Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity
Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity
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DOI：
10.1016/j.ijengsci.2005.01.006
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发表时间：
2005-09-01
影响因子：
6.6
通讯作者：
Maugin, GA
中科院分区：
文献类型：
--
作者：
Lazar, M;Maugin, GA
本文的目的是在Mindlin梯度弹性框架下研究位错和位错的弹性应力场和应变场。我们考虑具有一种材料长度(梯度系数)的Mindlin第一梯度弹性的简单但严格的形式。利用应力函数方法，我们得到了各向同性无限伸展介质中所有六种类型的Volterra缺陷(位错和位错)的修正应力函数。利用这些应力函数，我们得到了位错和位错的应力场和应变场的精确解析解。弹性应变和应力的这些解的一个优点是它们在缺陷线上没有奇点。它们是有限的，在缺陷核心区有极大值或极小值。在缺陷线上，应力和应变要么为零，要么具有有限的最大值。当可能发生断裂和破坏时，应力的最大值可以作为临界应力水平的量度。因此，在这样一个简单的梯度理论中，应力和弹性应变奇点都被消除了。此外，对于非奇异应力，我们还给出了非局部埃林根弹性中非局部应力的关系式。(C)2005爱思唯尔有限公司。保留所有权利。
The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity. We consider simple but rigorous versions of Mindlin's first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislocations and disclinations) situated in an isotropic and infinitely extended medium. By means of these stress functions, we obtain exact analytical solutions for the stress and strain fields of dislocations and disclinations. An advantage of these solutions for the elastic strain and stress is that they have no singularities at the defect line. They are finite and have maxima or minima in the defect core region. The stresses and strains are either zero or have a finite maximum value at the defect line. The maximum value of stresses may serve as a measure of the critical stress level when fracture and failure may occur. Thus, both the stress and elastic strain singularities are removed in such a simple gradient theory. In addition, we give the relation to the nonlocal stresses in Eringen's nonlocal elasticity for the nonsingular stresses. (c) 2005 Elsevier Ltd. All rights reserved.