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Optimal shape design in biomimetics based on homogenization and adaptivity

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  • Hoppe, Ronald H.W.
  • Petrova, Svetozara I.

Abstract

Optimal shape design of microstructured materials has recently attracted a great deal of attention in materials science. The shape and the topology of the microstructure have a significant impact on the macroscopic properties. The paper is devoted to the shape optimization of new biomorphic microcellular silicon carbide ceramics produced from natural wood by biotemplating. This is a novel technology in the field of biomimetics which features a material synthesis from biologically grown materials into ceramic composites by fast high-temperature processing. We are interested in finding the best material-and-shape combination in order to achieve the optimal prespecified performance of the composite material. The computation of the effective material properties is carried out using the homogenization method. Adaptive mesh-refinement technique based on the computation of recovered stresses is applied in the microstructure to find the homogenized elasticity coefficients. Numerical results show the reliability of the implemented a posteriori error estimators.

Suggested Citation

  • Hoppe, Ronald H.W. & Petrova, Svetozara I., 2004. "Optimal shape design in biomimetics based on homogenization and adaptivity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(3), pages 257-272.
    • Handle: RePEc:eee:matcom:v:65:y:2004:i:3:p:257-272
    DOI: 10.1016/j.matcom.2004.01.002
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    Cited by:

    1. Hoppe, Ronald H.W. & Petrova, Svetozara I., 2007. "Elasto-plasticity model in structural optimization of composite materials with periodic microstructures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(6), pages 468-480.

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