The classical problem of bounding the effective bulk modulus of isotropic polycrystalline aggregates built from a single anisotropic phase is studied. For three-dimensional composites we find that the Voigt and Reuss bounds are each attained by multi-layered laminate geometries, and hence are optimal. For two-dimensional composites, the Reuss lower bound is proved to be optimal while a new, optimal, upper bound is derived.
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Avellaneda et al. (1989) studied this question.
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