An approach based on distributed dislocations and disclinations for crack problems in couple-stress elasticity
An approach based on distributed dislocations and disclinations for crack problems in couple-stress elasticity
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DOI：
10.1016/j.ijsolstr.2008.05.012
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发表时间：
2008-10
期刊：
影响因子：
--
通讯作者：
P. Gourgiotis;H. Georgiadis
中科院分区：
文献类型：
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作者：
P. Gourgiotis;H. Georgiadis
在经典弹性力学中，分布位错技术被证明是研究裂纹问题的一种有效方法。目前的工作是为了扩展这种技术在研究裂纹问题的偶应力弹性，即在一个理论占微观结构的影响。这种扩展并不明显，因为在分析裂纹问题的理论中涉及到转动和偶应力。在这里，该技术被引入到研究的情况下，模式I裂纹。由于在偶应力弹性中出现的边界条件的性质，裂纹由连续分布的爬位错和约束楔向错（“约束楔向错”的概念首次引入本工作）来模拟。这些分布在物体中产生标准应力和偶应力。特别是，它示出的模式-I的情况下是由一个系统的耦合奇异积分方程与柯西型和对数内核。该系统的数值解表明，裂纹固体受偶应力弹性行为在一个更刚性的方式（具有增加的刚度）相比，由经典弹性固体。此外，在裂纹尖端区域的应力水平是明显高于经典弹性预测。
The technique of distributed dislocations proved to be in the past an effective approach in studying crack problems within classical elasticity. The present work is intended to extend this technique in studying crack problems within couple-stress elasticity, i.e. within a theory accounting for effects of microstructure. This extension is not an obvious one since rotations and couple-stresses are involved in the theory employed to analyze the crack problems. Here, the technique is introduced to study the case of a mode I crack. Due to the nature of the boundary conditions that arise in couple-stress elasticity, the crack is modeled by a continuous distribution of climb dislocations and constrained wedge disclinations (the concept of ‘constrained wedge disclination’ is first introduced in the present work). These distributions create both standard stresses and couple stresses in the body. In particular, it is shown that the mode-I case is governed by a system of coupled singular integral equations with both Cauchy-type and logarithmic kernels. The numerical solution of this system shows that a cracked solid governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a solid governed by classical elasticity. Also, the stress level at the crack-tip region is appreciably higher than the one predicted by classical elasticity.