[1] |
Adams, B.; Olson, T., The mesostructure-properties linkage in polycrystals, Prog. Mater. Sci., 43, 1-88 (1998) |
[2] |
Allais, L.; Bornert, M.; Bretheau, T.; Caldemaison, D., Experimental characterization of the local strain field in a heterogeneous elastoplastic material, Acta. Metall. Mater., 42, 11, 3865-3880 (1994) |
[3] |
Aravas, N.; Cheng, C.; Ponte Castañeda, P., Steady-state creep of fiber-reinforced composites: constitutive equations and computational issues, Int. J. Solids Struct., 32, 15, 2219-2244 (1995) · Zbl 0874.73041 |
[4] |
Berveiller, M.; Zaoui, A., An extension of the self-consistent scheme to plastically-flowing polycrystals, J. Mech. Phys. Solids, 26, 325-344 (1979) · Zbl 0395.73033 |
[5] |
Bornert, M.; Ponte Castañeda, P., Second-order estimates of the self-consistent type for viscoplastic polycrystals, Proc. R. Soc. Lond. A, 356, 3035-3045 (1998) · Zbl 0916.73025 |
[6] |
Castelnau, O.; Canova, G. R.; Lebensohn, R. A.; Duval, P., Modelling viscoplastic behavior of anisotropic polycrystalline ice with a self-consistent approach, Acta Mater., 45, 4823-4834 (1997) |
[7] |
deBotton, G.; Ponte Castañeda, P., Elastoplastic constitutive relations for fiber-reinforced solids, Int. J. Solids Struct., 30, 1865-1890 (1993) · Zbl 0782.73006 |
[8] |
deBotton, G.; Ponte Castañeda, P., Variational estimates for the creep behavior of polycrystals, Proc. R. Soc. Lond. A, 448, 121-142 (1995) · Zbl 0829.73077 |
[9] |
Duval, P.; Ashby, M. F.; Anderman, I., Rate-controlling processes in the creep of polycrystalline ice, J. Phys. Chem., 87, 4066-4074 (1983) |
[10] |
Gilormini, P., A critical evaluation of various nonlinear extensions of the self-consistent model., (Pineau, A.; Zaoui, A., Micromechanics of plasticity and damage of multiphase materials (1996), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), 67-74 |
[11] |
Hashin, Z.; Shtrikman, S., A variational approach to the theory of the elastic behaviour of multiphase materials, J. Mech. Phys. Solids, 11, 127-140 (1963) · Zbl 0108.36902 |
[12] |
Hervé, E.; Zaoui, A., Modelling the effective behaviour of non-linear matrix inclusion composites, Eur. J. Mech., A/Solids, 9, 6, 505-515 (1990) · Zbl 0729.73910 |
[13] |
Hill, R., The elastic behavior of a crystalline aggregate, Proc. Phys. Soc. Lond., 65, 349-354 (1952) |
[14] |
Hill, R., Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, 13, 89-101 (1965) · Zbl 0127.15302 |
[15] |
Hutchinson, J. W., Elastic-plastic behaviour of polycrystalline metals and composites, Proc. R. Soc. Lond. A, 319, 247-272 (1970) |
[16] |
Hutchinson, J. W., Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. R. Soc. Lond. A, 348, 101-127 (1976) · Zbl 0319.73059 |
[17] |
Hutchinson, J. W., Creep and plasticity of hexagonal polycrystals as related to single crystal slip, Metall. Trans. A, 8, 1465-1469 (1977) |
[18] |
Kröner, E., Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls, Z. Phys., 151, 504-518 (1958) |
[19] |
Kröner, E., Zur plastischen Verformung des Vielkristalls, Acta Metall., 9, 155-161 (1961) |
[20] |
Kröner, E., Bounds for effective elastic moduli of disordered materials, J. Mech. Phys. Solids, 25, 137-155 (1977) · Zbl 0359.73020 |
[21] |
Laws, N., On the thermostatics of composite materials, J. Mech. Phys. Solids, 21, 9-17 (1973) |
[22] |
Lebensohn, R.; Tomé, C. N., A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys, Acta Metall. Mater., 41, 2611-2624 (1993) |
[23] |
Levin, V., Thermal expansion coefficients of heterogeneous materials, Mekh. Tverd. Tela, 2, 83-94 (1967) |
[24] |
Masson, R.; Bornert, M.; Suquet, P.; Zaoui, A., An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals, J. Mech. Phys. Solids, 48, 1203-1227 (2000) · Zbl 0984.74068 |
[25] |
Molinari, A.; Canova, G. R.; Ahzi, S., A self-consistent approach of the large deformation polycrystal viscoplasticity, Acta Metall., 35, 2983-2994 (1987) |
[26] |
Nebozhyn, M. V.; Gilormini, P.; Ponte Castañeda, P., Variational self-consistent estimates for viscoplastic polycrystals with highly anisotropic grains, C.R. Acad. Sci. Paris, Série IIb, 328, 11-17 (2000) · Zbl 0986.74018 |
[27] |
Nebozhyn, M. V.; Gilormini, P.; Ponte Castañeda, P., Variational self-consistent estimates for cubic viscoplastic polycrystals: the effects of grain anisotropy and shape, J. Mech. Phys. Solids, 49, 313-340 (2001) · Zbl 1048.74010 |
[28] |
Ponte Castañeda, P., The effective mechanical properties of nonlinear isotropic composites, J. Mech. Phys. Solids, 39, 45-71 (1991) · Zbl 0734.73052 |
[29] |
Ponte Castañeda, P., Exact second-order estimates for the effective mechanical properties of nonlinear composite materials, J. Mech. Phys. Solids, 44, 6, 827-862 (1996) · Zbl 1054.74708 |
[30] |
Ponte Castañeda, P.; Suquet, P., Nonlinear composites, Adv. Appl. Mech., 34, 171-302 (1998) · Zbl 0889.73049 |
[31] |
Ponte Castañeda, P.; Willis, J. R., Variational second-order estimates for nonlinear composites, Proc. R. Soc. Lond. A, 455, 1799-1811 (1999) · Zbl 0984.74071 |
[32] |
Qiu, Y. P.; Weng, G. J., The influence of inclusion shape on the overall elastoplastic behavior of a two-phase isotropic composite, Int. J. Solids Struct., 27, 1537-1550 (1991) · Zbl 0825.73420 |
[33] |
Suquet, P.; Ponte Castañeda, P., Small-contrast perturbation expansions for the effective properties of nonlinear composites, C. R. Acad. Sci. Paris, Série II, 317, 1515-1522 (1993) · Zbl 0844.73052 |
[34] |
Talbot, D. R.S.; Willis, J. R., Variational principles for inhomogeneous non-linear media, IMA J. Appl. Math., 35, 39-54 (1985) · Zbl 0588.73025 |
[35] |
Taylor, G. I., Plastic strain in Metals, J. Inst. Metals, 62, 307-315 (1938) |
[36] |
Willis, J. R., Bounds and self-consistent estimates for the overall properties of anisotropic composites, J. Mech. Phys. Solids, 25, 185-202 (1977) · Zbl 0363.73014 |
[37] |
Willis, J. R., Variational and related methods for the overall properties of composites, Adv. Appl. Mech., 21, 1-78 (1981) · Zbl 0476.73053 |
[38] |
Willis, J. R., Upper and lower bounds for nonlinear composite behavior, Mat. Sci. Eng. A, 175, 7-14 (1994) |
[39] |
Zaoui, A., Masson, R., 2000. Micromechanics-based modeling of plastic polycrystals: an affine formulation. Mat. Sci. Eng. A285, 418-424.; Zaoui, A., Masson, R., 2000. Micromechanics-based modeling of plastic polycrystals: an affine formulation. Mat. Sci. Eng. A285, 418-424. |