Abstract
A two-phase random aggregate of isotropic, incompressible, power-law viscous spheres is considered. The various extensions of the self-consistent model to nonlinear materials found in the literature are applied to predict the behaviour of this composite. It is shown that most of them violate an upper bound established recently.
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References
Bao, G., Hutchinson, J.W., and McMeeking, R.M. (1991) The flow stress of dual-phase, non-hardening solids, Mech. Mater. 12, 85–94.
Berveiller, M. and Zaoui, A. (1981) A simplified self-consistent scheme for the plasticity of two-phase metals, Res Mechanica Letters 1, 119–124.
Gilormini, P. (1994) Modèles autocohérents pour les matériaux hétérogènes non linéaires, Rapport no 154, Laboratoire de Mécanique et Technologie, Cachan, France.
Gilormini, P. (1995) Insuffisance de l’extension classique du modèle autocohérent au comporttement non linéaire, C.R. Acad. Sci. Paris II b 320, 115–122.
Gilormini, P. and Germain, Y. (1986) A finite element analysis of the inclusion problem for power law viscous materials, Int. J. Solids Structures 23, 413–437.
Gilormini, P. and Vernusse, Ph. (1992) Tenseur d’Eshelby et problème d’inclusion dans le cas isotrope transverse incompressible, C.-R. Acad. Sci. Paris II 314, 257–261.
Hill, R. (1965a) Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids 13, 89–101.
Hill, R. (1965b) A self-consistent mechanics of composite materials, J. Mech. Phys. Solids 13, 213–222.
Hutchinson, J.W. (1976) Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. Roy. Soc. London A 348, 101–127.
Lebensohn, R.A. and Tomé, C.N. (1993) 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.
Molinari, A., Canova, G.R., and Ahzi, S. (1987) A self-consistent approach of the large deformation polycrystal viscoplasticity, Acta Metall. 35, 2983–2994.
Molinari, A. and Tóth, L.S. (1994) Tuning a self consistent viscoplastic model by finite element results -I. Modeling, Acta Metall. Mater. 42, 2453–2458.
Ponte Castaneda, P. (1991) The effective mechanical properties of nonlinear isotropic composites, J. Mech. Phys. Solids 39, 45–71
Suquet, P. (1993) Overall potentials and extremal surfaces of power law or ideally plastic composites, J. Mech. Phys. Solids 41, 981–1002.
Suquet, P. and Ponte Castañeda, P. (1993) Small-contrast perturbation expansions for the effective properties of nonlinear composites, C.R. Acad. Sci. Paris II 317, 1515–1522
Talbot, D.R.S. and Willis, J.R. (1985) Variational principles for nonlinear inhomogeneous media, IMA J. Appl. Math. 35, 39–54.
Tóth, L.S. and Molinari, A. (1994) Tuning a self consistent viscoplastic model by finite element results — II. Application to torsion textures, Acta Metall. Mater. 42, 2459–2466.
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© 1996 Kluwer Academic Publishers
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Gilormini, P. (1996). A Critical Evaluation for Various Nonlinear Extensions of the Self-Consistent Model. In: Pineau, A., Zaoui, A. (eds) IUTAM Symposium on Micromechanics of Plasticity and Damage of Multiphase Materials. Solid Mechanics and its Applications, vol 46. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1756-9_9
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DOI: https://doi.org/10.1007/978-94-009-1756-9_9
Publisher Name: Springer, Dordrecht
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