The Variational Approach to Estimation of the Dielectric Permittivity of a Unidirectional Fibrous Composite / V. S. Zarubin, G. N. Kuvyrkin, and I. Yu. Savel'eva. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 1. P. 3-11 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 1-9].
Based on the dual variational formulation of an electrostatic problem in an inhomogeneous anisotropic dielectric, we construct two-side bounds for possible values of second rank tensor components for the dielectric permittivity of a unidirectional fibrous composite taking into account mutual positions of anisotropic 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 permittivity. Some estimates of the greatest error appearing in the choice of true values of each component of the dielectric permittivity tensor of the composite in the form of a half-sum of its boundary values are obtained. A successive improvement of two-side bounds for domains where the components of this tensor should lie is carried out. A quantitative analysis of calculation dependencies is presented.
Key words: unidirectional fibrous composite, dual variation formulation of the electrostatic problem, dielectric permeability tensor.