On symmetry properties of the total stress tensor for electromagnetic deformable solids

What is it about?

As a generalization of the symmetry of the stress tensor of continuum mechanics, the paper investigates symmetry properties arising in models of magneto- and electro-mechanical interaction. First the balance of angular momentum is considered thus obtaining a symmetry condition that is applied as a mathematical constraint on the admissible constitutive equations. Next the restrictions imposed by the Second Law of Thermodynamics are investigated and, among others, a further symmetry condition is determined. The joint validity of the two symmetry conditions implies that the dependence on the electromagnetic fields has to be through two classes of variables involving the deformation gradients that prove to be Euclidean invariants. The simplest selection of the variables is just that of the Lagrangian fields of the literature. Furthermore, we observe that the variables of a class allow a positive magnetostriction, the other one a negative magnetostriction. Some applications to (NO) Fe-Si are outlined.

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Why is it important?

For the first time it is shown that the choice of different classes of variables (Euclidean invariants) can lead to magneto- or electro-striction phenomena with different signs. No recourse is made to the splitting of the stress tensor as the sum of the mechanical stress and the magnetic (Maxwell) stress. This avoids non-uniqueness problems and questions about the appropriate form of the total stress.

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