Chen Lin, de Borst René
Department of Civil and Structural Engineering University of Sheffield Sheffield UK.
Int J Numer Anal Methods Geomech. 2019 Feb 10;43(2):625-640. doi: 10.1002/nag.2882. Epub 2018 Nov 25.
Powell-Sabin B-splines, which are based on triangles, are employed to model cohesive crack propagation without a predefined interface. The method removes limitations that adhere to isogeometric analysis regarding discrete crack analysis. Isogeometric analysis requires that the initial mesh be aligned a priori with the final crack path to a certain extent. These restrictions are partly related to the fact that in isogeometric analysis, the crack is introduced in the parameter domain by meshline insertions. Herein, the crack is introduced directly in the physical domain. Because of the use of triangles, remeshing and tracking the real crack path in the physical domain is relatively standard. The method can be implemented in existing finite element programmes in a straightforward manner through the use of Bézier extraction. The accuracy of the approach to model free crack propagation is demonstrated by several numerical examples, including discrete crack modelling in an L-shaped beam and the Nooru-Mohamed tension-shear test.
基于三角形的鲍威尔 - 萨宾B样条被用于在没有预定义界面的情况下对粘结裂纹扩展进行建模。该方法消除了等几何分析在离散裂纹分析方面的局限性。等几何分析要求初始网格在一定程度上先验地与最终裂纹路径对齐。这些限制部分与以下事实有关：在等几何分析中，裂纹是通过网格线插入在参数域中引入的。在此，裂纹是直接在物理域中引入的。由于使用了三角形，在物理域中重新划分网格并跟踪实际裂纹路径相对较为规范。该方法可以通过使用贝塞尔提取以直接的方式在现有的有限元程序中实现。通过几个数值例子证明了该方法对自由裂纹扩展建模的准确性，包括L形梁中的离散裂纹建模和努鲁 - 穆罕默德拉伸 - 剪切试验。
