Collaborative Research: Optimal Design of Responsive Materials and Structures

合作研究：响应材料和结构的优化设计

• 批准号: 2009289
• 负责人: Kaushik Bhattacharya
• 金额: $ 27.6万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2009289&HistoricalAwards=false
• 关键词: Collaborative; Research; Optimal; Design; Responsive

This project is motivated by the confluence of two technological advances. The first is 3D printing and other novel manufacturing technologies. The second is the development of active materials whose properties can be altered by electrical or magnetic fields and heat. It is now becoming possible to 3D print active materials like shape-memory alloys and liquid crystal elastomers. This paves the way for responsive structures whose shape can be controlled by external stimuli. Further, combining them with structural materials can endow them with functions that are of use for many applications including soft robotics, wearable and prosthetic devices, microfluidics, cleanup of hazardous chemicals, targeted drug delivery, and tissue engineering. However, there is no known way to systematically design such devices. This project will develop a methodology for the systematic design of responsive structures and meta-materials which are complex assemblies of distinct materials and voids, especially optimal design where one seeks the best function at the least cost. These optimal design problems lead to substantial mathematical problems. Conversely, a better mathematical understanding of these problems can lead to new design approaches. By providing robust methodologies for the design and synthesis of responsive structures and meta-materials, this research will have a significant technological impact. It will also provide for the training of two graduate students and several undergraduate researchers. It will generate new opportunities for engaging K-12 students in STEM, and for promoting STEM education amongst underrepresented groups.The investigators will study mathematical questions motivated by the vision of incorporating structural and responsive materials (materials whose response function depends on external stimuli) into integrated functional materials and structures which can change shape and can be combined with structural materials to endow them with function. Such materials include shape-memory alloys, photo-sensitive elastomers, or liquid crystal elastomers with controlled orientation. The design of such structures is challenging. In structural materials, topology optimization combined with additive manufacturing has proven to be an extremely powerful tool, and mathematical analysis played a very important role in making it so. Indeed, the most straightforward formulation is an ill-posed problem in the calculus variations, and this has been addressed using relaxation (for example, the homogenization method) and regularization (for example, perimeter penalization). Naive formulations of optimal design problems using responsive materials are still ill-posed and their relaxation and regularization are open. For example, while optimal design with structural materials typically leads to min-max problems, extension to responsive materials requires maximizing a linear combination of minima. Trajectory optimization, unilateral constraints (due to limits in response), and issues surrounding manufacturability are also of interest. The research will provide a robust mathematical foundation that can form the basis for methodologies for the design and synthesis of integrated functional materials and structures.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.

该项目是由两个技术进步的融合激励的。第一个是3D打印和其他新颖的制造技术。第二个是活性材料的发展，其性能可以通过电场或磁场和热量来改变。现在，3D打印活性材料（例如形状内存合金和液晶弹性体）变得有可能。这为可以通过外部刺激控制的响应式结构铺平了道路。此外，将它们与结构材料结合起来可以赋予它们用于许多应用程序的功能，包括软机器人，可穿戴和假肢设备，微流体，清理有害化学品，有针对性的药物输送和组织工程。但是，没有已知的方法可以系统地设计此类设备。该项目将开发一种用于系统设计的方法，用于响应式结构和元物质，这是不同材料和空隙的复杂组件，尤其是最佳设计，其中人们以最少的成本寻求最佳功能。这些最佳设计问题导致了实质性的数学问题。相反，对这些问题的更好数学理解可以导致新的设计方法。通过为响应式结构和元物质的设计和合成提供强大的方法论，这项研究将产生重大的技术影响。它还将提供两名研究生和几位本科研究人员的培训。它将为使K-12学生吸引STEM，并在代表性不足的群体中促进STEM教育的新机会。研究人员将研究以将结构和响应材料（其响应功能取决于外部刺激依赖外部刺激的材料）合并到可以改变形状的综合功能材料的愿景中，这些材料将结构和响应材料（其响应功能取决于外部刺激）与结构材料结合到结构性材料中，以使其与功能相结合。这样的材料包括形状内存合金，光敏弹性体或具有控制取向的液晶弹性体。这种结构的设计具有挑战性。在结构材料中，拓扑优化与添加剂制造相结合已被证明是一种非常强大的工具，而数学分析在使其如此重要的过程中起着非常重要的作用。实际上，最直接的配方是微积分变化中的一个问题，并且已经使用弛豫（例如，均质化方法）和正则化（例如，周围惩罚）解决了这一点。使用响应材料的最佳设计问题的天真表述仍然不足，其放松和正则化是开放的。例如，虽然具有结构材料的最佳设计通常会导致最小的最大问题，但响应材料的扩展需要最大程度地提高最小值的线性组合。轨迹优化，单方面约束（由于响应的限制）以及围绕生产性问题的问题也引起了人们的关注。这项研究将提供一个强大的数学基础，可以构成整体功能材料和结构设计和综合方法的基础。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛影响的审查标准通过评估来通过评估来支持的。

项目成果

Optimal design of responsive structures

• DOI: 10.1007/s00158-022-03200-5
• 发表时间: 2021-07
• 期刊: Structural and Multidisciplinary Optimization
• 影响因子: 3.9
• 作者: Andrew Akerson;B. Bourdin;K. Bhattacharya

Minimum compliance with obstacle constraints: an active set approach

最低限度遵守障碍物约束：主动集方法

• DOI: 10.1007/s00158-022-03199-9
• 发表时间: 2022
• 期刊: Structural and Multidisciplinary Optimization
• 影响因子: 3.9
• 作者: Tran, Nha Van;Bourdin, Blaise
• 通讯作者: Bourdin, Blaise

Optimal structures for failure resistance under impact

冲击下抗失效的最佳结构

• DOI: 10.1016/j.jmps.2022.105172
• 发表时间: 2023
• 期刊: Journal of the Mechanics and Physics of Solids
• 影响因子: 5.3
• 作者: Akerson, Andrew