Structural morphology and constitutive behaviour of microheterogeneous materials
Résumé
One of the main specific aspects of continuum micromechanics is related to the fact that one has generally to deal with ill-defined bodies: only partial information on the statistical distribution of the constituent phases of the considered random inhomogeneous materials is available. The first chapter briefly reports the main classical ways to use such an information in the context of linear elasticity for the derivation of bounds and estimates; attention is then focused on isotropic particulate composites and especially on Hashin’s composite spheres assemblage. New estimates are proposed for the overall shear modulus which include Hashin’s bounds as well as the three-phase model estimate: improved Hashin-Shtrikmantype bounds are conjectured from this analysis. The second chapter presents a proof of this guess as well as a generalization of the method used for arbitrary “morphological representative patterns”; the classical HashinShtrikman variational procedure is adapted to such a morphological analysis. Applications to the derivation of bounds and estimates for the overall elastic moduli are developed both for isotropic and anisotropic distributions of the patterns. In the third chapter, we lay the stress on behavioral aspects of this approach, with special emphasis on the viscoelastic coupling. Whereas it is easy to study the influence of morphological characteristics on the overall behaviour of linearly viscoelastic materials, this is more difficult to do for nonlinear behaviours: Hill’s treatment of the rate-independent classical self-consistent model is highlighted and extended to rate-dependent behaviours but this remains an approximation and new ways have still to be explored.
Domaines
Matériaux
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