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Elastic properties of a unidirectional composite reinforced with hexagonal array of fibers

Czaplinski T., Drygaś P., Gluzman S., Mityushev V., Nawalaniec W., Zietek G.

Archives of Mechanics

2018

Vol. 70, nr 3

207--239

It is difficult to measure the transverse shear modulus of the fibrous composites. Thus, theoretical investigations by means of analytical and numerical techniques are paramount. In particular, they are important for the regime with high-concentration of fibers. We apply general techniques to study the mechanical properties of unidirectional fibers with a circular section embedded into the matrix and organized into the hexagonal array. Our theoretical considerations are designed to include two regimes, of low and high concentrations of inclusions. The former regime is controlled by Hashin–Shtrikman lower bounds, while the latter is controlled by square-root singularity. We derived the analytical formulae for the effective shear, Young and bulk moduli in the form of the rational expressions valid up to O(f7) by the method of functional equations. The obtained formulae contains elastic constants of components in a symbolic form as well as the concentration f. The general scheme based on the asymptotically equivalent transformations is developed to extend the obtained analytical formulae to the critical concentration of touching fibers. A comparison with the numerical FEM is performed for all concentrations of inclusions. Good agreement is achieved for all available concentrations.

Multiple polarized beam interferometers for array generation with improved efficiency

Patra A. S., Khare A.

Optica Applicata

2008

Vol. 38, nr 3

495-502

A highly efficient multiple polarized beam interferometer for the generation of hexagonal array is reported. An expression for the intensity distribution is worked out using Jones' calculus and computed pattern is compared with the experimental results. The array pattern could be scanned over large longitudinal distances without loss of distortion. Fringe visibility of interferograms has been studied as a function of relative state of polarization of the interfering beams. Some of the potential applications of such arrays are also proposed.