Eshelby问题中棱上各点位移梯度的跳跃

THE JUMP OF DISPLACEMENT GRADIENT ACROSS THE EDGE IN THE ESHELBY’S PROBLEM

利用调和函数的积分方法,来研究各向同性材料非光滑界面Eshelby问题中,棱上各点位移梯度的跳跃,最终获得棱上各点应力张量的跳跃值.首先讨论Eshelby位移场的连续性,并将棱上各点位移梯度场的连续部分和跳跃部分分离开;再由各向同性的Green函数获得位移梯度场和应力场在核与基体间跳跃的显式表示.最后对应力场在界面上的跳跃进行讨论.

The integral method of harmonic function is employed to study the jump of displacement gradient across the edge in the Eshelby＇s problem. Firstly,the continuity of displacement is discussed and then the displacement gradient field is divided into continuous and discontinuous parts. Secondly, using Green function of isotropic body,the explicit expression of the displacement gradient field and stress field＇s difference between core and foundation can be expressed explicitly. Finally,the jump of stress field across the unsmoothed interface is discussed in detail.