本研究主要使用分子力學最小能量方法以及代表性單位晶格能量等效模型來探討不同螺旋性之石墨烯薄膜的彈性性質與破壞行為，考慮一代表性單位晶格受任意方向之平面加載的變形，在分子力學方法中僅考慮碳原子間之鍵長與鍵角所產生的能量變化，以最小能量假設求得穩態原子之分佈，在小變形下藉由應變能密度可求得彈性性質，而在大加載下配合以臨界鍵長作為判斷破壞的依據，用以預測石墨烯薄膜的破壞應變，並有效的發現不同螺旋性之石墨烯薄膜的彈性性質呈現平面內等向性，但破壞則具有方向性。
另外以代表性單位晶格的能量等效之概念，建立一有限尺寸之能量等效樑元素模型，探討能量等效模型之彈性性質與破壞行為，並與分子力學方法的結果比較，探討模擬的合理性，其結果顯示不同螺旋性之石墨烯薄膜能量等效模型呈現等向性的彈性性質，但不等向性的破壞行為。
此外沿用能量等效模型探討完整石墨烯薄膜與有缺陷之石墨烯薄膜的破壞行為，並分析有裂紋之扶手椅型與鋸齒型石墨烯薄膜受簡單拉伸加載時的破壞行為，即為分析扶手椅型與鋸齒型受第I型破裂(Opening fracture)之應力強度因子(Stress intensity factor)與應變能釋放率(Strain energy release rate)，根據連體力學之理論，本研究成功訂定了扶手椅型與鋸齒型受第I型破裂的臨界應力強度因子以及臨界應變能釋放率，且因為石墨烯薄膜呈現的破壞非等向性，扶手椅型石墨烯薄膜展現了比其他不同螺旋性之石墨烯薄膜較具抗破壞的行為。

This research developed molecular mechanics minimum energy method and energy equivalent model by the unit cell of graphene to investigate the elastic properties and fracture behavior for all chiralities. In molecular mechanics method was consider a representative unit cell of graphene and only bond stretching and bending were considered in the infinite graphene sheet under in-plane loading. The deformation of the graphene could be calculated under the minimum energy assumption. Also, the fracture criteria based on critical bond length was used to predict the fracture strain of graphene. We found that the elastic behavior of graphene is isotropic for all chiralities, in contrast to its anisotropic fracture behavior.
We use the concept of energy equivalent to a representative of the unit lattice Establish of a finite size of the equivalent energy beam element model to investigate the elastic properties and fracture behavior, and compare with the results of molecular mechanics method. It showed that the isotropic/anisotropic features of elasticity/fracture are good in the two-dimensional tensile systems.

Then we adopted the energy equivalent model to discuss failure behavior on the graphene which is complete or has defects. And analysis the armchair graphene or zigzag graphene has cracks and stretch by simple tensile loading which is the mode-I type fracture. According to the continuous mechanics, we successfully set up the critical strain energy release rate with armchair and zigzag graphene by mode-I fracture. Also owing to its anisotropy failure behavior, armchair graphene exhibited greater anti-destroyed behavior than any other chirality of graphene.

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