Adaptive grid refinement for computation of the homogenized elasticity tensor

Abstract

Optimal structural design of microstructured materials is one of the central issues of material science. The paper deals with the shape optimization of microcellular biomorphic silicon carbide ceramics produced from natural wood by biotemplating. Our purpose is to achieve an optimal performance of the new composite materials by solving a nonlinear optimization problem under a set of equality and inequality constraints. The microscopic geometric quantities serve as design parameters within the optimization procedure. Adaptive grid-refinement technique based on reliable and efficient a posteriori error estimators is applied in the microstructure to compute the homogenized elasticity coefficients. Some numerical results are included and discussed. Keywords: biomorphic microcellular ceramics, shape optimization, homogenization technique, adaptive refinement, a posteriori error estimators. © Springer-Verlag 2004.