zbMATH — the first resource for mathematics

On the application of Mori-Tanaka’s theory involving transversely isotropic spheroidal inclusions. (English) Zbl 0719.73005
Summary: Based on the new structure recently established by the second author for the Mori-Tanaka theory [see the foregoing entry (Zbl 0719.73004)], the effective elastic moduli of three types of composites containing transversely isotropic spheroidal inclusions are explicitly derived. For a multiphase composite with aligned, identically shaped inclusions, the derived moduli are believed to be generally reliable, where the three extreme cases involving circular fibers, spheres, and thin discs all lie on or within the respective Hashin-Shtrikman-Walpole bounds. For a multiphase aligned composite whose inclusion phases differ in shape, the M-T moduli tensor can lose its diagonal symmetry, which, for a hybrid composite containing fibers and another aligned spheroids, is found to be severest when the spheroids take the shape of thin disks, and tends to decrease as their aspect ratio increases. When the transversely isotropic spheroidal inclusions are randomly oriented in an isotropic matrix, the M-T moduli with spherical inclusions are shown to always lie on or within the isotropic Hashin-Shtrikman-Walpole bounds. Such a desired property however is not always assured with other inclusion shapes, where the needle and disc-like inclusions may cause the M-T moduli and Walpole’s self-consistent estimates to lie outside the H-S-W bounds.

74E05 Inhomogeneity in solid mechanics
Full Text: DOI
[1] Weng, G.J., Int. J. engng. sci., 28, 1111, (1990)
[2] Mori, T.; Tanaka, K., Acta metall., 21, 571, (1973)
[3] Walpole, L.J., J. mech. phys. solids, 14, 151, (1966)
[4] Walpole, L.J., J. mech. phys. solids, 14, 289, (1966)
[5] Walpole, L.J., J. mech. phys. solids, 17, 235, (1969)
[6] Eshelby, J.D., (), 376
[7] Hashin, Z.; Shtrikman, S., J. mech. phys. solids, 11, 127, (1963)
[8] Hill, R., J. mech. phys. solids, 12, 199, (1964)
[9] Hashin, Z., J. mech. phys. solids, 13, 119, (1965)
[10] Dvorak, G.J., ()
[11] Walpole, L.J., Adv. appl. mech., 21, 169, (1981)
[12] Christensen, R.M., Mechanics of composite materials, (1979), Wiley New York
[13] Hill, R., J. mech. phys. solids, 13, 89, (1965)
[14] Takao, Y.; Taya, M., J. comp. mater., 21, 140, (1987)
[15] Tandon, G.P.; Weng, G.J., Polymer comp., 5, 327, (1984)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.