包体模型应力集中的定量研究

THE QUANTITATIVE STUDY OF STRESS CONCENTRATION OF THE INCLUSION MODEL

本文采用二维弹性介质圆形包体模型，运用连续介质力学理论求解出包体内外的应力场、位移场、平均应力、最大剪应力以及能量密度的解析解，从而讨论了硬、软包体的应力集中特征：（１）硬包体内能够积累很高的平均应力和最大剪应力，而软包体内无法形成高应力区；（２）硬包体内能量密度的增量率比软包体大；（３）包体内的最大剪应力、平均应力和能量密度的增量率随ｋ的增大而增大；（４）硬、软包体皆能在包体边界以外近区形成应力和能量增量率集中区，而其集中区的大小和位置与边界条件（σ２／σ１）有关；（５）当ｒ／Ｒ增大时，包体产生的应力场和能量分布场皆衰减为无包体时的均匀场，并且与θ有关，形成不均匀场。

In this paper, analytical solutions of stress field, displacement field, average stress, maximum shear stress and energy density inside and outside the inclusion are obtained using round inclusion model of two-demensional elastical medium and continuous medium mechanics, and stress concentration characteristics of hard and soft inclusions are discussed too. The conclusion is that (1) there are higher average stress and maximum shear stress in hard inclusions than in soft ones; (2) there is higher rate of energy density increment in hard inclusion than in soft one; (3) when k increases, the maximum shear stress, the average stress and the rate of energy density increment increase in the hard inclusion; (4) concentrative regions of the stress and the energy density increment rate lie in the region near the boundary of hard inclusion and soft one, and their sizes and locations are related to the boundary condition (σ2/σ1) and (5) when r/R increases, both the stress field and energy distribution produced by inclusion attenuate to a uniform field without inclusion and form a non-uniform field due to the angle θ.