A comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai equations
type: Item
instance of: scholarly article
title: A comparison of homogenization, Hashin-Shtrikman bounds and the Halpin-Tsai equations
zbMATH Open document ID: 0898.35007
DOI: 10.1023/A:1023034411371
published in: Applications of Mathematics
publication date: 1998-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/32980
review text: The effective parameters of composite materials can be computed by homogenization from properties of the components. Since this computation is not simple (the formulae contain solutions of auxiliary partial differential equations) their estimates are useful. The paper deals with unidirectional elastic fiber composite. Using homogenization the effective parameters (the bulk modulus \(k\) and shear modulus \(\mu \)) are computed for carbon-epoxy composites with different volume fraction of the components. The results are compared with Hashin-Shtrikman bounds, the values are close to the lower bounds. Halpin-Tsai equations with a fitting parameter \(\xi \) represent another approximation of \(k\) and \(\mu \). Using the Hashin-Shtrikman bounds optimal bounds on the fitting parameter \(\xi \) are derived.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74E05
zbMATH DE Number: 1203987
zbMATH Keywords: auxiliary partial differential equations
zbMATH Keywords: unidirectional elastic fiber composite
zbMATH Keywords: fitting parameter
author: Peter Wall
MaRDI profile type: Publication
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OpenAlex ID: W1559679998
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description: scientific article; zbMATH DE number 1203987