M-積分是研究物體具有裂縫之破壞行為的重要參數。本論文結合有限元素法研究針對三維線彈性材料具有裂縫之物體受混合載重作用計算其M-積分的數值分析。首先依序針對具有任意形狀之二維裂縫問題以及具有任意形狀之三維裂縫問題，進行M-積分式的理論推導，其次証明M-積分具有與積分曲面無關的性質。 在三維問題，對單裂縫的M-積分計算結果顯示與積分曲面無關和具有與原點無關的特性；多裂縫問題的M-積分計算，則需對所有裂縫的幾何形狀中心做計算，並且裂縫的幾何位置亦會影響M-積分。 此外，三維的有限元素網格遠比二維的複雜，因此有效的試體網格 是本論文研究的重點。關於三維單裂縫和多裂縫問題M-積分的積分區域在定義上有所不同，因此本論文將對三維單裂縫和多裂縫問題所對應的M-積分進行數值分析。 關鍵詞：M-積分、有限元素法、與積分曲面無關、原點無關、幾何形狀中心 The M-integral is the one of major parameter for the fracture behavior. In this paper, a numerical procedure, incorporated with the finite element method, is developed for calculation of the 3D linear elastic solid is subjected to mixed-mode load with 3D cracks. First, verify M-integral for the arbitrary shaped cracks in 2D problem and the arbitrary shaped cracks in 3D problem. Second, verify the property of surface independent. In the 3D single crack problem, M-integral computation result can verify the property of surface independent and origin independent. In the 3D multiple cracks problem, M-integral computation result is associated with geometric center, and cracks geometric position influence computation result. Furthermore, 3D FEM mesh is more complicated than 2D FEM mesh, so testing a good and useful mesh is also important in this research. The definition of integral region is different between the single crack and multiple cracks in 3D, and therefore calculate M-integral for the single crack problem and multiple cracks problem in this research. Keywords : M-integral, finite element method, surface independent, origin independent, geometric center
