本文以分子動力學的模擬方法，對奈米碳管及其相關複合材料進行壓縮以及拉伸模擬，並探討其線性與非線性力學行為。本研究以控制模擬試體之位移上下端邊界層的位移，以固定其速率，分析兩端固定之奈米試體，在承受單軸向的壓縮以及拉伸位移負荷之下，所呈現出來的力學性質與挫屈行為。藉由模擬計算所得之應變與應變能關係圖中，觀察此力學系統之能量變化；由能量不連續處，探討發生挫屈時的臨界應變；並利用於平衡處之能量曲率來求得楊氏係數。此外，分子動力學模擬之優勢在於可分析非常微小的時間尺度之下的各原子之間的暫態行為，本研究利用此項優勢，詳細呈現奈米碳管複合材料在承受單軸向外力時，其動態行為的表現，以了解奈米碳管內含物與基材之間的原子－原子間交互及其牽引作用。
在第二章中，單壁奈米碳管發生挫屈時的尺度效應在本章節被討論。研究結果發現，奈米碳管的管壁厚度大約為0.066奈米，且可利用巨觀的薄殼理論來做預測。此外，管徑較小的奈米碳管具有較大的挫屈應變，此現象與尤拉實心柱迥異。
　　在第三章中，不同細長比(SR)對於多壁奈米碳管發生挫屈時的機械性質被討論於此。研究結果顯示，在SR固定的條件下，SR較小的奈米碳管，其挫曲型態與圓柱型連體薄殼(continuum shell)之挫曲變形特徵類似；而SR較大的奈米碳管，則呈現尤拉柱(Eular column)的挫曲特徵。同時亦發現，管徑較小的奈米碳管有較大的挫曲強度。
　　在第四章中，多壁奈米碳管的楊氏係數可以利用軸向壓縮以及拉伸的試驗方法求得。其求得的楊氏係數分佈大約在0.85到1.16 TPa之間，同時亦發現其挫曲強度及楊氏係數皆是取決於最外層的碳管管徑。此外，模擬條件時所設定之邊界固定層數亦會影響模擬結果，當上下層各固定2、3或是4層原子時，其能量曲線是相當一致的，但若只固定一層時，其所計算出的結果便會略低於此，原因為當邊界只固定一層時，並無法有效的模擬嵌入型邊界條件。
　　在第五章中，探討了奈米碳管複合材料的問題，本章節以一單壁奈米碳管鑲嵌於鋁基作為其奈米碳管複合材料，並對其受軸向外力時的挫屈行為加以分析討論。其結果顯示，當CNT在鋁基內部從挫屈型態欲回覆到直立柱型態時，其能量曲線並未有一較大的落差，而是一平滑的曲線，此和單一根單壁奈米碳管在做拉伸時的能量有顯些不同。而當CNT在鋁基內部從直立柱型態到挫屈變形時，所需的應變會比單一根單壁奈米碳管增大約14.5%。

This thesis adopts the molecular dynamics (MD) simulation methods to simulate the mechanical behavior of carbon nanotubes (CNTs) and CNT-composites. Specifically, buckling and Young’s modulus of the material systems are discussed by simulation. Through displacement control the upper and lower boundary layers, the specimens are compressed or stretched uniaxially, and their mechanical properties are analyzed. The energy jumps of energy-strain curves from the simulation indicate the occurrence of buckling, and therefore buckling strains can be defined by the jump. The calculation of Young’s modulus would be carried out through the energy curvature around zero strain. Moreover, we observe and study the transient behavior of atoms at atomic time scales.
In Chapter 2, the scaling phenomena of the buckling of single-walled carbon nanotubes are investigated. It is found that the buckling strain of CNTs, with the wall thickness of 0.066 nm, can be predicted by a model of macroscopic shells for various lengths with a given slenderness ratio. Faurthermore, smaller nanotubes exhibit larger buckling strain, i.e. high buckling-resistance, completely different from an Euler solid column.
In Chapter 3, this discussed the mechanical buckling of multi-walled carbon nanotubes under the different slenderness ratio. The results shows, under constant ratio of slenderness, the CNTs with small SR behave like a continuum shell object. For large SR’s, multi-walled CNTs exhibit the characteristics of the Euler columns. In addition, smaller nanotubes possess higher buckling-resistance. The buckling strength of multiwalled nanotubes is controlled by the size of their outermost shell.
In Chapter 4, the Young’s modulus of a multi-walled carbon nanotube (MWNT) is studied. From results of MD simulations of uniaxial loading and unloading on a MWNT, the Young’s modulus of a MWNT is about the range between 0.85 to 1.16 TPa. Moreover, the Young’s modulus of a MWNT is also depended on the outer SWNT type. Besides, the number of the fixed end layers will influence the simulation results. The energy curve of fixed one layer has a bit less lower than fixed two, three, or four layers on each the top and bottom.
In Chapter 5, study of buckling shapes of a single-walled carbon nanotube reinforced aluminum composite. The results show that when the embedded single-walled CNT deforms from the buckled to straight states, the total energy curve shows no discontinuities, indicating the energy release in this regard is continuous up to the C0 function. However, when the single-walled CNT deforms from the straight to buckled states, the corresponding energy jump is about 14.5%. The amount of energy being released or absorbed in the process indicates the applicability of using the CNTs for building novel composites.

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