双I—型裂纹断裂动力学问题的非局部理论解

研究了非局部理论双中I－型裂纹弹性波散射的力学问题，并利用富里叶变换使本问题的求解转换为三重积分方程的求解，进而采用新方法和利用一维非局部积分核代替二维非局部积分核来确定裂纹尖端的应力状态，这种方法就是Schmidt方法，所得结是比艾林根研究断裂静力学问题的结果准确和更加合理，克服了艾林根研究断裂静力学问题时遇到的数学困难，与经典弹性解相比，裂纹尖端不再出现物理意义下不合理的应力奇异性，并能够解释宏观裂纹与微观裂纹的力学问题。

Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory

The scattering of harmonic waves by two collinear symmetric cracks is studied using the non_local theory. A one_dimensional non_local kernel was used to replace a two_dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non_local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.