Introducing Structural Approximation Method for Modeling Nanostructures

Abstract

In this work a new method for analyzing nanostructured materials has been proposed to accelerate the simulations for solid crystalline materials. The proposed Structural Approximation Method (SAM) is based on Molecular Dynamics (MD) and the accuracy of the results can also be improved in a systematic manner by sacrificing the simulation speed. In this method a virtual material is used instead of the real one, which has less number of atoms and therefore fewer degrees of freedom, compared to the real material. The number of differential equations that must be integrated in order to specify the state of the system will decrease significantly, and the simulation speed increases. To generalize the method for different materials, we used dimensionless equations. A fuzzy estimator is designed to determine the inter-atomic potential of the virtual material such that the virtual material represents the same behavior as the real one. In this paper Gaussian membership functions, singleton fuzzifier, center average defuzzifier, and Mamdani inference engine has been used for designing the fuzzy estimator. We also used the Gear predictor-corrector numerical integration method to integrate the governing differential equations. A FCC nano-bar of copper under uniform axial loading along [1 0 0] has been considered. The Sutton-Chen inter-atomic potential is used. The strain of this nano-bar has been calculated using the MD and the proposed method. Comparing the results show that while the proposed method is much faster, its results remain in an acceptable range from the results of MD method.