Eur.J.Mech. - A/Solids 34, 21-37, 2012
B. Klusemann1, H.J. Böhm2, B. Svendsen1
1Material Mechanics, RWTH Aachen,
2Institute of Lightweight Design and Structural Biomechanics,
TU Wien, Vienna, Austria
The purpose of this work is comparing three strategies for dealing with
inhomogeneities of non-elliptical shape in the context of homogenization
First, classical mean-field methods and two relatively new approaches, IDD and
ESCS, are used in combination with analytical expressions for the Eshelby
tensor based on its irreducible decomposition.
The second strategy to be investigated is the Mori-Tanaka method in combination
with the replacement tensor approach, which uses numerical models of dilute
inhomogeneities embedded in large matrix regions.
The third approach consists of the direct Finite Element discretization of
The elasticity tensors and directional Young’s moduli are first studied for
arrangements of aligned inhomogeneities of three different shapes and of
combinations of these shapes.
Subsequently the three modeling strategies are applied to a real
Comparisons are not only carried out with respect to phase volume fractions,
but also with respect to the contrast in the elastic phase properties.
All calculations are restricted to plane strain conditions and to isotropic