15 Homogenization-Based Mechanical Behavior Modeling of Composites …
277
Gel’fand, I. M., & Shilov, G. E. (1964). Generalized functions, v1: Properties and operations. New
York: Academic Press.
Germain, P. (1973). La méthode des puissances virtuelles en mécanique des milieux continus,
première partie: théorie du second gradient. Journal de mécanique, 12(2), 235–274.
Gong, L., Kyriakides, S., & Jang, W.-Y. (2005). Compressive response of open-cell foams. Part I:
Morphology and elastic properties. International Journal of Solids and Structures, 42, 1355–1379.
Grossa, D., Dineva, P., & Rangelov, T. (2007). BIEM solution of piezoelectric cracked finite solids
under time-harmonic loading. Engineering Analysis with Boundary Elements, 31, 152–162.
Han, Y., Zhang, D., Chung, L. L., Sun, J., Zhao, L., Zou, X., et al. (2009). A tri-continuous mesoporous material with a silica pore wall following a hexagonal minimal surface. Nature Chemistry,
1, 123–127.
Hashin, Z., & Shtrikman, S. (1963). A variational approach to the theory of elastic behavior of
multi-phase materials. Journal of the Mechanics and Physics of Solids, 11, 127–140.
Helgason, S. (1980). The Radon transform. Progress in Mathematics, (vol. 5). Boston: Birkhausser.
Hervé, E., & Zaoui, A. (1993). N-layered inclusion-based micromechanical modeling. International
Journal of Engineering Science, 31(1), 1–10.
Hervé, E., & Zaoui, A. (1995). Elastic behaviour of multiply coated fibre reinforced composites.
International Journal of Engineering Science, 33(10), 1419–1433.
Hill, R. (1952). The elastic behavior of a crystalline aggregate. Proceedings of the Physical Society,
A, 65(5), 349–354.
Hill, R. (1965). Continuum micro-mechanics of elastoplastic polycrystals. Journal of the Mechanics
and Physics of Solids, 13(2), 89–101.
Hori, M., & Nemat-Nasser, S. (1993). Double-inclusion model and overall moduli of multi-phase
composites. Mechanics of Materials, 14(3), 189–206.
Hou, P. F., & Leung, A. Y. T. (2004). A spheroidal inclusion in an infinite magneto-electroelastic
material. International Journal of Engineering Sciences, 42, 1255–1273.
Hu, G. K., & Weng, G. J. (2000). The connections between the double inclusion model and the
Ponte Castaneda-Willis, Mori Tanaka, and Kuster-Toksoz models. Mechanics of Materials, 32,
495–503.
Huang, J. H., Chiu, Y. H., & Liu, H. K. (1998). Magneto-electro-elastic Eshelby tensors for a
piezoelectric–piezomagnetic composite reinforced by ellipsoid inclusions. Journal of Applied
Physics, 83(10), 5364–5370.
Kennett, B. L. N., Kerry, N. J., & Woodhouse, J. H. (1978). Symmetries in the reflection and
transmission of elastic waves. Geophysical Journal, Royal Astronomical Society, 52(2), 215–229.
Khutorianski, N., & Sosa, H. (1995). Dynamic representation formulas and fundamental solutions
for piezoelectricity. International Journal of Solids and Structures, 32(22), 3307–3325.
Kinney, J. H., Stölken, J. S., Smith, T. S., Ryaby, J. T., & Lane, N. E. (2005). An orientation
distribution function for trabecular bone. Bone, 36(2), 193–201.
Kinoshita, N., & Mura, T. (1971). Elastic fields of inclusions in anisotropic media. Physica Status
Solidi A, 5, 759–768.
Korringa, J. (1973). Theory of elastic constants of heterogeneous media. Journal of Mathematical
Physics, 14, 509–513.
Kröner, E., (1958). Berechnung der elastischen constanten des vielkristalls aus den konstanten des
einkristalls. Zeitschrift fur Physik, 151–504.
Kröner, E. (1990). Modified Green functions in the theory of heterogeneous and/or anisotropic
linearly elastic media. In Weng, G. J., Taya, M., & Abe, H. (Eds.), Micromechanics and
inhomogeneity (pp. 197–211). New York: Springer.
Lahellec, N. L., & Suquet, P. (2004). Nonlinear composites: A linearization procedure, exact
to second-order in contrast and for which the strain-energy and affine formulations coincide.
Comptes Rendus de l’Académie des Sciences, Paris, Mechanics series, 332(9), 693–700.
Lee, J., Boyd, J. G., & Lagoudas, D. C. (2005). Effective properties of three-phase electromagnetoelastic composites. International Journal of Engineering Science, 43, 790–825.
277
Gel’fand, I. M., & Shilov, G. E. (1964). Generalized functions, v1: Properties and operations. New
York: Academic Press.
Germain, P. (1973). La méthode des puissances virtuelles en mécanique des milieux continus,
première partie: théorie du second gradient. Journal de mécanique, 12(2), 235–274.
Gong, L., Kyriakides, S., & Jang, W.-Y. (2005). Compressive response of open-cell foams. Part I:
Morphology and elastic properties. International Journal of Solids and Structures, 42, 1355–1379.
Grossa, D., Dineva, P., & Rangelov, T. (2007). BIEM solution of piezoelectric cracked finite solids
under time-harmonic loading. Engineering Analysis with Boundary Elements, 31, 152–162.
Han, Y., Zhang, D., Chung, L. L., Sun, J., Zhao, L., Zou, X., et al. (2009). A tri-continuous mesoporous material with a silica pore wall following a hexagonal minimal surface. Nature Chemistry,
1, 123–127.
Hashin, Z., & Shtrikman, S. (1963). A variational approach to the theory of elastic behavior of
multi-phase materials. Journal of the Mechanics and Physics of Solids, 11, 127–140.
Helgason, S. (1980). The Radon transform. Progress in Mathematics, (vol. 5). Boston: Birkhausser.
Hervé, E., & Zaoui, A. (1993). N-layered inclusion-based micromechanical modeling. International
Journal of Engineering Science, 31(1), 1–10.
Hervé, E., & Zaoui, A. (1995). Elastic behaviour of multiply coated fibre reinforced composites.
International Journal of Engineering Science, 33(10), 1419–1433.
Hill, R. (1952). The elastic behavior of a crystalline aggregate. Proceedings of the Physical Society,
A, 65(5), 349–354.
Hill, R. (1965). Continuum micro-mechanics of elastoplastic polycrystals. Journal of the Mechanics
and Physics of Solids, 13(2), 89–101.
Hori, M., & Nemat-Nasser, S. (1993). Double-inclusion model and overall moduli of multi-phase
composites. Mechanics of Materials, 14(3), 189–206.
Hou, P. F., & Leung, A. Y. T. (2004). A spheroidal inclusion in an infinite magneto-electroelastic
material. International Journal of Engineering Sciences, 42, 1255–1273.
Hu, G. K., & Weng, G. J. (2000). The connections between the double inclusion model and the
Ponte Castaneda-Willis, Mori Tanaka, and Kuster-Toksoz models. Mechanics of Materials, 32,
495–503.
Huang, J. H., Chiu, Y. H., & Liu, H. K. (1998). Magneto-electro-elastic Eshelby tensors for a
piezoelectric–piezomagnetic composite reinforced by ellipsoid inclusions. Journal of Applied
Physics, 83(10), 5364–5370.
Kennett, B. L. N., Kerry, N. J., & Woodhouse, J. H. (1978). Symmetries in the reflection and
transmission of elastic waves. Geophysical Journal, Royal Astronomical Society, 52(2), 215–229.
Khutorianski, N., & Sosa, H. (1995). Dynamic representation formulas and fundamental solutions
for piezoelectricity. International Journal of Solids and Structures, 32(22), 3307–3325.
Kinney, J. H., Stölken, J. S., Smith, T. S., Ryaby, J. T., & Lane, N. E. (2005). An orientation
distribution function for trabecular bone. Bone, 36(2), 193–201.
Kinoshita, N., & Mura, T. (1971). Elastic fields of inclusions in anisotropic media. Physica Status
Solidi A, 5, 759–768.
Korringa, J. (1973). Theory of elastic constants of heterogeneous media. Journal of Mathematical
Physics, 14, 509–513.
Kröner, E., (1958). Berechnung der elastischen constanten des vielkristalls aus den konstanten des
einkristalls. Zeitschrift fur Physik, 151–504.
Kröner, E. (1990). Modified Green functions in the theory of heterogeneous and/or anisotropic
linearly elastic media. In Weng, G. J., Taya, M., & Abe, H. (Eds.), Micromechanics and
inhomogeneity (pp. 197–211). New York: Springer.
Lahellec, N. L., & Suquet, P. (2004). Nonlinear composites: A linearization procedure, exact
to second-order in contrast and for which the strain-energy and affine formulations coincide.
Comptes Rendus de l’Académie des Sciences, Paris, Mechanics series, 332(9), 693–700.
Lee, J., Boyd, J. G., & Lagoudas, D. C. (2005). Effective properties of three-phase electromagnetoelastic composites. International Journal of Engineering Science, 43, 790–825.