Consistent immersed volumetric Nitsche methods for composite analysis
Consistent immersed volumetric Nitsche methods for composite analysis
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DOI：
10.1016/j.cma.2021.114042
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发表时间：
2021-11
影响因子：
7.2
通讯作者：
Jiarui Wang;G. Zhou;M. Hillman;A. Madra;Y. Bazilevs;Jing Du;K. Su
中科院分区：
文献类型：
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作者：
Jiarui Wang;G. Zhou;M. Hillman;A. Madra;Y. Bazilevs;Jing Du;K. Su
为复杂的复合材料微结构生成高质量的贴体网格是一项重要的任务。特别是，复合材料的显微CT图像可以包含许多不规则形状的夹杂物。在现有的方法中，浸入边界法，离散机构独立提供了解决这些类型的问题的潜力，因为匹配的离散化是不需要的。然而，这些技术仍然需要明确的参数化的接口，这可能是相当大的数量。为了避免复杂微结构复合材料的贴体网格生成困难，克服表面型方法中存在的问题，本文发展了浸入式体积Nitsche方法。这些方法是使用Nitsche的技术，以执行体积的连续性之间的夹杂物和背景域。结果表明，所提出的弱形式是完全一致的组合问题的强形式。本方法允许C 0近似的前景离散化，和C 1近似的背景。通过解决齐次和非齐次复合基准问题来证明这些方法的有效性，其中表明Nitsche方法的非对称版本在所有设置中都是最稳健的。
Generating quality body-fitting meshes for complex composite microstructures is a non-trivial task. In particular, micro-CT images of composites can contain numerous irregularly-shaped inclusions. Among the methods available, immersed boundary methods that discretize bodies independently provide potential for tackling these types of problems since a matching discretization is not needed. However, these techniques still entail the explicit parameterization of the interfaces, which may be considerable in number. In this work, immersed volumetric Nitsche methods are developed in order to avoid the difficulty of generating body fitting meshes for composite materials with complicated microstructures, and overcome the issues in the surface-type methods. These approaches are developed using Nitsche’s techniques to enforce volumetric continuity between the inclusion and background domains. It is shown that the proposed weak forms are fully consistent with the strong form of the composite problem. The present approach permits C 0 approximations for the foreground discretization, and C 1 approximations for the background. The effectiveness of these methods is demonstrated by solving homogeneous and inhomogeneous composite benchmark problems, where it is shown that the non-symmetric version of Nitsche’s approach is the most robust in all settings.