On the electrostriction effect in finitely deformable dielectrics

What is it about?

The paper investigates models of electrostriction in electro-active solid materials subject to finite deformations. By following a new approach though within the basic laws of continuum mechanics, we show that the balance of angular momentum implies a symmetry condition for the Cauchy stress tensor, the electric field and the electric polarization. By checking the thermodynamic consistency it is observed that the symmetry condition holds for variables involving jointly the deformation gradient and the electric field or the polarization. This scheme in turn is found to satisfy both the thermodynamic consistency and the objectivity principle. Finally electrostriction is examined in a one-dimensional setting by determining the deformation of an isotropic electro-elastic solid induced by an electric field.

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Why is it important?

The symmetry condition arising from the balance of angular momentum naturally shows that the stress is induced by both deformation and the electric and polarization fields, without resorting to the arbitrary addition of the so-called Maxwell tensor. Furthermore, it is shown that a proper dependence on (Euclidean) invariant forms of polarization or electric field field results in elongations or contractions of the sample, just as it is observed in real materials (see Table 1).

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