本研究是以分子動力學模擬奈米級微結構在不同結構和不同尺寸下承受位移邊界條件拉伸時，結構的變形機制和應力分析。首先，本文模型是採用FCC面心結構及HCP最緊密堆積來作為結構的研究，原子間的勢能函數採用Tight-Binding多體勢能來計算，並遵循牛頓第二運動定律，在整個數值計算方面採用Gear 五階預測修正法來計算系統原子受力後的位置和速度等物理量，並使用Verlet 鄰近表列和截斷勢能法的演算法則來計算原子間的相互作用力，以減少整個電腦數值模擬的運算時間。
本論文所探討的內容可分為三部分，分別為：(1)針對完美單晶銅結構與完美鈦結構的拉伸變形研究(2)包含了空孔點缺陷的拉伸變形結構研究(3)針對尺寸縮小後所造成的表面效應影響作一探討。
由拉伸的模擬結果發現： (1)使用分子動力學模擬計算的結果，發現應力曲線不平滑，這都是巨觀所沒有的現象。(2)缺陷會造成極限應力及楊氏係數的影響。(3)表面效應對於奈米微結構的影響很大，使得原為常數的楊氏係數成為變數，另外，鈦的極限應力也會隨著尺寸的縮小而增加；但銅就沒有那麼明顯了。半徑的變化對楊氏係數的影響很小。

In this study, the deformation mechanism and stress analysis of the nanostructure have been simulated by molecular dynamics for various structures and sizes under tensile loading with displacement boundary condition. First, the FCC and HCP structures models are adojted. The many body potential functions for intermolecular are described by the tight-binding potential. Following the second law of Newton, the Gear fifth order predictor-corrector method is adopted to calculate atom’s physical properties, such as position and velocity, etc. To reduce the computer simulation time, the algorithms of Verlet neighbor list and cut-off potential are applied to calculate the interactive force between atoms.
Three parts are discussed, respective, (1) the nanostructure in the perfect of single crystal copper structure and perfect titanium structure. (2) the tensile deformation mechanism and stress analysis of the point defects effects. (3)the significance of effect as size reduced.
The results of loading : (1) the results of molecular dynamics simulation find the stress curve weren’t smooth. Those phenomenon can’t find in macroscopic. (2) defects will effect the limit stress and young’s modulus. (3) surface effect heavy in the nano-structure. On the one hand it use the Young’s modulus become variable and on the other the limit stress of titanium will decrease with the size increase. But copper will not clear in limited stress. Radius will not effect the young’s modulus.

目錄
中文摘要................................................I
英文摘要...............................................II
致謝..................................................III
目錄...................................................IV
表目錄................................................VII
圖目錄...............................................VIII
符號說明...............................................XI

第一章 緒論...........................................1
1.1 前言................................................1
1.2 研究動機與目的......................................4
1.3 文獻回顧............................................5
1.3.1 一般分子動力學文獻回顧.........................5
1.3.2分子動力學應用於固體力學之文獻回顧 ............7
1.4 本文架構...........................................10

第二章 物理模型與勢能函數...........................11
2.1 物理模型介紹......................................11
2.2 邊界條件設定......................................13
2.3 分子間作用力與勢能函數............................14
2.4 運動方程式........................................18

第三章 數值計算法..................................19
3.1 選擇的勢能函數..................................19
3.2 原子級應力表示式 ……………………………………….21
3.3 物理參數和無因次量..............................24
3.4 設定初始值......................................26
3.5 Gear 五階預測修正法.............................28
3.6 截斷勢能與Verlet表列 ..........................32
3.7 熱平衡..........................................35
3.8 程式流程圖......................................37

第四章 實例研究..................................39
4.1 完美結構的拉伸變形機制和應力分析.................40
4.1.1 完美銅結構...................................40
4.1.2 完美鈦結構...................................42
4.1.3 完美銅結構與完美鈦結構的結果比較..................44
4.2 含空孔的拉伸變形機制和應力分析...................48
4.2.1 含缺陷的單晶銅……………………………………….49
4.2.2 含缺陷的鈦晶體……………………………………….51
4.2.3 完美銅結構與含缺陷銅的比較……………………….53
4.2.4 完美鈦結構與含缺陷鈦的比較……………………….54
4.3 尺寸效應的應力分析...............................55
4.3.1 r、H對楊氏係數的影響……………………………….56
4.3.2 H對楊氏係數的影響…………………………………..58
4.3.3 r對楊氏係數的影響…………………………………..59
第五章 總結與建議.................................107
5.1 總結..………………………………………………………107
5.2 建議.……………………………………………………….108
參考文獻............................................109

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