Ronald H. W. Hoppe and Svetozara I. Petrova
Institute of Mathematics
University of Augsburg
Germany
emails: {hoppe,petrova}@math.uni-augsburg.de
The optimization of the macroscopic behavior of microstructured materials using microscopic quantities as design variables is a well established discipline in materials science. The paper deals with structural optimization of microcellular biomorphic ceramic materials. We apply advanced optimization techniques to the mechanical macromodel obtained by homogenization. The homogenized elasticity tensor and its dependence on the design variables are computed numerically involving adaptive finite element approximations of elasticity problems in the 3-D periodicity cell. Efficient iterative solvers based on algebraic multigrid method (AMG) and incomplete Cholesky (IC) decomposition as preconditioners of the stiffness matrix are proposed in the application of PCG method.