Extraction of stress intensity factors from Irwin's integral using high‐order XFEM on triangular meshes
Extraction of stress intensity factors from Irwin's integral using high‐order XFEM on triangular meshes
复制标题
DOI：
10.1002/nme.4698
复制
发表时间：
2015-04
影响因子：
2.9
通讯作者：
G. Song;H. Waisman;M. Lan;I. Harari
中科院分区：
文献类型：
--
作者：
G. Song;H. Waisman;M. Lan;I. Harari
本文谨献给Ted Belytscho教授70岁生日。他对断裂力学和扩展有限元法的开创性贡献极大地启发了我们的工作。本文利用高阶扩展有限元（XFEM）公式，扩展了我们最近从Irwin积分中提取应力强度因子（SIFs）的工作。通过将XFEM中的前r项（r为从裂纹尖端到任何其他材料点的距离）与Irwin积分的解析展开相匹配，得到了SIFs的封闭形式解。因此，对XFEM离散系统进行求解可以直接得到SIFs，并在矩形结构网格上得到了准确的SIFs。然而，扩展到非结构化四边形元素可能不是微不足道的。为此，我们将公式推广到三角元，得到了封闭形式表达式的显著简化。此外，该公式直接适用于非结构化网格，无需额外的工作。因此，本文被认为是迈向自动化和将该方法扩展到更一般应用的重要一步。数值结果表明，在一些纯模态和倾斜裂纹基准问题上，在结构化和非结构化网格上，都能得到准确一致的SIFs。还研究了一条裂缝接近一个孔洞和两条裂缝相互接近的例子。后者说明了该方法优于J积分类方法的优点，因为当裂缝接近并且不需要重新网格划分时，仍然可以计算SIFs。因此，潜在地，这种方法可以更严格地解决裂缝合并，分支和接近边界。版权所有©2014 John Wiley & Sons， Ltd。
This paper is dedicated to Professor Ted Belytscho's 70th birthday. His seminal contributions to Fracture Mechanics and the extended finite element method have significantly inspired us in this work. The current paper extends our recent work on the extraction of stress intensity factors (SIFs) from Irwin's integral, using a high‐order extended FEM (XFEM) formulation. By matching leading r terms (r being the distance from the crack tip to any other material point) in XFEM with analytical expansion of Irwin's Integral, a closed‐form solution for SIFs is obtained. Hence, SIFs can directly be obtained upon solution of the XFEM discrete system, which were shown to be accurate on structured rectangular meshes. However, extension to unstructured quadrilateral elements may not be trivial. To this end, we extend the formulation to triangular elements, where significant simplification of the closed‐form expression is obtained. Moreover, the formulation is directly applicable to unstructured meshes without extra work. Hence, this paper is considered a significant step toward automating and extending this method to more general applications. Numerical results show that accurate and consistent SIFs can be obtained on some pure mode and inclined crack benchmark problems, on structured and unstructured meshes. Examples of a crack approaching a hole and two cracks approaching each other are also investigated. The latter illustrates the advantage of this method over a J‐integral class of methods, as SIFs can still be calculated when cracks are in proximity and no remeshing is required. Hence, potentially, this method can address crack coalescence, branching and proximity to boundaries more rigorously. Copyright © 2014 John Wiley & Sons, Ltd.