奈米尺度結構由於其表面原子所佔比例較高，表面原子特性將影響奈米結構物理、化學特性，使其具有尺寸相關之特性。本研究提出一方法，利用有限單元法以及原子等效理論，建立一原子-連體力學分析法（Atomistic-Continuum Mechanics Method），以進行奈米尺度原子結構之力學模擬分析。透過原子-連體力學法，可大量簡化原子結構模型，得以在有限的計算資源中，進行更有效率，並保持相當精度的計算。為探討此法之可行性，本研究將建立以鋰原子結構為基礎的模型，分析材料在奈米尺度下（微觀）之楊氏模數及蒲松比等材料性質，並與塊材（巨觀）的材料性質做一比較及討論。
於本研究中提出預力假設，說明鋰原子於不受外力之穩定狀態實存在預力：在鋰原子體心立方結構中，對角線方向相鄰原子間存在壓預力；而軸方向相鄰原子間則存在張預力。在此預力假設下，穩定狀態之奈米結構不再維持立方體的形狀，其表面原子會產生平面外之位移，形成近似球狀的結構。於奈米結構楊氏模數、蒲松比等材料力學性質研究中，奈米結構楊氏模數會高於該材料之塊材性質，而蒲松比則低於塊材性質。此外，該力學性質將隨著奈米結構尺寸大小變化，成為尺寸（Size-dependent）相關的材料性質。本研究中將進行缺陷對於完美晶格結構強度影響之初步探討，分析結果顯示，點缺陷會降低該結構的強度，使其楊氏模數下降。當點缺陷的數目增加，楊氏模數下降的幅度亦會增加。
與分子動力學相比較，於相同原子個數及種類下，利用本研究之原子-連體力學分析法分析該奈米結構，其所需數值計算時間上比分子動力學方法少。於本研究中最大的奈米結構約含有60萬個原子，此模型於約需在一般個人電腦中計算八小時，若以相同大小模型進行分子動力學計算，則需以平行電腦才能負擔其龐大的計算量，故本研究發展之原子-連體力學法於奈米結構的研究中有其計算速度上之優勢。
本研究主要目標在於原子-連體力學法之方法建立，於合理的假設下，將原本離散的原子結構轉換成為連續體結構，並利用有限單元法分析該結構之力學性質。於此方法中吾人可確認傳統連體力學理論用於奈米尺度分析之可行性，及該方法使用於原子個數超過百萬之大型奈米結構力學性質分析的能力。

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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