On the modeling of magneto-mechanical effects (magnetostriction, Villari effect, etc.) in solids

What is it about?

The paper develops a macroscopic approach to magnetostriction consistent with continuum thermodynamics. This is performed by following two different procedures depending on whether a three-dimensional or a one-dimensional setting is considered. In the three-dimensional case constitutive equations involve Euclidean invariant variables that 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. Based on the relations established through the thermodynamic consistency, a detailed set of constitutive equations are set up so as to fit the experimental data from a one-dimensional sample under tensile stresses and magnetic fields.

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Why is it important?

The results established here show a threefold interest. First,they constitute an explicit mathematical model of magnetostriction in terms of elementary functions. Secondly, from the conceptual side, for a spatial description the dependence on the magnetic field H and the deformation F has to be in a joint form. Thirdly, in a one-dimensional setting, the the magnetization M depends on the product f(S)k(H), thus taking into account for the non-monotonic behavior with respect to the stress S. Remarkably, this model fits the cross-coupling behavior expressed by experimental data.

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