Ferromagnetism

The theory of the nonlinear elastic Kelvin medium whose particles perform translational and rotational motion, with large displacements and rotations, and may freely rotate about their axes of symmetry, is proposed. The constitutive and dynamic equations are obtained basing upon the fundamental laws of the Eulerian mechanics. The exact analogy is established between the equations for a particular case of Kelvin medium and the equations of elastic ferromagnetic insulators in the approximation of quasimagnetostatics (1998 - 2001) [1 - 3]. It is shown that the existing theories of magnetoelastic materials did not take into account one of the couplings between magnetic and elastic subsystem, which is allowed by fundamental principles. This coupling is important for the description of magnetoacoustic resonance, and may manifest itself in nonlinear theory as well as in the linear one for the case of anisotropic materials.
  1. Grekova E.F., Zhilin P.A. Ferromagnets and Kelvin's Medium: Basic Equations and Magnetoacoustic Resonance // “Nonlinear Oscillations in Mechanical Systems”. Proc. of the XXV-XXIV Summer Schools. Vol. 1. St.-Petersburg, 1998. P. 259-281.
  2. Grekova E.F., Zhilin P.A. Equations for non-linear elastic polar media and analogies: Kelvin medium, non-classical shells, and ferromagnetic insulators // Izvestiya VUZov. Severo-Kavkazskii region. Estestvennye nauki (Transactions of Universities. South of Russia. Natural sciences). Special issue “Nonlinear Problems of Continuum Mechanics”. 2000. P. 24-46. (In Russian.)
  3. Grekova E.F., Zhilin P.A. Basic equations of Kelvin's medium and analogy with ferromagnets // Journal of elasticity. Vol. 64. P. 29-70. (2001).