General Expressions for the Description of the Influence of Stresses on Dielectric Permittivity or Magnetic Permeability
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GENERAL EXPRESSIONS FOR THE DESCRIPTION OF THE INFLUENCE OF STRESSES ON DIELECTRIC PERMITTIVITY OR MAGNETIC PERMEABILITY I. B. Prokopovych
UDC 539.30
We construct general expressions for the description of the influence of initial stresses on the dielectric permittivity and magnetic permeability of materials capable of taking into account various nonlinear effects and the phenomena of inherent or induced anisotropy. It is shown that the indicated influence is proportional to the tensor modulus of striction of the material and depends on the piezoeffect modulus. However, the last dependence is insignificant if the inverse piezoeffect is comparable with striction.
The effect of initial stresses on the changes in the electromagnetic state (EMS) of a body (as a rule, on wave perturbations) serves as a basis for the optical and magnetic nondestructive monitoring of stresses. Effects of this sort are also applied in fiber optics to preserve the polarization of light signals (in fibers with induced distributions of residual stresses nonaxisymmetric in the cross section). Therefore, the theoretical investigation of the influence of the stress-strain state (SSS) on the variations of the EMS (in particular, to reveal its relationship with other effects in anisotropic materials) is of high importance for the contemporary mechanics of deformable media. In the theoretical and experimental studies of the influence of stresses on the behavior of the EMS, the most important applied role is played by the expressions reflecting the influence of stresses on linear perturbations of the EMS, i.e., δ d = ε ⋅ δe, where δ d and δ e are, respectively, the increments of induction and intensity and the second-rank tensor ε is either dielectric permittivity or magnetic permeability (for definiteness, we use the conventional notation for the electric parameters of state). Thus, the influence of stresses on the linear perturbations of the EMS can be regarded as their influence on permittivity. The theoretical investigation of the influence of initial stresses on the state of a material is connected with the following difficulties: First, the linear theory (in which the potential of state is regarded as a quadratic function of basic parameters of the state) does not take into account account this influence. Moreover, the classical linear theory connecting stresses with compatible strains and the corresponding field of displacements is inapplicable to the study of the influence of initial stresses because it is impossible to determine the initial strains and field of displacements corresponding to the initial stresses without knowledge about the other parameters of state (thermal, electromagnetic, and chemical). As a characteristic example of initial stresses with unknown initial strains, one can mention residual stresses. Generally speaking, in analyzing the actual (but not theoretical) stresses formed in industrial structures (but not in laboratory specimens), we, as a rule, never know what kind of strains is responsible for their appearance
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