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利用无限介质中的格林函数,本文首先导出一般形状的夹杂所产生的拘束应力场,夹杂中的无应力应变εij*可以是位置的函数,在此基础上,给出了平面问题的全部计算公式,文中把裂纹或空腔看做是其弹性常数为零的一种特殊的异性夹杂,在物体受到外加应力场的作用时,计算了与椭圆空腔等效的夹杂的无应力应变,对于扁平形状的夹杂,在其端点附近显示出与裂纹完全类似的r-1/2式应力奇点,算出了相应的应力强度因子,对于本文结果的一些应用做了讨论,例如椭圆空腔与外加应力场的交互作用,马氏体转变和形变孪晶所伴随形成的微观裂纹等。Using Green functions in an infinite medium, the constraint stress field of an inclusion with general shape is given. The stress free strains of the inclusion may be functions of position. On this basis, all calculating formulas for plane problems are given. We consider cracks or holes as special inhomogeneities with elastic constants equal to zero. For a body stressed by the applied field, the stress-free strains of the equivalent inclusion have been calculated. For oblate inclusions, near the end of major axis of ellipse, the stress field exhibits a r-1/2 stress singularity similar to that of a crack. Some applications, including the interaction of a hole with the applied field, micro-crack nucleation due to martensite plates and deformation twins, are discussed.
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