Comptes Rendus
Characterization of a class of polycrystals whose effective elastic bulk moduli can be exactly determined
Comptes Rendus. Mécanique, Volume 331 (2003) no. 9, pp. 623-629.

Necessary and sufficient conditions are established for the stress response of a linearly elastic material to an isotropic stain to be hydrostatic. In the 3D case, these conditions are satisfied not only by the isotropic and cubic materials but also by all other anisotropic materials provided appropriate restrictions are imposed. In the 2D case, only the isotropic and square materials have an isotropic stress response to an isotropic strain. Using a uniform field argument, the elastic bulk modulus of a polycrystal consisting of monocrystals compatible with the established conditions is shown to equal that of any constituent monocrystal. Thus, Hill's relevant result about a polycrystal composed of cubic monocrystals is generalized.

Les conditions nécessaires et suffisantes sont établies pour que la réponse en contrainte d'un matériau élastique linéaire à une déformation isotrope soit hydrostatique. Dans le cas 3D, ces conditions sont satisfaites non seulement par les matériaux isotropes et cubiques mais aussi par d'autres matériaux anisotropes si des restrictions appropriées sont imposées. Dans le cas 2D, les matériaux isotropes et à symétrie carrée sont les seuls pouvant avoir une réponse isotrope à une sollicitation isotrope. Utilisant un argument de champs uniformes, il est montré que le module de compression isotrope d'un polycristal composé de monocristaux compatibles avec les conditions établies est égal à celui d'un monocristal constituant quelconque. Ceci généralise le résultat de Hill établi pour un polycristal constitué de monocristaux cubiques.

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DOI: 10.1016/S1631-0721(03)00148-7
Keywords: Computational solid mechanics, Anisotropic elasticity, Uniform hydrostatic stress, Bulk modulus, Polycrystals, Micromechanics
Mot clés : Mécanique des solides numérique, Elasticité anisotrope, Contrainte hydrostatique uniforme, Module de compression, Polycristaux, Micromécanique

Qi-Chang He 1

1 Laboratoire de mécanique, Université de Marne-la-Vallée, 19, rue A. Nobel, 77420 Champs sur Marne, France
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Qi-Chang He. Characterization of a class of polycrystals whose effective elastic bulk moduli can be exactly determined. Comptes Rendus. Mécanique, Volume 331 (2003) no. 9, pp. 623-629. doi : 10.1016/S1631-0721(03)00148-7. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00148-7/

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