Numerical homogenization procedures for materials with complex micro-structure

Prof. Dr.-Ing. habil. Alexander Düster

April 29, 2011, 9 a.m. HF 9904

Two di erent numerical procedures to homogenize foamed and heteroge-
neous materials will be presented. In the rst part of the talk the FE approach
will be considered and applied to compute foamed materials. The FE method
is a two-scale (micro/macro) approach where both the macro-model and the
micro-model are discretized with nite elements. The constitutive model is
replaced by attaching to each integration point on the macro-level a micro-
model, representing the micro-structure of the material. The homogenization
of the micro-model yields the constitutive answer, i.e. the stress-strain relation.
Several numerical examples will demonstrate the properties of this two-scale
approach. Since the FE method is computationally very demanding we will
consider in the second part of the presentation an alternative approach which
is based on the computation of e ective material properties. This approach uti-
lizes the Finite Cell Method (FCM) which can be interpreted as a combination
of a ctitious domain method with nite elements of high-order. Starting from
a computed tomography of the material of interest the FCM can be applied
to compute its e ective material properties very eciently. Several examples
ranging from porous and reinforced materials to foams will demonstrate this
approach.