| Summary: | 碩士 === 國立清華大學 === 動力機械工程學系 === 93 === A novel atomistic-continuum mechanics method (ACM) based on the finite element method is proposed to simulate the mechanical characteristics, such as the Young’s modulus and Poisson’s ratio of nano-scaled structures. Moreover the nano-scaled body centered cubic (BCC) structures of Lithium (Li) are treated as the test vehicle in this research to validate the capability of the proposed method.
The ACM method transfers an originally discrete atomic structure into an equilibrium continuum model by atomistic-continuum transfer elements. The ACM model simplifies the complexities of interaction forces among atoms, while the calculation accuracy is still acceptable and the computational time is affordable. To compare with molecular dynamics method (MD), the ACM method has benefits on computer calculation. In this research, it is capable to analyze a big model with more than 600,000 atoms, and only takes 8 hours CPU time in PC to get a result. In MD analysis, it will need a super computer to handle such a big model. As a result, the atomistic-continuum method shows potentials for the large model analysis.
In this research, the nano-scaled BCC structures of Li are applied to analyze its Young’s modulus and Poisson’s ratio. The “pre-force” assumption is introduced. In the BCC structure, it is assumed that there are compressive pre-forces among the diagonal arranged atoms, and tensile pre-forces among the axial arranged atoms. The pre-force assumption will induce a bubble-like phenomenon when nano structures are in minimum energy. In the analysis results, the nano-scaled Li structure has higher Young’s modulus and lower Poisson’s ratio than bulk properties. Moreover, as the size of nano-scaled structure becomes larger, the Young’s modulus and Poisson’s ration become different. The material properties are no more constants in nano-scale structure. They are size-dependent properties. Besides, when point defects exist in nano-scaled structures, the Young’s modulus is decreased and the Poisson’s ration is increased, all compared with perfect nano structures.
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