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Article Dans Une Revue Journal of the Mechanics and Physics of Solids Année : 2000

An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals

Résumé

Variational approaches for nonlinear elasticity show that Hill’s incremental formulation for the prediction of the overall behaviour of heterogeneous materials yields estimates which are too stiff and may even violate rigorous bounds. This paper aims at proposing an alternative ‘affine’ formulation, based on a linear thermoelastic comparison medium, which could yield softer estimates. It is first described for nonlinear elasticity and specified by making use of Hashin–Shtrikman estimates for the linear comparison composite; the associated affine self-consistent predictions are satisfactorily compared with incremental and tangent ones for power-law creeping polycrystals. Comparison is then made with the second-order procedure and some limitations of the affine method are pointed out; explicit comparisons between different procedures are performed for isotropic, two-phase materials. Finally, the affine formulation is extended to history-dependent behaviours; application to the self-consistent modelling of the elastoplastic behaviour of polycrystals shows that it offers an improved alternative to Hill’s incremental formulation.
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Dates et versions

hal-01666054 , version 1 (18-12-2017)

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Paternité - Pas d'utilisation commerciale

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Renaud Masson, Michel Bornert, Pierre Suquet, André Zaoui. An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals. Journal of the Mechanics and Physics of Solids, 2000, 48 (6-7), pp.1203-1227. ⟨10.1016/S0022-5096(99)00071-X⟩. ⟨hal-01666054⟩

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