Tuesday, 12 October 2004 - 3:55 PM

This presentation is part of : Rajagopal Symposium

Electrodynamics and Thermomechanics of Material Bodies

Roger L. Fosdick, University of Minnesota, University of Minnesota, Minneapolis, MN 55455

This talk begins with a brief review of classical electrodynamics for a given aether frame, including certain invariance properties of Maxwell's equations under Euclidean changes of frame. We then postulate, in the given aether frame, a balance of energy and a Clausius-Duhem inequality for the parts of a material body. The form-invariance of these fundamental postulates under Galilean changes of frame is taken as axiomatic and the consequences are discussed. We then report a theorem which gives a necessary and sufficient condition for the balance of energy and the Clausius-Duhem inequality to be form-invariant under more general Euclidean changes of frame from the aether frame. We then consider electromagnetic-thermomechanical processes, defined for the body and its environment, and investigate the notion of isolated processes when the environment consists of the vacuum and several fixed, charged, rigid conductors. In this case, a Lyapunov function is identified and we use this function to motivate the form of the functional that one might minimize in order to obtain possible equilibrium states within the purely static setting of thermo-electrostatics for elastic, electromagnetic materials.

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