Poisson Voronoi (PV) tessellations as artificial microstructures are widely used in investigations of material deformation behaviors. However, a PV structure usually describes a relative homogeneous field. This work presents a simple numerical method for generating 2D/3D artificial microstructures based on hierarchical PV tessellations. If grains/particles of a phase cover a large size span, the concept of “artificial phases” can be used to create a more realistic size distribution. From case to case, detailed microstructural features cannot be directly achieved by commercial or free softwares, but they are necessary for a deep or thorough study of the material deformation behavior. PV tessellations created in our process can fulfill individual requirements from material designs. Another reason to use PV tessellations is due to the limited experimental data. Concerning the application of PV microstructures, four examples are given. The FE models and results will be presented in consecutive works, i.e. “part II: applications”.

中文翻译：

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一种应用于微机械有限元模拟的分层 Poisson Voronoi 微结构生成数值方法——第一部分：方法

Poisson Voronoi (PV) 镶嵌作为人工微结构被广泛用于材料变形行为的研究。然而，PV 结构通常描述一个相对均匀的场。这项工作提出了一种基于分层 PV 镶嵌生成 2D/3D 人工微结构的简单数值方法。如果一个相的晶粒/颗粒覆盖大尺寸跨度，则可以使用“人造相”的概念来创建更真实的尺寸分布。从案例到案例，详细的微观结构特征无法通过商业或免费软件直接实现，但它们对于深入或彻底研究材料变形行为是必要的。在我们的过程中创建的 PV 镶嵌可以满足材料设计的个性化要求。使用 PV 镶嵌的另一个原因是由于实验数据有限。关于光伏微结构的应用，给出了四个例子。有限元模型和结果将在后续作品中呈现，即“第二部分：应用程序”。