Geodesic
The variational approach to estimation of the dielectric permittivity of a unidirectional fibrous composite
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2017), pp. 3-11

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Based on the dual variation formulation of an electrostatic problem in a non-uniform anisotropic dielectric, we construct two-side bounds for possible values of the second rank tensor components for the dielectric permeability of a unidirectional fibrous composite taking into account the mutual positions of anysotropic reinforcing fibers in the plane perpendicular to their axes. We consider variants of arrangement of cross sections of fibers such that the composite is transversal-isotropic or orthotropic relative to the property of dielectric permeability. Some estimates of the greatest error appearing in the choice of true values of each component of the dielectric permeability tensor of the composite in the form of a half-sum of its boundary values are obtained. A successive improvement of two-side boundaries for domains where the component of this tensor should lie is carried out. A quantitative analysis of calculation dependencies is presented. 
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     author = {V. S. Zarubin and G. N. Kuvyrkin and I. Yu. Savelyeva},
     title = {The variational approach to estimation of the dielectric permittivity of a unidirectional fibrous composite},
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V. S. Zarubin; G. N. Kuvyrkin; I. Yu. Savelyeva. The variational approach to estimation of the dielectric permittivity of a unidirectional fibrous composite. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2017), pp. 3-11. http://geodesic.mathdoc.fr/item/VMUMM_2017_1_a0/