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首页> 外文期刊>International Journal of Engineering Science >Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method
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Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method

机译：扩展扩展有限元/快速行进法求解多个共面裂纹的疲劳裂纹扩展

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摘要

A numerical technique for modeling fatigue crack propagation of multiple coplanar cracks is presented. The proposed method couples the extended finite element method (X-FEM) [Int. J. Numer. Meth. Engng. 48 (11) (2000) 1549] to the fast marching method (FMM) [Level Set Methods & Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press, Cambridge, UK, 1999]. The entire crack geometry, including one or more cracks, is represented by a single signed distance (level set) function. Merging of distinct tracks is handled naturally by the FMM with no collision detection or mesh reconstruction required. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity [Comput. Meth. Appl. Mech. Engng. 139 (1996) 289]. This enables the domain to be modeled by a single fixed finite element mesh with no explicit meshing of the crack surfaces. In an earlier study [Engng. Fract. Mech. 70 (1) (2003) 29], the methodology, algorithm, and implementation for three-dimensional crack propagation of single cracks was introduced. In this paper, simulations for multiple planar cracks are presented, with crack merging and fatigue growth carried out without any user-intervention or remeshing.
机译：提出了一种模拟多个共面裂纹疲劳裂纹扩展的数值技术。所提出的方法与扩展有限元方法（X-FEM）[Int。 J.纽默方法g。 48（11）（2000）1549]转换为快速行进方法（FMM）[水平集方法和快速行进方法：计算几何中不断发展的界面，流体力学，计算机视觉和材料科学，剑桥大学出版社，英国剑桥， 1999]。整个裂纹几何图形（包括一个或多个裂纹）由单个带符号的距离（水平集）函数表示。 FMM自然地处理不同轨道的合并，而无需碰撞检测或网格重建。 FMM结合巴黎裂缝增长法被用来推进裂缝前沿。在X-FEM中，将不连续函数和二维渐近裂纹尖端位移场添加到有限元逼近中，以使用单位分配的概念解决裂纹问题。方法应用机甲g。 139（1996）289]。这样就可以通过单个固定的有限元网格对区域进行建模，而无需对裂纹表面进行明确的网格划分。在较早的研究中[Engng。分形。机甲70（1）（2003）29]，介绍了单裂纹三维裂纹扩展的方法，算法和实现。在本文中，提出了多个平面裂纹的模拟，并且在没有任何用户干预或重新镶嵌的情况下进行了裂纹合并和疲劳增长。

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