  The development of materials with specific structural properties is of huge
practical interest, for example, for medical applications or for the
development of light weight structures in aeronautics. In this article, we
combine shape optimization and homogenization for the optimal design of the
microstructure in scaffolds. Given the current microstructure, we apply the
isogeometric boundary element method to compute the effective tensor and to
update the microstructure by using the shape gradient in order to match the
desired effective tensor. Extensive numerical studies are presented to
demonstrate the applicability and feasibility of the approach.
