Vol. 2, No. 8, 2007

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ISSN: 1559-3959
Representative volume element and effective elastic properties of open cell foam materials with random microstructures

Sergey Kanaun and Oleksandr Tkachenko

Vol. 2 (2007), No. 8, 1607–1628
Abstract

This work is devoted to the problem of the numerical simulation of effective elastic properties of open-cell foam materials. The Laguerre tessellation procedure is used for the construction of skeletons of random foam microstructures with prescribed distributions of cell diameters. A four-parametric approximation of the ligament shapes in the open-cell foams is proposed. A version of the finite element method, based on the Timoshenko beam finite element, is developed for calculating stresses and strains in the foam ligaments and the solution of the homogenization problem. The size of the representative volume element for reliable calculations of the effective elastic properties of the foam materials is evaluated on the basis of a series of numerical experiments. The dependences of the effective elastic properties of the open-cell foams on cell size distributions and on ligament shapes are obtained and analyzed.

Keywords
open-cell foams, representative volume element, random space tessellation, homogenization problem, finite element method, elastic constants
Milestones
Received: 19 June 2006
Accepted: 8 May 2007
Published: 1 October 2007
Authors
Sergey Kanaun
Departamento de Ingenieria Mecánica
Instituto Tecnológico y de Estudios Superiores de Monterrey
Campus Estado de México
Carretera Lago de Guadalupe 4 km Atizapan
Edo de México, 52926
Mexico
Oleksandr Tkachenko
Departamento de Ingenieria Mecánica
Instituto Tecnológico y de Estudios Superiores de Monterrey
Campus Estado de México
Carretera Lago de Guadalupe 4 km Atizapan
Edo de México, 52926
Mexico