Deformable Magnetically Saturated Media. I. Field Equations

In this article we propose a variational approach to the study of nonlinear elastic solids in which magnetization is constant in magnitude. The emphasis is placed upon the application of the different invariances used in modern continuum mechanics: Euclidean invariance, objectivity, and material symmetry. In Part I, a variational treatment is given in the spirit of ``oriented media theory.'' A comparison is made with the results of a direct treatment starting with the postulation of balance laws. Part II is devoted to the development of constitutive equations for a variety of material classes.