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Computation of the Linear Elastic Properties of Random Porous Materials With a Wide Variety of Microstructure.

Computation of the Linear Elastic Properties of Random
Porous Materials With a Wide Variety of Microstructure.
(1995 K)

Roberts, A. P.; Garboczi, E. J.

Mathematical, Physical and Engineering Sciences Royal
Society of London, Series A. Vol. 458, No. 2021.
Proceedings. 2002, 1033-1054 pp, 2002.

### Keywords:

porous materials; structure-property relationships;
theoretical mechanics; porour media; elasticity;
percolation

### Abstract:

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A finite-element method is used to study the elastic
properties of random three-dimensional porous materials
with highly interconnected pores. We show that the
Young's modulus, E, is practically independent of the
Poisson's ratio of the solid phase, {upsilon}s, over the
entire solid fraction range, and the Poisson's ratio,
{upsilon}, becomes independent of {upsilon} s as the
percolation threshold is approached. We represent this
behavior of {upsilon} in a flow diagram. This
interesting but approximate behaviour is very similar to
the exactly known behavior in two-dimensional porous
materials. In addition, the behavior of {upsilon} versus
{upsilon} s appears to imply that information in the
dilute porosity limit can affect behavior in the
percolation threshold limit. We summarize the finite
element results in terms of simple structure-property
relations, instead of tables of data, to make it easier
to apply the computational results. Without using
accurate numerical computations, one is limited to
various effective medium theories and rigorous
approximations like bounds and expansions. The accuracy
of these equations is unknown for general porous media.
To verify a particular theory it is important to check
that it predicts both isotropic elastic moduli; i.e.,
prediction of the Young's modulus alone is necessary but
not sufficient. The subleties of the Poisson's ratio
behavior actually provide a very effective method for
showing differences between the theories and
demonstrating their ranges of validity. We find that for
moderate- to high-porosity materials, none of the
analytical theories is accurate and at present,
numerical techniques must be relied upon.
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