含孔洞弹性材料裂纹的应力分析
On stress analysis for cracks in elastic materials with voids
摘要：
本文研究了一类特殊多孔弹性材料中位错裂纹的经典问题，用Cowin-Nunziato模型描述。本文提出了一种将裂纹应力集中问题化为积分方程的方法。通过傅立叶积分变换，问题被减少到一些积分方程。对于平面应变问题，我们直接数值处理的超奇异积分方程。在轴对称情况下，对于硬币形裂纹，问题归结为第二类正则Fredholm积分方程。在这两种情况下，我们研究应力集中系数，并研究其行为与材料的孔隙率。更特别的是，在相同条件下，与由骨架材料制成的经典弹性介质相比，具有空隙的介质中的应力集中系数总是更高。此外，可以看出，对于较大的裂纹，孔隙度的影响变得更加显著;从物理的角度来看，这也是非常自然的。
英文摘要：
The paper deals with classical problem for cracks dislocated in a certain very specific porous elastic material, described by a Cowin-Nunziato model. We propose a method based upon a reducing of stress concentration problem for cracks to some integral equations. By applying Fourier integral transforms the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. In the axially symmetric case, for the penny-shaped crack, the problem is reduced to a regular Fredholm integral equation of the second kind. In the both cases we study stress-concentration factor, and investigate its behavior versus porosity of the material. More in particular the stress concentration factor in the medium with voids is always higher, under the same conditions, than in the classical elastic medium made of material of the skeleton. Further, as can be seen, the influence of the porosity becomes more significant for larger cracks; that is also quite natural from a physical point of view.
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