zbMATH — the first resource for mathematics

Exact results for the local fields and the effective moduli of fibrous composites with thickly coated fibers. (English) Zbl 1328.74032
Summary: Fibrous composites that consist of thickly coated cylindrical fibers embedded in a matrix are considered. All of the three phases of the composite are assumed to be transversely isotropic. The study consists of three parts. In the first part exact relations are derived for the influence functions that connect applied uniform overall fields to the induced local fields in piezomagnetoelectric systems. We consider the case of coated fibers with a concentrically circular cross section, and contrast the derived relations with the more limited ones that could be obtained in the case of coated fibers with an arbitrary cross section. The derivation is based on the ability to create uniform strain, electric and magnetic fields in the composite by the application of certain mechanical, electric, magnetic and thermal loadings. In the second part of the study, exact microstructure-independent connections are derived for a subgroup of the effective moduli of the homogenized piezomagnetoelectric composite which exhibits overall transverse isotropy. In the third part of the study, the derived exact connections between the effective moduli are reduced to the setting of thermoelasticity; allowing the coating to be thin and highly stiff or highly compliant, we make contact with the exact connections derived lately in the literature for two-phase fibrous thermoelastic composites with surface-stress-type and spring-type imperfect interfaces.

74F05 Thermal effects in solid mechanics
74F15 Electromagnetic effects in solid mechanics
Full Text: DOI
[1] Benveniste, Y., The effective mechanical behavior of composite materials with imperfect contact between the constituents, Mech. Mater., 4, 197-208, (1985)
[2] Benveniste, Y., Exact results in the micromechanics of fibrous piezoelectric composites exhibiting pyroelectricity, Proc. R. Soc. Lond. A, 441, 59-81, (1993)
[3] Benveniste, Y., On the micromechanics of fibrous piezoelectric composites, Mech. Mater., 18, 183-193, (1994)
[4] Benveniste, Y., Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases, Phys. Rev. B, 51, 16424-16427, (1995)
[5] Benveniste, Y., A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media, J. Mech. Phys. Solids, 54, 708-734, (2006), (Corrigendum: 2007. J. Mech. Phys. Solids 55, 666-667.) · Zbl 1120.74323
[6] Benveniste, Y.; Dvorak, G. J., Uniform fields and universal relations in piezoelectric composites, J. Mech. Phys. Solids, 40, 1296-1312, (1992) · Zbl 0763.73046
[7] Benveniste, Y.; Miloh, T., Imperfect soft and stiff interfaces in two-dimensional elasticity, Mech. Mater., 6, 309-323, (2001)
[8] Bravo-Castillero, J.; Rodriguez-Ramos, R.; Guinovart-Diaz, R.; Mechkour, H.; Brenner, R.; Camancho-Montes, H.; Sabina, F. J., Universal relations and effective coefficients of magneto-electro-elastic perforated structures, Q. J. Mech. Appl. Math., 65, 61-85, (2012) · Zbl 1248.74034
[9] Chen, T., Piezoelectric properties of mutiphase fibrous composites - some theoretical results, J. Mech. Phys. Solids, 41, 1781-1794, (1993) · Zbl 0798.73045
[10] Chen, T., Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects, Acta Mech., 196, 205-217, (2008) · Zbl 1139.74045
[11] Chen, T.; Dvorak, G. J., Fibrous nanocomposites with interface stress: hill׳s and levin׳s connections for effective moduli, Appl. Phys. Lett., 88, 211912, (2006)
[12] Cribb, J. L., Shrinkage and thermal expansion of a two-phase material, Nature, 220, 576-577, (1968)
[13] Dinzart, F.; Sabar, H., Magnetoelectric effect in coated fibrous-magnetic-piezoelectric composites, J. Intell. Mater. Syst. Struct., 23, 1249-1261, (2012)
[14] Duan, H. L.; Karihaloo, B. L., Thermo-elastic properties of heterogeneous materials with imperfect interfaces - generalized levin׳s formula and hill׳s connections, J. Mech. Phys. Solids, 55, 1036-1052, (2007) · Zbl 1170.74017
[15] Dvorak, G. J., On uniform fields in heterogeneous media, Proc. R. Soc. Lond. A, 431, 89-110, (1990) · Zbl 0726.73002
[16] Dvorak, G. J.; Benveniste, Y., On micromechanics of inelastic and piezoelectric composites, (Tatsumi, T.; Watanabe, E.; Kambe, T., Theoretical and Applied Mechanics 1996, Proceedings of the XIXth International Congress of Theoretical and Applied Mechanics, (1997), Elsevier Science B. V. Amsterdam, The Netherlands), 217-237
[17] Fiebig, M., Revival of the magnetoelectric effect, J. Phys. D - Appl. Phys., 38, R123-R152, (2005)
[18] Grabovsky, Y.; Milton, G. W.; Sage, D. S., Exact relations for effective tensors of composites: necessary conditions and sufficient conditions, Commun. Pure Appl. Math., 53, 300-353, (2000) · Zbl 1041.74057
[19] Guinovart-Diaz, R.; Rodriguez-Ramos, R.; Bravo-Castillero, J.; Sabina, F. J.; Galindo, G. M.; Wang, Y. S., Plane magneto-electro-elastic noduli of fiber composites with interphase, Mech. Adv. Mater. Struct., 20, 552-563, (2013)
[20] Hashin, Z., Thermoelastic properties of fiber-composites with imperfect interface, Mech. Mater., 8, 333-348, (1990)
[21] Hashin, Z.; Rosen, B. W., The elastic moduli of fiber reinforced materials, J. Appl. Mech., 29, 223-232, (1964)
[22] He, L. H.; Cheng, Z. Q., Correspondence relations between the effective thermoelastic properties of composites reinforced by spherically anisotropic particles, Int. J. Eng. Sci., 34, 1-8, (1996) · Zbl 0900.73449
[23] Hill, R., Theory of mechanical properties of fiber-reinforced materials. I. elastic behavior, J. Mech. Phys. Solids, 12, 199-212, (1964)
[24] Kuo, H.-Y., Multicoated elliptic fibrous composites of piezoelectric and piezomagnetic phases, Int. J. Eng. Sci., 49, 561-575, (2011) · Zbl 1231.74123
[25] Kuo, H.-Y., Effective property of multiferroic composites with imperfect interfaces, Smart Mater. Struct., 22, 105005, (2013)
[26] Kuo, H.-Y.; Pan, E., Effective magnetoelectric effect in multicoated circular fibrous multiferroic composites, J. Appl. Phys., 109, 104801, (2011)
[27] Kuo, H.-Y.; Bhattacharya, K., Fibrous composites of piezoelectric and piezomagnetic phases, Mech. Mater., 60, 157-170, (2013)
[28] Levin, V. M., Thermal expansion coefficients of heterogeneous materials, Mekh. Tverd. Tela, 2, 88-94, (1967), (English translation in Mech. Solids 2, 58-61 (1967)
[29] Milton, G. W., Composites: a myriad of microstructure independent relations, (Tatsumi, T.; Watanabe, E.; Kambe, T., Theoretical and Applied Mechanics 1996, Proceedings of the XIXth International Congress of Theoretical and Applied Mechanics, (1997), Elsevier Science B. V. Amsterdam, The Netherlands), 443-460
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.