Mathematics of Microstructure in Origami, Robotics, and Electrochemistry

该项目将专注于基础数学研究，以更好地理解构成电池的材料的行为，以及下一代机器人使用的材料。这一基本认识将转化为新的计算机方法，用于准确预测这类材料的行为。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可用的更好的性能，以及比目前的试错实验室实验更快和更便宜。新材料可以实现新技术，对美国具有重大的社会和经济效益。学生培训和外展活动将与研究计划相结合。该项目的科学目标是使用变分技术来表征电池和机器人材料模型中微观结构对材料和结构的响应。虽然在工程和科学方面的应用范围很广，但通过变分的框架，研究在数学上是统一的。在分析电池内部的断裂时，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。

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.