Abstract
The proof of existence results for the equations describing deformable solid materi als with coupled electromagnetic and elastic effects is complicated by two contradictory technical re quirements.
1. The descriptions of the constitutive equations and elastic effects are best done using a material (Lagrangian) coordinate formulation.
2. Because electromagnetic fields produced by unshielded materials must be described outside of the deformed body (actually on all of space), it is natural to use a spatial (Eulerian) coordinate formulation for these effects.
In order to avoid this problem, many authors have studied only small motions of the material so that material coordinates could be extended to all of space. While this approach has sometimes been successful, it has clear drawbacks in many of the applications suggested for magnetostrictive sensors and actuators.
This article describes technical tools in which material coordinates are used to describe elastic ef fects, spatial coordinates are used to describe magnetic fields, and spatial fields are "pulled back" to material coordinates so that the two can be combined. This will allow us to give existence results in micromagnetics for large deformations. In addition, results on nonattainment of minima and con struction of minimizing sequences are obtained.
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