On the modeling of magneto-mechanical effects in solids

The paper develops a thermodynamically-consistent approach to magnetostriction. This is performed by following two different approaches depending on whether a three-dimensional or a one-dimensional setting is considered. In the three-dimensional case the symmetry condition required by the balance of angular momentum results in the need of appropriate variables in the constitutive equations. These variables prove to be Euclidean invariant and comprise the so-called Lagrangian fields usually adopted in the literature. The consequences of the second law of thermodynamics are then determined for a solid described by the temperature, the deformation gradient, and the magnetic field. With this background the magnetostriction is modelled for linear or nonlinear magnetic laws. Next a one-dimensional setting is addressed mainly in connection with available experimental data. The symmetry condition becomes ineffective and hence the classical Eulerian fields are used. Based on the relations established through the thermodynamic consistency a detailed set of constitutive equations, for magnetization and strain, is established. These equations are set up so as to fit the experimental data from a one-dimensional sample under tensile stresses and magnetic fields.