Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling
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DOI：
10.1002/nme.3063
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发表时间：
2011-04
影响因子：
2.9
通讯作者：
X. Zhuang;C. Augarde;S. Bordas
中科院分区：
文献类型：
--
作者：
X. Zhuang;C. Augarde;S. Bordas
使用数值方法进行断裂建模在二维情况下借助扩展有限元法（XFEM）等技术已经相当先进。无网格方法在这些问题上的应用有些滞后，但无网格（特别是在三维情况下）的潜在优势促使人们继续对其发展进行研究。在不明确对裂纹面进行建模（例如不作为单元的边）的方法中，采用两种方法将位移跳跃与裂纹表面相关联：可见性准则和衍射方法。可见性准则易于实施且计算高效，特别是在水平集坐标的帮助下。然而，据报道使用可见性准则在裂纹尖端周围会出现虚假的不连续性，而在三维中实施衍射方法比可见性准则要复杂得多。在本文中，提出了一种绑定方法来消除可见性准则的困难，从而在保留可见性准则优点的同时确保裂纹尖端闭合。该公式基于水平集坐标和无单元伽辽金方法的使用，通常适用于二维或三维的单裂纹或多裂纹问题。本文解释了该公式，并针对一些二维裂纹问题对该方法进行了验证。版权所有©2011约翰威立父子有限公司
Fracture modelling using numerical methods is well‐advanced in 2D using techniques such as the extended finite element method (XFEM). The use of meshless methods for these problems lags somewhat behind, but the potential benefits of no meshing (particularly in 3D) prompt continued research into their development. In methods where the crack face is not explicitly modelled (as the edge of an element for instance), two procedures are instead used to associate the displacement jump with the crack surface: the visibility criterion and the diffraction method. The visibility criterion is simple to implement and efficient to compute, especially with the help of level set coordinates. However, spurious discontinuities have been reported around crack tips using the visibility criterion, whereas implementing the diffraction method in 3D is much more complicated than the visibility criterion. In this paper, a tying procedure is proposed to remove the difficulty with the visibility criterion so that crack tip closure can be ensured while the advantages of the visibility criterion can be preserved. The formulation is based on the use of level set coordinates and the element‐free Galerkin method, and is generally applicable for single or multiple crack problems in 2D or 3D. The paper explains the formulation and provides verification of the method against a number of 2D crack problems. Copyright © 2011 John Wiley & Sons, Ltd.