Griffith界面裂纹散射问题的数学建模

建立两相材料Griffith界面裂纹的弹性波散射问题的数学模型,主要考虑SV波及P波斜入射的情况.利用Fourier积分变换法和适当的界面条件将弹性波散射的边界值问题归结为关于裂纹位错密度函数的Cauchy奇异积分方程组,并给出了详细的推导过程.

The Mathematical Model of Elastic Wave Scattering from the Grifftth Crack

The purpose of this paper is to obtain a simple mathematical model about a Griffith crack located at the interface of two bonded dissimilar elastic half-space. The crack is opend by the interaction of a plane harmonic elastic wave, and incident slantwise on the crack. By using Fourier transform method and applying appropriate interfacial conditions, the boundary value problem of wave scattering is reduced to a vectorial Cauchy singular integrate equation (SIE) for the dislocation density function across the crack faces. The detailed derivation is given.