Collaborative Research: Computational Design of Multi-functional Minimal-Surface Lattice Structures

三重周期极小表面(TPMS)晶格广泛存在于自然界中，在工程应用中具有越来越大的应用前景。它们的几何性质便于通过添加制造技术进行制造，并且它们表现出良好的机械和运输性能。然而，在设计和使用这些格子时，一个突出的挑战是缺乏对循环载荷引起的材料破坏准则的考虑，这对许多潜在的应用是至关重要的。该奖项支持基础研究，以制定新的计算技术，在强度、耐用性、运输和可制造性标准方面有效地设计多功能TPMS格子结构，并允许对部件内的单元单元设计进行调制。这项研究有可能大幅提高轻质最小表面晶格的可行性和应用范围，在医疗保健、福利和能源效率等要求苛刻的应用中，例如具有增强的骨丢失预防的多孔整形植入物，用于膜蒸馏的具有高传质效率的膜蒸馏隔板用于海水淡化和废水处理，以及设计的具有高功率输出和能量存储的电池电极。该奖项还将支持为工业设计本科生、K-12教师和工程学研究生开发探索用最小表面晶格设计人工制品的工程和美学方面的教学模块。为了实现制定有效的计算技术来设计通过加法制造制造的TPMS晶格的目标，该项目将利用最小表面的数学结构和表面微分几何中的工具与拓扑优化技术相结合：1)设计满足强度、渗透性和可制造性要求的厚度分级晶格；2)在晶格设计中融入机械疲劳要求；以及3)调整结构部件内的晶格单元格的设计和取向，以提供更好的性能。此外，还将探索系统地改变组件内单元格的局部几何形状的设计技术。通过金属添加剂制造TPMS晶格以及表面形态分析、成像和机械测试将被进行，以告知制造工艺所规定的晶格设计的几何极限，并验证通过制定的计算技术获得的晶格设计的性能。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Triply periodic minimal-surface (TPMS) lattices are widely present in nature and are finding increasing viability for use in engineering applications. Their geometric properties facilitate fabrication via additive manufacturing techniques, and they exhibit good mechanical and transport properties. However, an outstanding challenge in the design and use of these lattices is the lack of consideration for material failure criteria arising from cyclic loading, which is critical for many potential applications. This award supports fundamental research to formulate novel computational techniques to efficiently design multi-functional TPMS lattice structures with regards to strength, durability, transport, and manufacturability criteria, and to allow for modulation of the unit cell design within the component. This research has the potential to substantially increase the viability and range of applications of lightweight minimal-surface lattices in demanding applications in healthcare, welfare, and energy efficiency, such as porous orthopedic implants with enhanced bone-loss prevention, spacers for membrane distillation with high mass transfer efficiency for desalination and wastewater treatment, and architected battery electrodes with high power output and energy storage. This award will also support the development of teaching modules that explore the engineering and aesthetic aspects of designing artifacts with minimal-surface lattices for undergraduate industrial design students, K-12 teachers, and engineering graduate students.To achieve the goal of formulating efficient computational techniques to design TPMS lattices fabricated via additive manufacturing, this project will exploit the mathematical structure of minimal surfaces and couple tools in the differential geometry of surfaces with topology optimization techniques to: 1) design thickness-graded lattices that satisfy strength, permeability and manufacturability requirements; 2) incorporate mechanical fatigue requirements in the lattice design; and 3) modulate the design and orientation of the lattice unit cell within the structural component to render superior performance. Further, design techniques that systematically vary the local geometry of the unit cell within the component will be explored. Fabrication via metal additive manufacturing of TPMS lattices as well as surface morphological analysis, imaging and mechanical testing will be conducted both to inform geometric limits on the lattice design dictated by the manufacturing process, and to validate the performance of lattice designs obtained with the formulated computational techniques.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.