平面准晶中的路径守恒积分及其应用

Path Independent Integral and Its Application in Plane Quasicrystals

目的建立平面准晶中能量型路径守恒积分及其对偶形式，并确定准晶裂纹体裂尖应力奇异性阶数．方法建立过程中利用了平面准晶弹性理论的基本控制方程和高斯定理．结果与结论给出了平面准晶体在静态、动态和运动裂纹情形时的路径守恒积分及其对偶形式，给出了守恒性证明，得到准晶裂纹体裂尖应力具有－１／２奇异性。

Aim To establish the path independent integral and its dual form of energy type, and to determine the singularity order of stresses near the crack tip in plane quasicrystals. Methods The basic governing equations of plane quasicrystals and Gauss's theorem were applied in the establishment. Results and Conclusion The path independent integral and its dual form for the static, dynamic and moving cracks were obtained and their path independence was proved. By the given path independent integral, the conclusion that near the tip of crack in plane quasicrystals the stress singularity with the order of -1/2, which is correspondent to the analytic solution, was drawn.