Electromagneto-Thermomechanics: Theory and Numerical Implementation

Electromagnetically coupled interactions underpin numerous technologies in transportation, manufacturing, and defense, enabling actuation, temperature control, and shape manipulation. Applications such as magnetic levitation trains, eddy current braking systems, magnetic induction heating, electromagnetic launchers, and electromagnetic metal forming rely on these interactions for performance and efficiency. Despite their widespread importance, a comprehensive theoretical framework capable of capturing the highly coupled interactions among electric currents, magnetic fields, thermal effects, material motion, and large elastic-plastic deformations does not yet exist. This research aims to develop such a framework, providing predictive capabilities essential for advanced engineering applications. Two national-priority areas exemplify the significance of this work. In nuclear fusion, tokamak reactors require metallic components that withstand extreme magnetic and thermal loads, presenting unique structural challenges. In advanced manufacturing, electromagnetic forming offers reduced material waste, but predicting final part geometry remains an intricate problem. This project will establish a unified, fully coupled design and analysis approach to improve reliability, efficiency, and performance, while simultaneously training graduate students in the interdisciplinary integration of electromagnetism, solid mechanics, and numerical simulation. The project will formulate a fully coupled electromagneto-thermomechanical theory for conductive solids, incorporating (i) eddy-current electromagnetism, (ii) large-deformation, high-rate thermo-visco-plasticity of metals, and (iii) heat transport with contributions from both Joule heating and plastic dissipation. Numerical implementation will be performed in the open-source finite-element platform FEniCSx, enabling rigorous simulation studies. Initial simulations will validate the theory against experimental results from the literature, while subsequent studies will examine the interplay of electromagnetic, thermal, and mechanical phenomena in electromagnetic forming and tokamak structural components. The outcomes will provide mechanistic insight, predictive capability, and practical guidance for the design of advanced electromagnetic systems. Developed simulation tools will be openly shared with the research community, fostering broader adoption and supporting workforce development in computational mechanics, materials science, and applied electromagnetism. 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. NSF Award ID: 2550218 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Eric Stewart | Institution: University of Cincinnati Main Campus, CINCINNATI, OH | Award Amount: $337,949 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2550218 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2550218.html