Basic Equations and Relations of Magnetoelasticity of Magnetoactive Deformable Bodies

In this chapter, based on the basic coupled nonlinear equations and relations of mechanics and quasi-static electrodynamics of a continuous medium, by linearization, a system of magnetoelasticity equations, surface conditions and constitutive equations are obtained that describe the behavior of perturbations in a magnetically active (both soft ferromagnetic or superconducting, and magnetostrictive) medium interacting with an external magnetic field. The presentation is given in curvilinear coordinates with the use of tensor analysis and the Lagrange method for describing the motion of a continuous medium. We also note that in this chapter, when presenting the well-known basis of the theory of magnetoelasticity of magnetoactive bodies, the methods of presentation from the monograph Bagdasaryan G.Y., Mikilyan M.A. Effects of Magnetoelastic Interactions in Conductive Plates and Shells. Springer, 2016 are widely used.