We present results of a two-scale model of disordered cellular materials
where we describe the microstructure in an idealized manner using a beam
network model and then make a transition to a Cosserat-type continuum model
describing the same material on the macroscopic scale. In such scale
transitions, normally either bottom-up homogenization approaches or top-down
reverse modelling strategies are used in order to match the macro-scale
Cosserat continuum to the micro-scale beam network. Here we use a different
approach that is based on an energetically consistent continuization scheme
that uses data from the beam network model in order to determine continuous
stress and strain variables in a set of control volumes defined on the scale of
the individual microstructure elements (cells) in such a manner that they form
a continuous tessellation of the material domain. Stresses and strains are
determined independently in all control volumes, and constitutive parameters
are obtained from the ensemble of control volume data using a least-square
error criterion. We show that this approach yields material parameters that are
for regular honeycomb structures in close agreement with analytical results.
For strongly disordered cellular structures, the thus parametrized Cosserat
continuum produces results that reproduce the behavior of the micro-scale beam
models both in view of the observed strain patterns and in view of the
macroscopic response, including its size dependence
