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

三周期最小表面（TPMS）晶格广泛存在于自然界中，并且在工程应用中越来越具有可行性。它们的几何特性有利于通过增材制造技术进行制造，并且它们具有良好的机械和传输特性。然而，在这些网格的设计和使用中，一个突出的挑战是缺乏对循环载荷引起的材料失效标准的考虑，这对许多潜在的应用至关重要。该奖项支持基础研究，以制定新的计算技术，有效地设计多功能TPMS晶格结构，考虑强度、耐久性、运输和可制造性标准，并允许组件内的单元格设计调制。这项研究有可能大大提高轻质最小表面晶格在医疗保健、福利和能源效率方面的可行性和应用范围，例如具有增强骨质流失预防功能的多孔骨科植入物，用于脱盐和废水处理的具有高传质效率的膜蒸馏隔膜，以及具有高功率输出和能量存储的结构电池电极。该奖项还将支持教学模块的开发，这些模块将为工业设计本科学生、K-12教师和工程研究生探索设计具有最小表面网格的人工制品的工程和美学方面。为了实现制定有效的计算技术来设计通过增材制造制造的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耦合工具与拓扑优化技术：1)设计满足强度，渗透率和可制造性要求的厚度梯度晶格；2)在点阵设计中纳入机械疲劳要求；3)调整结构部件内晶格单元的设计和方向，以提供优越的性能。此外，设计技术，系统地改变局部几何单元内的组件将被探索。通过金属增材制造制造TPMS晶格以及表面形态分析，成像和机械测试将进行，以通知由制造过程决定的晶格设计的几何限制，并验证通过公式计算技术获得的晶格设计的性能。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.