Mater.Trans. 47(9), 2213-2218, 2006.
T. Daxner, R. Bitsche, H.J. Böhm
Institute of Lightweight Design and Structural Biomechanics,
TU Wien, Vienna, Austria
The simulation of the mechanical behavior of idealized cellular structures
is important as it gives insight into the principal deformation mechanisms
that govern the mechanical behavior of real cellular structures, such as
polymer foams or metallic foams, making accessible at least qualitative
information about properties that are difficult to determine otherwise, for
example the effective strength under hydrostatic loading.
For capturing the mechanics of a closed-cell foam material in a meaningful way,
three-dimensional models are employed in the context of the Finite Element
The modeling approach presented in this paper employs generic, periodic unit
cell models with the extension of providing physically sound microstructures
by basing these models on surfaces of minimal energy calculated with the
program Surface Evolver.
This program is able to minimize the energy of a surface subject to given
constraints, for example a prescribed initial geometry and, where required,
Accordingly, space-filling polyhedra with cells being separated by walls of
minimal total area can be predicted, such as Lord Kelvin's
tetrakaidecahedra or the Weaire-Phelan partition, the latter being
energetically more favorable.
These physics-based configurations are good representations of solidified (dry)
The results obtained by Finite Element stress and deformation analyses comprise
the full tensor of elasticity and its dependence on the effective density; the
non-planar faces resulting from the surface energy minimization are shown to
influence the behavior for very low effective densities.
By studying the behavior up to the onset of yielding on the effective,
macro-mechanical level including the effects of multi-axial loading conditions,
valuable information for the homogenized representation of closed-cell foams is