Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming and tedious process.In this study, we propose a novel representation method and design approach for porous units that can be infinitely spliced to form a porous structure. We use periodic B-spline functions to represent periodic or symmetric porous units. Starting from a voxel representation of a porous sample, the discrete distance field is computed. To fit the discrete distance field with a periodic B-spline, we introduce the constrained least squares progressive-iterative approximation algorithm, which results in an implicit porous unit. This unit can be subject to optimization to enhance connectivity and utilized for topology optimization, thereby improving the model's stiffness while maintaining periodicity or symmetry. The experimental results demonstrate the potential of the designed complex porous units in enhancing the mechanical performance of the model. Consequently, this study has the potential to incorporate remarkable structures derived from artificial design or nature into the design of high-performing models, showing the promise for biomimetic applications.

翻译：多孔结构是具有众多微小孔隙的复杂固体材料，广泛应用于医学、化学工程和航空航天等领域。然而，使用计算机辅助工具设计此类结构是一项耗时繁琐的过程。本研究提出了一种新型表示方法和设计策略，用于生成可无限拼接形成多孔结构的多孔单元。我们采用周期B样条函数表示周期或对称的多孔单元。基于多孔样本的体素表示，计算其离散距离场。为利用周期B样条拟合离散距离场，我们引入带约束的最小二乘渐进迭代逼近算法，从而获得隐式多孔单元。该单元可进行优化以增强连通性，并用于拓扑优化，从而在保持周期性或对称性的同时提升模型刚度。实验结果表明，所设计的复杂多孔单元在增强模型力学性能方面具有潜力。因此，本研究有望将人工设计或自然界中发现的特殊结构融入高性能模型的设计中，展现出仿生应用的广阔前景。