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Effective elastic properties of periodic fibrous composites. Limit cases. Applications to porous and nonlinear materials

Bravo-Castillero J., Guinovart-Diaz R., Sabina F. J., Valdiviezo-Mijangos O. C., Sabina-de-Lis J. C.

Computer Assisted Mechanics and Engineering Sciences

2006

Vol. 13, No. 2

305-322

The goal of this contribution is to provide, based on the asymptotic homogenization method, helpful exact formulae to compute the overall stiffnesses and engineering moduli of a transversely isotropic two-phase fibre reinforced composite with isotropic constituents. Comparison of the exact solution with known bounds is shown. In certain cases a bound is very close to the exact solution over a large interval. The bound then could be used as a good approximation to the exact solution. The exact formulae explicitly display Avellaneda and Swart's microestructural parameters, which have a physical meaning, and provide formulae for them. Hill's universal relations follow from the formulae. Limiting cases of rigid and empty fibers are included. An application of these results to improve bounds for the effective energy density of nonlinear dielectric fibrous composites is shown. Another application is related to bone poroelasticity.

Analytical expressions of effective constants for a piezoelectric composite reinforced with square cross-section fibres

Otero J., Bravo-Castillero J., Guinovart-Diaz R., Rodriguez-Ramos R., Maugin G. A.

Archives of Mechanics

2003

Vol. 55, nr 4

357-371

The purpose of this paper is to present analytical expresiion of the effective elastic, piezoelectric and dielectric constants of reinforced piezoelectric composite materials with unidirectional fibers periodically distributed in a square matrix, as obtained by means of the "double asymptotic homogenization" method. The cross-section of the fibers is square. Each periodic cell of the medium is a binary piezoelectric composite wherein both phases are homogeneous piezoelectric materials with transversely isotropic properties. Comparison between the derived theoretical predictions of characteristic parameters and the existing experimental results shows a rather good agreement. The results obtained in the present paper were verified by means of the universal relations of Schulgasser. Numerical computation of the effective properties can be realized without difficulties.