A Comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai Equations
نویسندگان
چکیده
منابع مشابه
The Halpin-Tsai Equations: A Review
The Halpin-Tsai equations are based upon the “selfconsistent micromechanics method” developed by Hill. Hermans eniplovetf this model to obtain a solution in terms of Hill’s “reduced moduli”. Halpin and ’Tsai have reduced Hernians’ solution to a simpler analytical form arid extended its use for a variety of filament geometries. The development of these niicromechanics relationships, which form t...
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In this paper we consider the problem of characterizing the set of the effective tensors of multiphase composites, including those of conductive materials and elastic materials. We first present a novel derivation of the Hashin-Shtrikman (HS) bounds for multiphase composites and the associated attainment condition. The attainment condition asserts that the HS bound is attainable if and only if ...
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This paper addresses the attainability of the Hashin-Shtrikman bounds for multiphase composites, including those of conductive materials and elastic materials. It presents a new derivation of these bounds that yield a necessary and sufficient condition for optimal microstructures. A key idea is a simple characterization of the gradient Young measures associated with optimal microstructures.
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The recently developed variational framework for polarization methods in nanocomposites is applied to the determination of a lower-bound on the shear modulus of a nanocomposite with monosized, spherical inclusions. This bound explicitly accounts for linear elastic effects in the matrix-inclusion interface. Even if the polarization fields involved in its derivation are much more intricate, this ...
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Although methods to determine optimal Hashin–Shtrikman bounds for polycrystals of cubic to monoclinic symmetry have been described, the calculation of bounds for triclinic crystals has not previously been possible. The recent determination of elastic moduli of common minerals with low symmetry provides motivation to extend the Hashin–Shtrikman formulation to lower symmetry. Here, Hashin– Shtrik...
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ژورنال
عنوان ژورنال: Applications of Mathematics
سال: 1997
ISSN: 0862-7940,1572-9109
DOI: 10.1023/a:1023034411371