Shape Optimization of Biomorphic Ceramics with Microstructures by Homogenization Modeling

Ronald H. W. Hoppe () and Svetozara I. Petrova ()
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Ronald H. W. Hoppe: University of Augsburg, Institute of Mathematics
Svetozara I. Petrova: University of Augsburg, Institute of Mathematics

A chapter in Analysis, Modeling and Simulation of Multiscale Problems, 2006, pp 395-424 from Springer

Abstract: Summary We consider the modeling, simulation, and optimization of microstructural cellular biomorphic ceramics obtained by biotemplating. This is a process in biomimetics, a recently emerged discipline in materials science where engineers try to mimick or use biological materials for the design of innovative technological devices and systems. In particular, we focus on the shape optimization of microcellular silicon carbide ceramic materials derived from naturally grown wood. The mechanical behavior of the final ceramics is largely determined by the geometry of its microstructure which can be very precisely tuned during the biotemplating process. Our ultimate goal is to determine these microstructural details in such a way that an optimal mechanical performance is achieved with respect to merit criteria depending on the specific application. Within the shape optimization problem the state variables are the displacements subject to the underlying elasticity equations, and the design variables are the geometrical quantities determining the microstructure. Since a resolution of the microstructure is numerically cost-prohibitive, we use the homogenization approach, assuming periodically distributed microcells. Adaptive mesh-refinement techniques based on reliable and efficient a posteriori error estimators are applied in the microstructure to compute the homogenized elasticity coefficients. The shape optimization problem on the macroscopic homogenized model is solved by primal-dual Newton-type interior-point methods. Various numerical experiments are presented and discussed.

Keywords: Topology Optimization; Inequality Constraint; Merit Function; Posteriori Error Estimator; Shape Optimization Problem (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-35657-8_14

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DOI: 10.1007/3-540-35657-6_14

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