A Mathematical Model for the Magnetoelastic Behavior of Anisotropic Magnetic Sensitive Materials Based on Continuum Theory

Abstract

Magnetoelastic behavior of a magnetic sensitive material has been analyzed theoretically in the present paper. The theory is formulated in the context of continuum electromagnetics. The solid medium is supposed to be made of elastic material with magnetic sensitivity and to be nonlinear, homogeneous, compressible, isothermal, has anisotropy. Magneto-elastic response of the material will show up as a stress and a magnetization field. From the formulation belonging to the constitutive equations, it has been observed that the stress and the magnetization have been derived from a scalar-valued thermodynamic potential defined in calculations. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on Green deformation tensor, magnetic field, and temperature distribution. The free energy function has been represented by a power series expansion and the type and number of terms taken into consideration in this series expansion has determined the non-linearity of the medium. Constitutive equations of symmetric stress, magnetization field and asymmetric stress have been obtained in both material and spatial coordinates. The quasi-linear constitutive equations which on material coordinates have been obtained by expressions (63)-(65). The quasi-linear constitutive equations have been given in expressions (70)-(72) on spatial coordinates. Finally, the quasi-linear constitutive equations of the symmetric stress and magnetization field are substituted in the relevant balance equations to obtain the field equations. The field equations containing the unknowns u(k) and phi coordinates have been obtained by expressions (75) and (76). Solution of these field equations under initial and boundary conditions forms the mathematical structure of specified a boundary value problem.