各向异性多孔结构的建模方法

The porous structure is very common in nature, and widely used in engineering and design. Modeling of porous structure is the core foundation in functional materials research and development, porous media studies, manufacturing of porous structure with three-dimensional printing and art design of porous structures. However, due to complex shape and topology of porous structure, the geometric modeling of the porous structure is extremely hard, which faces the problems, such as insufficient ability to describe the complex structure, unable to perform control and optimization on high-level on the geometric or mechanical properties of porous and also the resultant large-scale computing. This project will focus on the research and development of high-level modeling method of anisotropic porous structure based on the level set and texture synthesis method, in which the geometry, topology and mechanical properties can be guided and optimized guided by the anisotropic tensor field obtained from interactive design or stress analysis. The research topics include geometric modeling of porous structure based on level set and texture synthesis, design and control of anisotropy tensor field, local control of connectivity in the anisotropic porous structure, qualitative and quantitative description of the porous structure and also the integration and verification of the code system based on the related models and algorithms. The completion of this project will provide an effective modeling approach for porous structure design and satisfy the requirement of generating highly optimized porous structure in various applications.

多孔结构在自然界中极为常见，也广泛使用于设计和工程领域。多孔结构的建模是进行功能材料研发、多孔介质研究、多孔结构三维打印制造及多孔类艺术品设计等的核心问题。但是由于多孔结构的复杂几何和拓扑形态，多孔结构的建模面临模型描述能力不足、难以进行高层次几何或力学特性控制和优化设计及大规模计算等带来的若干瓶颈问题，是国际公认的难度大、探索性强的基础问题。本项目将基于水平集和纹理合成方法，利用交互设计或应力分析引导的各向异性张量场产生含有多孔结构的模型，研究几何、拓扑和力学特性可高层次优化设计的各向异性多孔结构建模方法。主要研究基于水平集和纹理合成的多孔结构几何建模模型，各向异性张量场的设计和控制，多孔结构的局部连通性控制，多孔结构的数学定性定量描述等关键技术，并对相关模型和算法进行系统集成和测试验证。本项目的完成将为多孔结构设计提供有效的建模方法，满足各种应用中对生成高度优化的多孔结构模型的需求。

本项目针对自然界中极为常见且广泛使用于设计和工程领域的多孔结构进行建模。多孔结构的建模是进行功能材料研发、多孔介质研究、多孔结构三维打印制造及多孔类艺术品设计等的核心问题。但是由于多孔结构的复杂几何和拓扑形态，多孔结构的建模面临模型描述能力不足、难以进行高层次几何或力学特性控制和优化设计及大规模计算等带来的若干瓶颈问题，是国际公认的难度大、探索性强的基础问题。本项目提出了一种对曲面进行纹理装饰和三维打印的新方法，一种从小尺寸多孔结构微CT数据三维样本产生一个大尺寸的多孔结构材料的方法，并设计了一种可视化方法分析多孔结构，建立多孔材料进行物理模型，各向异性张量场中Voronoi剖分的计算方法、结构力学性能优化，以及带容限重心Power剖分的高效计算方法研究。本项目为多孔结构设计提供有效的建模方法，满足各种应用中对生成高度优化的多孔结构模型的需求，同时实现了多孔结构几何建模模型，各向异性张量场的设计和控制，多孔结构的局部连通性控制，多孔结构的数学定性定量描述等关键技术，并对相关模型和算法进行系统集成和测试验证，本项目共发表论文7篇，其中7篇sci。

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