Kopisz, Małgorzata Coupled fields generated by linear differential operators: Electrodynamics of deformable continua. (English) Zbl 0702.73056 Zastosow. Mat. 20, No. 1, 125-135 (1988). A uniform formalism generating mathematical models of interactions of coupled fields in deformable media is presented. The advantage of the presented method lies in the fact that it can be used regardless of the physical interpretation of the considered coupled fields. The formulation proposed here has its origin in the paper of S. Drobot [ibid. 12, 323-345 (1971; Zbl 0227.73002)], where a method of describing purely mechanical interactions for the statical problem of a deformable Cosserat continuum is given. Interactions of coupled mechanics and electromagnetic fields in deformable media embedded in a four-dimensional space time \(T\times E^ 3\) are described with the aid of some linear differential operators. The Maxwell macroscopic equations have been written in the invariant form. The nonhomogeneous Maxwell equations are interpreted as the equations of equilibrium for the electromagnetic stress tensor. The homogeneous ones have been conveyed to the form of the so-called compatibility equations. In order to interpret the boundary conditions obtained on the basis of the presented method some generalization of the classical stress- principle of Euler-Cauchy has been admitted for the case of local electromagnetic and mechanic interactions in a deformable continuum embedded in space-time. The special cases of piezoelectricity and magnetoelasticity are discussed. MSC: 74F15 Electromagnetic effects in solid mechanics 78A40 Waves and radiation in optics and electromagnetic theory Keywords:four-dimensional space time; linear differential operators; Maxwell macroscopic equations; invariant form; nonhomogeneous Maxwell equations; equations of equilibrium for the electromagnetic stress tensor; compatibility equations; stress-principle of Euler-Cauchy; local electromagnetic and mechanic interactions; piezoelectricity Citations:Zbl 0227.73002 PDFBibTeX XMLCite \textit{M. Kopisz}, Zastosow. Mat. 20, No. 1, 125--135 (1988; Zbl 0702.73056)