Piezo-electricity represents the most known example of linear coupling among electrical and mechanical quantities in anisotropic solids. In a nonlinear context, the electromechanical coupling may also occur in isotropic solids. This is the case of electro-striction. In the presence of finite deformations, an additional source of coupling may arise. In fact, the electrical quantities that are customarily defined in the current configuration of the body are generally different in the reference configuration. As the referential or Lagrangian description seems to be preferable, whenever the boundary conditions for the electrical quantities are known for the undeformed body, a transformation law from the reference to the current configuration needs to be established for the polarisation, the electric field and the electric displacement. This transformation law is uniquely found by assuming that the electric charge is conserved in all configurations. According to this law the electrical quantities turn out to couple with the deformation gradient. Charge conservation also entails the form-invariance of the Maxwell equations in the various configurations. In contrast, the constitutive relationships fail to be form-invariant. Thus, a constitutive law, which is formally the same in two different configurations, generally describes the behaviour of two different materials.

### Coupling of electrical and mechanical quantities in solids

#### Abstract

Piezo-electricity represents the most known example of linear coupling among electrical and mechanical quantities in anisotropic solids. In a nonlinear context, the electromechanical coupling may also occur in isotropic solids. This is the case of electro-striction. In the presence of finite deformations, an additional source of coupling may arise. In fact, the electrical quantities that are customarily defined in the current configuration of the body are generally different in the reference configuration. As the referential or Lagrangian description seems to be preferable, whenever the boundary conditions for the electrical quantities are known for the undeformed body, a transformation law from the reference to the current configuration needs to be established for the polarisation, the electric field and the electric displacement. This transformation law is uniquely found by assuming that the electric charge is conserved in all configurations. According to this law the electrical quantities turn out to couple with the deformation gradient. Charge conservation also entails the form-invariance of the Maxwell equations in the various configurations. In contrast, the constitutive relationships fail to be form-invariant. Thus, a constitutive law, which is formally the same in two different configurations, generally describes the behaviour of two different materials.
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2004
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11568/87457`
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