Evaluation of Moduli of Elasticity for Composite with Lamellar Inclusions

This article presents a mathematical model that describes the interaction between the elements of the composite structure and the isotropic elastic medium. The moduli of elasticity of the medium are subject to determination as the required characteristics of the composite. Using the self-coordination method, a system of matrix ratios is obtained. It determines a non-linear connection between the required moduli of the composite and the volume concentration of inclusions, their elastic properties and elastic characteristics of the matrix. The variational approach is used to determine bilateral limits of possible values for the volume modulus of elastisity and shear modulus. The presented calculations can be used to predict elastic characteristics of a composite material reinforced by isotropic lamellar inclusions, including those in the form of nanostructed elements.

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