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Abstrakty
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.
Rocznik
Tom
Strony
305--322
Opis fizyczny
Bibliogr. 21 poz., rys., wykr.
Twórcy
autor
autor
autor
autor
- Facultad de Matematica y Computacion, Universidad de La Habana, San Lázaro y L, Vedado, Habana 4, CP-10400, Cuba
Bibliografia
- [1] M. Avellaneda, P. J. Swart. Calculating the perfomance of 1-3 piezoelectric composites for hydrophone applications: an effective medium approach. J. Acoust. Soc Am., 103: 1449-1467, 1998.
- [2] O. Bruno. The effective conductivity of strongly heterogeneous composites. Proc. R. Soc. Lond., A 433: 353-381, 1991.
- [3] R. M. Christensen, Mechanics of Composite Materials. Krieger, Malabar, FI., 1991.
- [4] S. C. Cowin, Bone poroelasticity. J. Biomechanics, 32: 217-238, 1999.
- [5] E.I. Grigolyuk, L. A. Fil’shtinskii, Perforated Plates and Shells (in Russian). Nauka, Moscow, 1970.
- [6] R. Guinovart-Diaz, R. Bravo-Castillero, J. Rodriguez-Ramos, F. J. Sabina. Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. I: Elastic and hexagonal symmetry. J. Mech. Phys. Solids, 49: 1445-1462, 2001.
- [7] Z. Hashin. Analysis of composite materials. A Survey. J. Appl. Mech., 50: 481-505, 1983.
- [8] R. Hill. Theory of mechanical properties of fibre-strengthened materials: I. Elastic behavior. J. Mech. Phys. Solids, 12: 199-212, 1964.
- [9] J. L. Katz, H. S. Yoon, S. Lipson, R. Maharidge, A. Maunier, P. Christel. The effects of remodeling on the elastic properties of bone. Calcified Tissue International, 36: 531-536, 1984.
- [10] S. A. Meguid, A. L. Kalamkarov. Asymptotic homogenization of elastic composite materials with a regular structure. Int. J. Solids Struc, 31: 2933-2944, 1994.
- [11] V. Z. Parton, B. A. Kudryavtsev, Engineering Mechanics of Composite Structures. CRC Press, Boca Raton, 1993.
- [12] L.D. Perez, A. Leon, J. Bravo-Castillero, Variational bounds for nonlinear fibrous composites. [In:] P. Kittl, G. Diaz, D. Mook, J. Geer, eds. Proc. Seventh Panamerican Congress of Applied Mechanics (PACAM VII), 105-108, 2002.
- [13] B. E. Pobedrya. Mechanics of Composite Materials (in Russian). Moscow State University, Moscow, 1984.
- [14] F. J. Sabina, R. Rodriguez-Ramos, J. Bravo-Castillero, R. Guinovart-Diaz. Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. I: Piezoelectric and hexagonal symmetry. J. Mech. Phys. Solids, 49: 1463-1479, 2001.
- [15] F. J. Sabina, J. Bravo-Castillero, Guinovart-Diaz, R. Rodriguez-Ramos, O. C. Valdiviezo-Mijangos. Overall behavior of two-dimensional periodic composites. Int. J. Solids Struc, 39: 483-497, 2002.
- [16] I. Sevostianov, M. Kachanov. Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone. J. Biomech., 33: 881-888, 2000.
- [17] D. R. S. Talbot, J. R. Willis. Some simple explicit bounds for the overall behavior of nonlinear composites. Int. J. Solids Struc, 29: 1981-1987, 1992.
- [18] D.R.S. Talbot. Bounds which incorporate morphological information for nonlinear composite dielectric. Proc. R. Soc. Lond., A 455: 3617-3628, 1999.
- [19] D. R. S. Talbot. Improved bounds for the effective properties of a nonlinear two-phase elastic composite. J. Mech. Phys. Solids, 48: 1285-1294, 2000.
- [20] S.W. Tsai, H.T. Hahn. Introduction to Composite Materials. Technomic, Westport, 1980.
- [21] D. Zhang, S. Weinbaum, S. C. Cowin, Estimates of the peak pressures in the bone pore water. J. Biomech. Eng., 120: 697-703, 1998.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0019-0009