function matrices
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