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Mathematics of Microstructure in Origami, Robotics, and Electrochemistry

折纸、机器人和电化学中的微观结构数学

基本信息

批准号：
2108784
负责人：
Irene Fonseca
金额：
$ 58.24万
依托单位：
Carnegie-Mellon University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2108784&HistoricalAwards=false
关键词：
Mathematics Microstructure Origami Robotics Electrochemistry

项目摘要

This project will focus on fundamental mathematical research to provide a better understanding of the behavior of materials that compose batteries, and materials for use in the next-generation of robots. This fundamental understanding will be translated into new computer methods for accurately predicting the behavior of such materials. Together, the fundamental understanding and predictive methods will enable the systematic design of new materials with much better properties than currently available, as well as being faster and less expensive than current trial-and-error laboratory experiments. The new materials can enable new technologies, with significant societal and economic benefits to the US. Training of students and outreach activities will be integrated with the research program.The scientific goal of this project is to use variational techniques to characterize the response of materials and structures due to microstructure in models of batteries and robotics materials. While the scope is broad in terms of application to engineering and science, the research is mathematically unified through the framework of the calculus of variations. In analyzing fracture within batteries, the project will integrate disparate bodies of knowledge on fluid-fluid and solid-solid phase transitions, and electrochemistry with fracture mechanics. With regards to soft robotics, the project will consider a phase-field model for micromagnetics which incorporates microstructure and long-range electric/magnetic interactions, as arising from Maxwell's equations.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.

该项目将专注于基础数学研究，以更好地了解组成电池的材料的行为，以及用于下一代机器人的材料。这种基本的理解将被转化为新的计算机方法，用于准确预测这种材料的行为。总之，基本的理解和预测方法将使新材料的系统设计具有比目前更好的性能，以及比目前的试错实验室实验更快，更便宜。新材料可以实现新技术，为美国带来重大的社会和经济效益。该项目的科学目标是利用变分技术来表征电池和机器人材料模型中的微观结构对材料和结构的响应。虽然在工程和科学应用方面的范围很广，但通过变分法的框架，研究在数学上是统一的。在分析电池内的断裂时，该项目将整合流体-流体和固-固相变以及电化学与断裂力学的不同知识体系。关于软机器人，该项目将考虑微磁学的相场模型，该模型结合了微观结构和远程电/磁相互作用，如麦克斯韦方程所产生的。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。