  Young's moduli of regular two-dimensional truss-like and eye-shape-like
structures are simulated by using the finite element method. The structures are
the idealizations of soft polymeric materials used in the electret
applications. In the simulations size of the representative smallest units are
varied, which changes the dimensions of the cell-walls in the structures. A
power-law expression with a quadratic as the exponential term is proposed for
the effective Young's moduli of the systems as a function of the solid volume
fraction. The data is divided into three regions with respect to the volume
fraction; low, intermediate and high concentrations. The parameters of the
proposed power-law expression in each region are later represented as a
function of the structural parameters, unit-cell dimensions. The presented
expression can be used to predict structure/property relationship in materials
with similar cellular structures. It is observed that the structures with
volume fractions of solid higher than 0.15 exhibit the importance of the
cell-wall thickness contribution in the elastic properties. The cell-wall
thickness is the most significant factor to predict the effective Young's
modulus of regular cellular structures at high volume fractions of solid. At
lower concentrations of solid, eye-like structure yields lower Young's modulus
than the truss-like structure with the similar anisotropy. Comparison of the
numerical results with those of experimental data of poly(propylene) show good
aggreement regarding the influence of cell-wall thickness on elastic properties
of thin cellular films.
