FINITE ANTI-PLANE SHEAR FIELD NEAR TIP OF A CRACK FOR A CLASS OF INCOMPRESSIBLE ELASTIC SOLIDS
FINITE ANTI-PLANE SHEAR FIELD NEAR TIP OF A CRACK FOR A CLASS OF INCOMPRESSIBLE ELASTIC SOLIDS
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DOI：
10.1007/bf00017296
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发表时间：
1977-01-01
影响因子：
2.5
通讯作者：
KNOWLES, JK
中科院分区：
文献类型：
--
作者：
KNOWLES, JK
本文涉及包含裂纹并在无限远处变形至有限简单剪切状态的无限板。板的材料被认为是均匀的、各向同性的、弹性的和不可压缩的，并且进一步被假定属于允许非平凡反平面剪切状态的一类材料。针对有限弹性的全非线性平衡理论进行了分析。详细研究了裂纹尖端附近的应力场；所考虑的特殊材料之一是，尽管存在无界位移梯度，但裂纹尖端附近的剪应力仍保持有界。指出并讨论了有限反平面剪切中的裂纹问题与气体通过平板的跨音速流动问题之间的类比。
The present paper is concerned with an infinite slab containing a crack and deformed at infinity to a state of finite simple shear. The material of the slab is taken to be homogeneous, isotropic, elastic, and incompressible, and is further assumed to belong to a class of materials which admit nontrivial states of anti-plane shear. The analysis is carried out for the fully nonlinear equilibrium theory of finite elasticity. The stress field near the crack-tips is studied in detail; one of the special materials considered is such that the shear stresses near a crack tip remain bounded, despite the presence of unbounded displacement gradients. An analogy between the crack problem in finite anti-plane shear and the problem of transonic flow of a gas past a flat plate is pointed out and discussed.