Abstract
Analytical formulae for the effective elastic constants of 2D composites with soft unidirectional fibers arranged in the hexagonal array are obtained for arbitrary concentration of fibers, from dilute case to percolation. It is supposed that every section of composites perpendicular to fibers is the hexagonal array with circular holes or soft inclusions. First, a polynomial approximation in concentration is obtained by application of functional equations. Further, an asymptotic analysis is applied to the obtained polynomial with using of the known asymptotic formulae in percolation regime. Finally, the formula for the effective shear modulus is suggested. It can be applied to the typical matrices made from ceramics, metals and polymers, and to other materials as well, e.g., for resin and thallium.
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