15 Homogenization-Based Mechanical Behavior Modeling of Composites …
279
Ponte-Castaneda, P., & Suquet, P. (1998). Non linear composites. Advances in Applied Mechanics,
34, 172–302.
Ponte-Castaneda, P., & Willis, J. R. (1995). The effect of spatial distribution on the effective behavior
of composite materials and cracked media. Journal of the Mechanics and Physics of Solids, 43(12),
1919–1951.
Ponte-Castaneda, P., & Willis, J. R. (1999). Variational second-order estimates for nonlinear
composites. Proceedings of the Royal Society London A, 455(1985), 1799–1811.
Poquillon, D., Lemaitre, J., Baco-Carles, V., Tailhades, Ph, & Lacaze, J. (2002). Cold compaction
of iron powders—Relations between powder morphology and mechanical properties. Powder
Technology, 126, 65–74.
Postma, G. W. (1955). Wave propagation in a stratified medium. Geophysics, 20(4), 780–806.
Rahali, Y., Giorgio, I., Ganghoffer, J. F., & dell’Isola, F. (2015). Homogenization à la Piola produces
second gradient continuum models for linear pantographic lattices. International Journal of
Engineering Science, 97, 148–172.
Ramm, A. G., & Katsevich, A. I. (1996). The radon transform and local tomography. Boca Raton,
FL: CRC Press.
Roberts, A. P., & Garboczi, E. J. (2002). Elastic properties of model random three-dimensional
open-cell solids. Journal of the Mechanics and Physics of Solids, 50, 33–55.
Rodin, G. J. (1996). Eshelby’s inclusion problem for polygons and polyhedra. Journal of the
Mechanics and Physics of Solids, 44, 1977–1995.
Ryoo, R. (2009). Porous materials: A tricontinuous mesoporous system. Nature Chemistry, 1, 105–
106.
Santalo, A. (1976). Integral geometry and geometric probability. In Encyclopedia of mathematics
and its applications. Reading, MA: Addison-Wesley Pub. Co.
Shrestha, S., & Banerjee, S. (2018). Virtual nondestructive evaluation for anisotropic plates using
symmetry informed sequential mapping of anisotropic Green’s function. Ultrasonics, 88, 51–63.
Sciarra, G., dell’Isola, F., & Coussy, O. (2007). Second gradient poromechanics. International
Journal of Solids and Structures, 44(20), 6607–6629.
Serra, J. (1982). Image analysis and mathematical morphology. London Academic Press.
Spagnuolo, M., Franciosi, P., & dell’Isola, F. (2020). A Green operator-based elastic modeling for
two-phase pantographic-inspired bi-continuous materials. International Journal of Solids and
Structures, 188, 282–308.
Suquet, P., (1995). Overall properties of nonlinear composites: A modified secant moduli theory and
its link with Ponte Castañeda’s nonlinear variational procedure. Comptes Rendus de l’Académie
des Sciences, Paris, Mechanics Series, 320(11), 563–571.
Suquet, P. (1997). Effective behavior of non linear composites. In P. Suquet (Ed.), Continuum
micromechanics, CISM course and lecture (Vol. 377, pp. 220–259). Berlin: Springer.
Tavaf, V., Saadatzi, M., Shrestha, S., & Banerjee, S. (2018). Quantification of material degradation
and its behavior of elastodynamic Greens function for computational wave field modeling in
composites. Materials Today Communications, 17, 402–412.
Torres, Y., Pavon, J. J., & Rodrıguez, J. A. (2012). Processing and characterization of porous titanium
for implants by using NaCl as space holder. Journal of Materials Processing Technology, 212,
1061–1069.
Traxl, R., & Lackner, R. (2018). Consideration of arbitrary inclusion shapes in the framework of
isotropic continuum micromechanics: The replacement Eshelby tensor approach. Mechanics of
Materials, 126, 126–139.
Udhayaraman, R., & Mulay, S. S. (2017). Multi-scale approach based constitutive modeling of plain
woven textile composites. Mechanics of Materials, 112, 172–192.
Veenstra, H., Verkooijen, P. C. J., Van Lent, B. J. J., Van Dam, J., De Boer, A. P., & Nijhof, A. P.
H. J. (2000). On the mechanical properties of co-continuous polymer blends: Experimental and
modeling. Polymer, 41, 1817–1826.
Walpole, L. J. (1967). The elastic field of an inclusion in an anisotropic medium. Proceedings of
the Royal Society London A, 300, 270–289.
279
Ponte-Castaneda, P., & Suquet, P. (1998). Non linear composites. Advances in Applied Mechanics,
34, 172–302.
Ponte-Castaneda, P., & Willis, J. R. (1995). The effect of spatial distribution on the effective behavior
of composite materials and cracked media. Journal of the Mechanics and Physics of Solids, 43(12),
1919–1951.
Ponte-Castaneda, P., & Willis, J. R. (1999). Variational second-order estimates for nonlinear
composites. Proceedings of the Royal Society London A, 455(1985), 1799–1811.
Poquillon, D., Lemaitre, J., Baco-Carles, V., Tailhades, Ph, & Lacaze, J. (2002). Cold compaction
of iron powders—Relations between powder morphology and mechanical properties. Powder
Technology, 126, 65–74.
Postma, G. W. (1955). Wave propagation in a stratified medium. Geophysics, 20(4), 780–806.
Rahali, Y., Giorgio, I., Ganghoffer, J. F., & dell’Isola, F. (2015). Homogenization à la Piola produces
second gradient continuum models for linear pantographic lattices. International Journal of
Engineering Science, 97, 148–172.
Ramm, A. G., & Katsevich, A. I. (1996). The radon transform and local tomography. Boca Raton,
FL: CRC Press.
Roberts, A. P., & Garboczi, E. J. (2002). Elastic properties of model random three-dimensional
open-cell solids. Journal of the Mechanics and Physics of Solids, 50, 33–55.
Rodin, G. J. (1996). Eshelby’s inclusion problem for polygons and polyhedra. Journal of the
Mechanics and Physics of Solids, 44, 1977–1995.
Ryoo, R. (2009). Porous materials: A tricontinuous mesoporous system. Nature Chemistry, 1, 105–
106.
Santalo, A. (1976). Integral geometry and geometric probability. In Encyclopedia of mathematics
and its applications. Reading, MA: Addison-Wesley Pub. Co.
Shrestha, S., & Banerjee, S. (2018). Virtual nondestructive evaluation for anisotropic plates using
symmetry informed sequential mapping of anisotropic Green’s function. Ultrasonics, 88, 51–63.
Sciarra, G., dell’Isola, F., & Coussy, O. (2007). Second gradient poromechanics. International
Journal of Solids and Structures, 44(20), 6607–6629.
Serra, J. (1982). Image analysis and mathematical morphology. London Academic Press.
Spagnuolo, M., Franciosi, P., & dell’Isola, F. (2020). A Green operator-based elastic modeling for
two-phase pantographic-inspired bi-continuous materials. International Journal of Solids and
Structures, 188, 282–308.
Suquet, P., (1995). Overall properties of nonlinear composites: A modified secant moduli theory and
its link with Ponte Castañeda’s nonlinear variational procedure. Comptes Rendus de l’Académie
des Sciences, Paris, Mechanics Series, 320(11), 563–571.
Suquet, P. (1997). Effective behavior of non linear composites. In P. Suquet (Ed.), Continuum
micromechanics, CISM course and lecture (Vol. 377, pp. 220–259). Berlin: Springer.
Tavaf, V., Saadatzi, M., Shrestha, S., & Banerjee, S. (2018). Quantification of material degradation
and its behavior of elastodynamic Greens function for computational wave field modeling in
composites. Materials Today Communications, 17, 402–412.
Torres, Y., Pavon, J. J., & Rodrıguez, J. A. (2012). Processing and characterization of porous titanium
for implants by using NaCl as space holder. Journal of Materials Processing Technology, 212,
1061–1069.
Traxl, R., & Lackner, R. (2018). Consideration of arbitrary inclusion shapes in the framework of
isotropic continuum micromechanics: The replacement Eshelby tensor approach. Mechanics of
Materials, 126, 126–139.
Udhayaraman, R., & Mulay, S. S. (2017). Multi-scale approach based constitutive modeling of plain
woven textile composites. Mechanics of Materials, 112, 172–192.
Veenstra, H., Verkooijen, P. C. J., Van Lent, B. J. J., Van Dam, J., De Boer, A. P., & Nijhof, A. P.
H. J. (2000). On the mechanical properties of co-continuous polymer blends: Experimental and
modeling. Polymer, 41, 1817–1826.
Walpole, L. J. (1967). The elastic field of an inclusion in an anisotropic medium. Proceedings of
the Royal Society London A, 300, 270–289.