A modified affine theory for the overall properties of nonlinear composites

Renald Brenner1,2, Olivier Castelnau1, Pierre Gilormini3
1Laboratoire des propriétés mécaniques et thermodynamiques des matériaux, CNRS, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse, France
2CEA-DEN, Service de recherches métallurgiques appliquées, CEA-Saclay, 91191 Gif-sur-Yvette cedex, France
3Laboratoire de mécanique et technologie, ENS de Cachan, CNRS, Université Paris-6, 94235 Cachan cedex, France

Tài liệu tham khảo

Hill, 1963, Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids, 11, 357, 10.1016/0022-5096(63)90036-X Buryachenko, 2001, Multiparticle effective field and related methods in micromechanics of composite materials, Appl. Mech. Rev., 54, 1, 10.1115/1.3097287 Ponte Castañeda, 1998, Nonlinear composites, Adv. Appl. Mech., 34, 171, 10.1016/S0065-2156(08)70321-1 Kreher, 1990, Residual stresses and stored elastic energy of composites and polycrystals, J. Mech. Phys. Solids, 38, 115, 10.1016/0022-5096(90)90023-W Masson, 2000, An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals, J. Mech. Phys. Solids, 48, 1203, 10.1016/S0022-5096(99)00071-X Bornert, 1998, Second-order estimates of the self-consistent type for viscoplastic polycrystals, Proc. Roy. Soc. London Ser. A, 454, 3035, 10.1098/rspa.1998.0290 Berveiller, 1979, An extension of the self-consistent scheme to plastically-flowing polycrystals, J. Mech. Phys. Solids, 26, 325, 10.1016/0022-5096(78)90003-0 Suquet, 1995, Overall properties of nonlinear composites: a modified secant moduli theory and its link with Ponte Castañeda's nonlinear variational procedure, C. R. Acad. Sci. Paris, Série IIb, 320, 563 Ponte Castañeda, 1991, The effective mechanical properties of nonlinear isotropic composites, J. Mech. Phys. Solids, 39, 45, 10.1016/0022-5096(91)90030-R Gilormini P., Brenner R., Castelnau O., A similarity between the classical and modified secant extensions of the self-consistent model, C. R. Acad. Sci. Paris, Série IIb (in press) Ponte Castañeda, 1996, Exact second-order estimates for the effective mechanical properties of nonlinear composite materials, J. Mech. Phys. Solids, 44, 827, 10.1016/0022-5096(96)00015-4