Assessment of Elastic Characteristics of a Composite with Short Isotropic Fibers

We built a mathematical model describing the interaction of the elements of the composite structure (short isotropic fibers and the matrix particles) with an isotropic elastic medium, whose moduli of elasticity are to be determined as the desired characteristics of the composite. The method of self-consistency helped to obtain the system of nonlinear matrix relations, establishing a connection between the desired composite moduli and the volume concentration of fibers and their elongation and elastic properties of the fibers and the matrix. We carried out a quantitative analysis of the mathematical model and defined the boundaries within which the influence of the fiber elongation is significant. The calculated dependences obtained made it possible to predict elastic properties of the composite reinforced with short fibers (including the form of nanostructured elements, for example carbon nanotubes).

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