Linear Elastic Properties of 2-D and 3-D Models of Porous Materials Made From Elongated Objects.
Linear Elastic Properties of 2-D and 3-D Models of
Porous Materials Made From Elongated Objects.
Meille, S.; Garboczi, E. J.
Modeling and Simulation in Materials Science and
Engineering, Vol. 9, 371-390, 2001.
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porous materials; elastic properties; morphology;
elastic moduli; finite elements; Young's modulus;
Poisson's ratio; statistical fluctuation; finite size
effect; digital resolution
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 in which the solid
backbone is formed by different random arrangements 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 average the numerical
results over random crystal orientation properly. The
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.