Reference: S. Meille and E.J. Garboczi, Mod. Sim. Mater. Sci. 9, (5), 371-390, 2001.

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Linear Elastic Properties of 2-D and 3-D Models of Porous Materials Made From Elongated Objects

S. Meille

INSA Lyon, GEMPPM Laboratory
20, Ave Albert Einstein
63621 Villeurbanne Cedex
and

Lafarge LCR
95, rue du Montmurier, BP 15
38 291 S^t Quentin Fallavier Cedex, FRANCE

E.J. Garboczi
National Institute of Standards and Technology
Building Materials Division
100 Bureau Drive Stop 8621
Gaithersburg, MD 20878-8621

Abstract

Porous materials are formed in nature and by man by many different processes. The nature of the pore space, which is usually the space left over as the solid backbone forms, is often controlled by the morphology of the solid backbone. In particular, sometimes the backbone is made from the random deposition of elongated crystals, which makes analytical techniques particularly difficult to apply. This paper discusses simple two and three dimensional porous models whose solid backbone is formed by different random arrangement of elongated solid objects (bars/crystals). We use a general purpose elastic finite element routine designed for use on images of random porous composite materials to study the linear elastic properties of these models. Both Young's modulus and Poisson's ratio depend on the porosity and the morphology of the pore space, as well as on the properties of the individual solid phases. The models are random digital image models, so that the effects of statistical fluctuation, finite size effect, and digital resolution error must be carefully quantified. It is shown how to properly average the numerical results over random crystal orientation. Relations between two and three dimensions are also explored, as most microstructural information comes from two dimensional images, while most real materials and experiments are three dimensional.

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