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Multifunctional materials and structures possess the ability to perform multiple tasks by combining structural integrity
with sensing and actuating capabilities. Recent progress in the development of such materials/structures
has made concepts like load-bearing antennas or load-bearing batteries feasible and formed new research possibilities.
Load-bearing antenna structures are multifunctional sensing and actuating devices integrated with a
load-bearing structure, i.e. they can simultaneously function as a mechanical structure and an electromagnetic
antenna. Such an antenna structure is subjected to mechanical forces, temperature gradients, and electromagnetic
fields, giving rise to highly-coupled nonlinear thermo-electro-magneto-mechanical (TEMM) behavior. The
current research focuses on modeling and characterizing the nonlinear 3-D coupled behavior of TEMM materials,
consistent with first principles. This theoretical framework is specifically aimed at modeling and analysis of
load-bearing antenna structures.
In this paper we demonstrate the development of analytical techniques and computational tools for multiscale,
multi-physics modeling of load-bearing antenna structures. The mathematical model, based predominantly
on first principles, employs the thermomechanical governing equations coupled with Maxwell's equations. Our
modeling has identified 92 nondimensional numbers which quantify the competition between physical effects in
the operation of load-bearing antenna. A fixed relative ordering of all competing effects determines a regime of
antenna/environment interaction. In this work, we demonstrate a comprehensive framework to derive the 3-D
governing equations for a given regime. For thin geometries, these equations are further reduced to 2-D model,
using series expansion and perturbation techniques. Mathematical modeling of thin electro-magneto-mechanical
plates can have applications like design and optimization of load-bearing antennas structures. This framework
can be extended to model various regimes of behavior of any device/material with coupled electro-magentomechanical
capabilites.
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