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I. Introduction

In this paper we consider the finite deformation of a magnetized and/or polarized elastic body, placed in an electro-magnetic field. We shall be concerned with the general dynamic problem, in which the body may be magnetically saturated or non-saturated, and may conduct currents. But we shall confine our considerations to the non-relativistic case, i.e. we assume the velocities to be small with respect to the velocity of light. In our theory we aim at a unification of electro-magnetic theory and continuum mechanics: we shall derive the force distribution of electro-magnetic origin and the influence of the deformation of the body on the field. The literature on the interactions of electric and/or magnetic fields with elastic media is extensive. Toupin, in a pioneering contribution [IJ has given an investigation of the interaction of an electrostatic field with a perfectly elastic dielectric. In a subsequent paper [2J he extended his results to include the effects of motion. For the magnetic case Tiersten [3J, [4J has developed a similar theory for the deformation of magnetically

saturated insulators. Brown, in his important monograph on magneto-elastic interactions [5J, has given a careful investigation of the behaviour of saturated, non-dissipative and non-conductive materials, mainly under static external loading. In his book he criticizes the papers by Toupin and Tiersten. His objections especially concern the electro-magnetic foundations of these papers. Brown himself bases his theory on the model of the dipolar, magnetic continuum. In a book by Akhieser, Bar'yakhtar and Pe1etminskii [6J, devoted to the theory of spin waves, but also containing a chapter on magneto-elastic interactions, more general aspects, e.g. magnetic dissipation and conductivity are taken into account. Both monographs [5J and [6J give J. L. Zeman et al. (eds.), Topics in Applied Continuum Mechanics © Springer-Verlag Wien 1974

72 some interesting applications. The book [6J also contains a good introduction to the physics of magnetic materials. Alblas has considered the magnetized body as a Cooserat-Continuum [7J and he developed this model for a more general class of problems [8J. The theory of [7J and [8J are generalized and extended in a subsequent paper [9J. Other references with respect to the literature may be found in [5J and [6J. A typical imperfection of the literature mentioned above is that the electro-magnetic foundations are not unambiguous. The only exception is the book by Brown [5J, but this book is limited to the magneto-static case. For instance

it is not at all obvious what has to be taken for the electric or

magnetic field intensity or the electro-magnetic energy. The origin of the difficulties may be found in the lack of knowledge of the electrodynamics of moving media. In contrast to electrodynamic theory of vacuum, the subject of moving media always has been controversial. In this paper

we shall found our considerations on Chu's new formula-

tion of electro-magnetism [IOJ. The basis of Chu's theo