Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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New third-order bounds on the effective moduli of $ N$-phase composites


Authors: N. Phan-Thien and G. W. Milton
Journal: Quart. Appl. Math. 41 (1983), 59-74
MSC: Primary 73K20
DOI: https://doi.org/10.1090/qam/700661
MathSciNet review: 700661
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Abstract: We develop some new bounds on the effective moduli of $ N$-phase composites. These new bounds are accurate up to and including terms of third order in $ O\left( {\left\vert {{K_i} - {K_j}} \right\vert,\left\vert {{\mu _i} - {\mu _j}} \right\vert} \right)$, where $ {K_i}$ and $ {\mu _i}$ are the bulk and shear modulus, respectively, of phase $ i$. These bounds use the same statistical information as McCoy's and Beran-Molyneux's bounds but are tighter than, or at worst coincident with, the latter bounds. We also present in the appendix a new perturbation solution for the effective moduli which only requires that $ \left\vert {\delta \mu } \right\vert = O\left( {\left\vert {{\mu _i} - {\mu _j}} \right\vert} \right)$ be small.


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DOI: https://doi.org/10.1090/qam/700661
Article copyright: © Copyright 1983 American Mathematical Society


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