Non-destructive, high-precision imaging techniques provide a wealth of information on
the internal structure of materials used for a variety of applications, ranging from
structural composites to biomedical devices. The main issue to deal with is the large
amount of generated data, and the numerical resources required to process it. In this
work high-resolution X-ray computed tomography is chosen to investigate a closed-cell
polyethylene terephthalate (PET) foam available in four different densities, typically used
for composite sandwiches. The resulting set of images is used for both morpho-structural
and finite element analyses. The material spatial distribution is computed by exploiting
the Mean Intercept Length (MIL) algorithm, as proposed by Moreno [1]. Other
macroscopic structural parameters are extracted, such as solid volume fraction and
mean structure thickness, with the aim of identifying a relationship with macroscopic
mechanical properties. Since the reconstruction of the entire inspected volume would
result into a prohibitive number of finite elements, a 2D statistical approach is developed.
The sets of images are divided into smaller subdomains for which individual morphostructural
properties are computed. The density and the material spatial distribution are
represented by a synthetic parameter called degree of anisotropy (DA): a 2D frequency
statistics is derived and for each sample the most frequent domain is detected and then
converted into a finite element mesh, by exploiting the marching cube algorithm. For each
domain finite element analyses are run under elementary loading conditions [2] and the
macroscopic stress and strain tensors evaluated through Gurson’s homogenization
algorithm; the homogenized compliance matrix is assembled to obtain a set of orthotropic
elastic constants. The approach is validated with uniaxial compression data; then, all the
sub-domains are considered as valid samples to be reconstructed and simulated to
broaden the range of investigated structural and mechanical properties. This larger
dataset allows the identification of global macroscopic relationships between structural
parameters and elastic constants.
REFERENCES
[1] R. Moreno, M. Borga and O. Smedby, Medical physics 39(7):4599-4612, 2012.
[2] V.Kouznetsova, M.G.D. Geers and W.A.M. Brekelmans, International Journal for
Numerical Methods in Engineering 54(8):1235-1260, 2002
