A continuum theory of deformable ferrimagnetic bodies. I. Field equations

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Abstract
The first part of this work concerns a thorough study of both global and local field equations that govern deformable (not necessarily linear elastic) ferrimagnets and antiferromagnets from a phenomenological viewpoint. The main tool used is a generalized version of d’Alembert’s principle, valid for both reversible and irreversible phenomena, simultaneously with the invariance requirement provided by the so‐called objectivity and applied a priori to generalized internal forces which represent the various interactions. All interactions taking place in such media are thus given a phenomenological description and are introduced via the duality inherent in the method. The development follows a rational and deductive mathematical scheme in which the notion of topological linear space of velocities plays a predominant role, so that particular cases follow by selecting the appropriate member of this space. In the following companion paper the allied thermodynamics and a thorough discussion of the relevant constitutive equations that follow therefrom are given. The formulation so obtained will allow the consideration of slight perturbations superimposed on bias fields.

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