THE DETERMINATION OF THE ELASTIC FIELD OF AN ELLIPSOIDAL INCLUSION, AND RELATED PROBLEMS
THE DETERMINATION OF THE ELASTIC FIELD OF AN ELLIPSOIDAL INCLUSION, AND RELATED PROBLEMS
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DOI：
10.1098/rspa.1957.0133
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发表时间：
1957-01-01
影响因子：
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通讯作者：
ESHELBY, JD
中科院分区：
文献类型：
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作者：
ESHELBY, JD
假设各向同性弹性固体内的某个区域会经历自发的形状变化，如果周围材料不存在，则该区域将发生某种规定的均匀变形。由于周围材料的存在，该区域的内部和外部都会存在应力。借助于一系列想象的切割、应变和焊接操作，可以非常简单地找到所产生的弹性场。特别地，如果该区域是椭圆体，则其内部的应变是均匀的并且可以用表格椭圆积分来表达。在这种情况下，可以解决进一步的问题。无限介质中的椭球区域具有与材料其余部分不同的弹性常数；这种不均匀性的存在如何干扰远距离施加的均匀应力场？结果表明，要回答几个物理或工程兴趣的问题，只需了解椭球体内部相对简单的弹性场。
It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material stresses will be present both inside and outside the region. The resulting elastic field may be found very simply with the help of a sequence of imaginary cutting, straining and welding operations. In particular, if the region is an ellipsoid the strain inside it is uniform and may be expressed in terms of tabulated elliptic integrals. In this case a further problem may be solved. An ellipsoidal region in an infinite medium has elastic constants different from those of the rest of the material; how does the presence of this inhomogeneity disturb an applied stress-field uniform at large distances? It is shown that to answer several questions of physical or engineering interest it is necessary to know only the relatively simple elastic field inside the ellipsoid.