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Mathematical Modeling and Design

  • Tohru Hirano and Kenji Wakashima

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For the design of functionally gradient materials (FGMs), necessary material properties, such as thermal-expansion-coefficient and Young's modulus in the specific region, are optimized by controlling the distribution profiles of composition and microstructures, as well as micropores in the materials. For this purpose, our research team employs the inverse design procedure in which both the basic material combination and the optimum profile of the composition and microstructures are determined with respect to the objective structural shape and the thermomechanical boundary conditions. Figure 1 shows the inverse design procedure for FGM, in which the final structure to be developed, as well as the boundary conditions, are specified first. After the fabrication method and an allowable material combination are selected from the FGM database, the estimation rules for the material properties of the intermediate compositions are determined based upon the micro-structure. Then, the temperature distribution and the thermal-stress distribution are calculated with the assumed profiles of the distribution functions for the constituents. Other possible combinations and different profiles are also investigated until the optimum is obtained.

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1.Hirano, T., Teraki, J., and Yamada, T., in Proc. 1st Int. Symp. on FGM, edited by Yamanouchi, M., Koizumi, M., Hirai, T., and Shiota, I. (FGM Forum, Tokyo, Japan, 1990) p. 5.
2.Eshelby, J.D., Proc. R. Soc. London A241 (1957) p. 376.
3.Wakashima, K., Otsuka, M., and Umekawa, S., J. Compos. Mater. 8 (1974) p. 391.
4.Kawasaki, A. and Watanabe, R., Proc. FGM'89 (1989) p. 35, in Japanese.
5.Hirano, T., Teraki, J., and Yamada, T., SMiRT 11 Trans. SD1 (1991) p. 49.
6.Sugano, Y., Ingenieur-Archiv 57 (1987) p. 147.
7.Teraki, J., Hirano, T., and Wakashima, K., Ceram. Trans. 34 (1993) p. 67.

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Mathematical Modeling and Design

  • Tohru Hirano and Kenji Wakashima

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