Mathematics of Microstructure in Origami, Robotics, and Electrochemistry

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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.