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.

该项目将着重于基本数学研究，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。这种基本理解将转化为新的计算机方法，以准确预测此类材料的行为。总之，基本的理解和预测方法将使具有比当前可用的更高特性的新材料的系统设计，并且比当前的试用和错误实验室实验更快，更便宜。新材料可以使新技术能够为美国带来巨大的社会和经济利益。对学生和外展活动的培训将与研究计划集成。该项目的科学目标是使用各种技术来表征由于电池和机器人材料模型中的微观结构而引起的材料和结构的响应。尽管该范围在工程和科学的应用方面很广，但该研究通过变异的框架在数学上统一。在分析电池内的断裂时，该项目将与裂缝力学上的流体流体和固体相变和固体相变的知识不同。关于软机器人技术，该项目将考虑一个微型磁性的相位场模型，该模型包含了微观结构和远程/磁相互作用，这是由麦克斯韦方程式引起的。本奖奖反映了NSF的法定任务，并被认为是通过基金会的知识上的智力和更广泛的影响来评估的支持。