平面准晶中的路径守恒积分及其应用

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。

准晶结构的几何特征

在多维空间的基础上,提出了一套构筑准晶空间几何的方法,系统地推导了5,8,10次和12次准晶的空间几何格子和平面几何格子,并拼构出了相应的准晶结构的几何点阵,在准晶多次对称之间,准晶与晶体之间,Penrose拼图与准晶结构几何格子之间建立了联系,运用两种或三种棱长相等、多面角不等的菱面体可以无间隙地按5,8,10,12次对称规律堆满整个欧氏空间,从准晶空间几何格子图形出发,推导出了准晶平面几何格子,进一步拼成准晶结构点阵,在此基础上,讨论了准晶结构几何点阵的基本特点、准晶结构模型与准晶几何点阵之间的内在联系,阐述了准晶体与晶体对称轴之间的关系式(2~k)^(1/2)(k=0,2,4,6,8,10,12)等准晶结构平面点阵的特点。

Anti-Plane Elasticity Problem and Mode Ⅲ Crack Problem of Cubic Quasicrystal

The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.