Methods of Mathematical-Physics Applied to Polymer Composites

Salvatore Mazzullo


The aim of this lecture note is twofold:
1. To provide a detailed analytical derivation of the Kerner’s classical homogenization formulae
because the original paper by E.H. Kerner is particularly concise and difficult to understand.
Moreover, in the past, the geometrical assumption the model uses to justify the mathematical
treatment of the homogenizing process was subject to great criticism. For this reason, the original
paper was critically re-examined, the homogenizing procedure newly stated as weight average
of matrix/particle and matrix/matrix stress distribution and the equations of the model were
re−derived accordingly. This critical effort confirmed that Kerner’s original formulae are correct.
2. To set−up a novel experimental method to predict the elastic properties of MgCl2 particles and
their derived Ziegler−Natta catalysts which are spherical in shape and have an average diameter
of few tenths of a micron. The novel method is derived by inverting Kerner’s classical model
which describes a particulate filled material consisting of micro-spheres randomly dispersed in a
matrix and perfectly bound to the matrix.

[DOI: 10.1685/SELN08003] About DOI

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