A New Methodology to Establish Upper Bounds on Open-Cell Foams Homogenized Properties

A New Methodology to Establish Upper Bounds on Open-Cell Foams Homogenized Properties

The methodology for determining the upper bounds on the homogenized linear elastic properties of cellular solids, described for the two-dimensional case in Dimitrovová and Faria (1999), is extended to three-dimensional open-cell foams. Besides the upper bounds, the methodology provides necessary and...

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Bibliographic Details
Main Author: Z. Dimitrovová
Format: Article
Language:English
Published: CTU Central Library 2004-01-01
Series:Acta Polytechnica
Subjects:
upper bounds on effective properties
open-cell foams
homogenization techniques
energy methods
optimization
optimal microstructures
Online Access:https://ojs.cvut.cz/ojs/index.php/ap/article/view/652
Description
Summary:The methodology for determining the upper bounds on the homogenized linear elastic properties of cellular solids, described for the two-dimensional case in Dimitrovová and Faria (1999), is extended to three-dimensional open-cell foams. Besides the upper bounds, the methodology provides necessary and sufficient conditions on optimal media. These conditions are written in terms of generalized internal forces and geometrical parameters. In some cases dependence on internal forces can be replaced by geometrical expressions. In such cases, the optimality of some medium under consideration can be verified directly from the microstructure, without any additional calculation. Some of the bounds derived in this paper are published for the first time, along with a proof of their optimality. 
ISSN:1210-2709
1805-2363

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