We present a new approach for the numerical homogenization of cellular and heterogeneous materials. The procedure is based on the finite cell method, which is applied to efficiently discretize representative volume elements for which effective material properties are computed. The starting point for our homogenization might be either a computer-aided design of a heterogeneous material or a three-dimensional computer tomography (CT-scan) of the specimen of interest. A fully automatic discretization in terms of finite cells, applying a hierarchic extension process to control the discretization error, is utilized to solve the corresponding boundary value problems arising during the homogenization. Special emphasis is placed on the numerical treatment of boundary conditions. To this end we apply the window method, which can be interpreted as a variant of the self-consistency method. Several numerical examples ranging from porous materials to fiber-reinforced composites will be presented, demonstrating the efficiency of our approach. The homogenization procedure will be also applied to a foam, a CT-scan of which is available.
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