A generalized variational model of magneto-thermo- elasticity for nonlinearly magnetized ferroelastic bodies

Based on a generalized variational principle of total energy functional, this paper presents a theoretical model to describe the magneto-thermo-elastic interaction of soft ferroelastic bodies with nonlinear magnetization under stationary thermal and magnetic fields. The energy functional of the magneto-thermo-elastic system is established by the summation of energy of sub-systems of nonlinearly magnetized magnetic field, thermal field, and mechanical deformation. By means of the manipulation of the mixed variational principle with independent variations of magnetic scalar potential, displacement vector, and temperature, all governing equations, which are nonlinear and coupling among magnetic, elastic and thermal fields, together with the expressions of magnetic forces are obtained from the variational approach. In order to valuate the obtained model, some existing models of the magneto-elasticity and the thermo-elasticity, which are validly demonstrated in literature, as special cases of the problem considered here are deduced out from the general case. Finally, an analytical analysis of magneto-thermo-elastic instability is conducted to a simply supported ferromagnetic rectangular thin plate under both a uniform distribution of temperature and a uniform transverse magnetic field by means of the linearized theory and the perturbation technique.