Voronoi‐based peridynamics and cracking analysis with adaptive refinement
Voronoi‐based peridynamics and cracking analysis with adaptive refinement
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DOI：
10.1002/nme.5596
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发表时间：
2017-08
影响因子：
2.9
通讯作者：
X. Gu;Qing Zhang;Xiaozhou Xia
中科院分区：
文献类型：
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作者：
X. Gu;Qing Zhang;Xiaozhou Xia
在数值计算中，最常用的方法是采用恒定层位的均匀离散。然而，与非均匀离散化和变化的视野不同，它不是自适应精化分析和多尺度建模的自然和内在组成部分。此外，它遇到离散困难，分析不规则结构。因此，为了分析非均匀离散和变化层位的问题，并解决由此产生的鬼力和虚假波反射问题，将基于均匀离散的双层位周波理论扩展到基于Voronoi图的非均匀离散，我们称之为基于Voronoi图的周波理论。我们也重新定义了伤害的定义。接下来，介绍了一种基于所提出的基于Voronoi的周波理论的自适应精化分析方法及其数值实现。最后，分别采用传统的基于键的周波方程和基于Voronoi的周波方程对4个基准问题进行了数值模拟。二维准静态弹性变形、二维波传播、二维动态裂纹扩展和Kalthoff-Winkler实验的三维模拟的例子证明了所提出的基于Voronoi的周波理论的效率和有效性。此外，自适应细化分析可以用来获得合理的裂纹路径和裂纹扩展速度，减少计算负担。
The most common technique for the numerical implementation of peridynamic theory is the uniform discretization together with constant horizon. However, unlike the nonuniform discretization and varying horizons, it is not a natural and intrinsic component of the adaptive refinement analysis and multiscale modeling. Besides, it encounters discretization difficulty in analyzing irregular structures. Therefore, to analyze problems with nonuniform discretization and varying horizons and solve the resulting problems of ghost forces and spurious wave reflection, the dual‐horizon peridynamics based on uniform discretization is extended to the nonuniform discretization based on Voronoi diagrams, for which we call it Voronoi‐based peridynamics. We redefine the damage definition as well. Next, an adaptive refinement analysis method based on the proposed Voronoi‐based peridynamics and its numerical implementation is introduced. Finally, the traditional bond‐based peridynamics and the Voronoi‐based peridynamics with or without refinement are used to simulate 4 benchmark problems. The examples of 2‐D quasi‐static elastic deformation, 2‐D wave propagation, 2‐D dynamic crack growth, and 3‐D simulation of the Kalthoff‐Winkler experiment demonstrate the efficiency and effectivity of the proposed Voronoi‐based peridynamics. Further, the adaptive refinement analysis can be used to obtain reasonable crack path and crack propagation speed with reduced computational burden.