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Mathematics and Mechanics of Solids
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Bounds for the Elastic Shear Moduli of Isotropic and Quasi-Symmetric Composites, and Exact Modulus of the Coated Sphere Assemblage

Duc Chinm Pham

Institute of Mechanics, 224 Doi Can, Hanoi, Vietnam

A relation between the geometric parameters appearing in the bounds for isotropic composites is found, which leads to some new results. Improved upper and lower bounds on the effective shear modulus of isotropic multicomponent materials are deduced, which are expressed in the moduli and volume fractions of the components and reduce to Hashin-Shtrikman bounds in the case of well-ordered composites (i.e., when the extremal bulk and shear moduli belong to the same phases). The respective improved bounds for the subclass of quasi-symmetric composites are given. The shear modulus of Hashin's celebrated coated sphere assemblage is determined. The model also verifies the optimality of the bounds for isotropic two-component materials over a certain range of parameters, including those of the well-ordered case.

Mathematics and Mechanics of Solids, Vol. 4, No. 1, 57-69 (1999)
DOI: 10.1177/108128659900400104
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