本文發展一套方法來預測石墨烯之破壞性質，透過多尺度的模擬來結合邊界元素和有限元素，其中，位於裂縫尖端附近的分子模型，是由非線性樑元素組成的六邊型晶格；而對於整個模型，視為連續體，透過邊界元素法來模擬。非線性樑元素的性質，是由位能和應變能等效而得出的，當推導出樑元素的性質時，連續體模型的材料性質可以透過施力在分子模型上來求得，值得注意的是，本文所使用的邊界元素法，其基本解以滿足裂縫無曳引力的邊界條件，所以無需對裂縫做切割，結合邊界元素和有限元素，並導入多尺度的概念，可以省下許多計算時間以及電腦負擔。裂縫尖端附近的受力情形，其精準度也改善線彈性破壞力學計算上的問題，進而可以預測出裂縫延伸的路徑，而在不同的模式下，預測出的路徑也不相同；為了要預測破壞模式一和模式二的破裂韌度，可以藉由改變施在連續體模型上的施力來求得，而不同方向的石墨烯，破裂韌度也會有所差異。
最後，本文與其他文獻比較後，預測裂縫延伸的路徑方向是一致的，所得之破壞韌度跟其他發表的文獻或是使用其他方法得出的值比對驗證，也都是落在可接受的範圍，證明本文發展的方法的可行性和數值精準度。

In this study, we use multiscale simulation to predict the fracture properties of graphene sheet. The nano-scale which is near the crack tip is formed by molecular dynamic-based nonlinear beam element, while the maco-scale is described by two-dimensional special boundary element. The main feature of special boundary element is that no meshes are required along the crack surface. Coupling the nonlinear beam element by 2D boundary element of multi-scale modeling, a vast of computational tome can be saved. To predict the atomistic bond-breaking, the stress-strain curve of the beam element is a standard. With this standard, mode I and mode II fracture toughness of graphene sheet can be predicted, in addition, the crack propagation is observed, too. The obtained values were then verified by the published results measured or predicted by the other methods.

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