Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-30T18:12:02.996Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal and Manufacturable Two-dimensional, Kagomé-like Cellular Solids

Published online by Cambridge University Press:  31 January 2011

S. Hyun  and
S. Torquato
S. Hyun
Affiliation:
Princeton Materials Institute and Department of Chemistry, Princeton University, Princeton, New Jersey 08544
S. Torquato
Affiliation:
Princeton Materials Institute and Department of Chemistry, Princeton University, Princeton, New Jersey 08544
Get access

Abstract

We used the topology optimization technique to obtain two-dimensional, isotropic cellular solids with optimal effective elastic moduli and effective conductivity. The overall aim was to obtain the best (simplest) manufacturable structures for these effective properties, i.e., single-length-scale structures. Three different but simple periodic structures arose due to the imposed geometric mirror symmetries: lattices with triangular-like cells, hexagonal-like cells, or Kagomé-like cells. As a general rule, the structures with the Kagomé-like cells provided the best performance over a wide range of densities, i.e., for 0 ≰ ф <0.6, where ф is the solid volume fraction (density). At high densities (ф > 0.6), Kagome-like structures were no longer possible, and lattices with hexagonal-like or triangular-like cells provide virtually the same optimal performance. The Kagomé-like structures were found to be a new class of cellular solids with many useful features, including desirable transport and elastic properties, heat-dissipation characteristics, improved mechanical strength, and ease of fabrication.

Type
Articles
Information
Journal of Materials Research , Volume 17 , Issue 1 , January 2002 , pp. 137 - 144
Copyright
Copyright © Materials Research Society 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Hashin, Z. and Shtrikman, S., J. Mech. Phy. Solids 11, 127 (1963); Z. Hashin, J. Mech. Phys. Solids 13, 119 (1965).CrossRefGoogle Scholar
Hashin, Z. and Shtrikman, S., J. Appl. Phys. 33, 3125 (1962).CrossRefGoogle Scholar
Lurie, K.A. and Cherkaev, A.V., J. Opt. Theor. Appl. 46, 571 (1985).CrossRefGoogle Scholar
Norris, A.N., Mech. Mater. 4, 1 (1985).CrossRefGoogle Scholar
Milton, G.W., in Homogenization and Effective Moduli of Materials and Media, edited by Eriksen, J.L., Kinderlehrer, D., Kohn, R., and Lions, J.L. (Springer-Verlag, New York, 1986).Google Scholar
Francfort, G.A. and Murat, F., Arch. Rat. Mech. Anal. 94, 307 (1986).CrossRefGoogle Scholar
Vigdergauz, S.B., Mech. Solids 24, 57 (1989); S.B. Vigdergauz, J. Appl. Mech. 3, 300 (1994).Google Scholar
Hyun, S. and Torquato, S., J. Mater. Res. 15, 1985 (2000).CrossRefGoogle Scholar
Bendsoe, M.P. and Kikuchi, N., Comp. Meth. Appl. Mech. Eng. 71, 197 (1988).CrossRefGoogle Scholar
Sigmund, O. and Torquato, S., J. Mech. Phys. Solids 45, 1037 (1997).CrossRefGoogle Scholar
Kittel, C., Introduction to Solid State Physics, 2nd ed. (John Wiley & Sons, New York, 1956).Google Scholar
Torquato, S., Gibiansky, L.V., Silva, M.J., and Gibson, L.J., Int. J. Mech. Sci. 40, 71 (1998).CrossRefGoogle Scholar
Christensen, R.M., Int. J. Solids Struc. 37, 93 (2000).CrossRefGoogle Scholar
Bendsoe, M.P. and Sigmund, O., Arch. Appl. Mech. 69, 635 (1999).Google Scholar
Hyun, S. and Torquato, S., J. Mater. Res. 16, 280 (2001).CrossRefGoogle Scholar
Karmarkar, N., Combinatoria 4, 373 (1984).CrossRefGoogle Scholar
Vigdergauz, S. (unpublished).Google Scholar
Syozi, I., Prog. Theor. Phys. VI, 306 (1951).CrossRefGoogle Scholar
Anderson, P.W., Phys. Rev. 102, 1008 (1956).CrossRefGoogle Scholar
Aeppli, G. and Chandra, P., Science 275, 177 (1997).CrossRefGoogle Scholar
Hagemann, I.S., Hunag, Q., Gao, X.P.A., Ramirez, A.P., and Cava, R.J., Phys. Rev. Lett. 86, 894 (2001).CrossRefGoogle Scholar
Higgins, M.J., Xiao, Y., Bhattacharya, S., Chaikin, P.M., Sethuraman, S., Bojko, R., and Spencer, D., Phys. Rev. Lett. 61, R894 (2000).Google Scholar
Torquato, S., Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer-Verlag, New York, 2002).CrossRefGoogle Scholar
Chen, J., Thorpe, M.F., and Davis, L.C., J. Appl. Phys. 77, 4349 (1995).CrossRefGoogle Scholar
Gibson, L.J. and Ashby, M., Cellular Solids, 2nd ed. (Pergamon Press, New York, 1997).CrossRefGoogle Scholar
Sypeck, D.J. and Wadley, H.N.G., J. Mater. Res. 16, 890 (2001).CrossRefGoogle Scholar
Chiras, S., Mumm, D.R., Evans, A.G., Wicks, N., Hutchinson, J.W., Dharmasena, K., Wadley, H.N.G., and Fichter, S., Int. J. Solids Struct. (in press).Google Scholar
Hyun, S., Karlsson, A.M., Torquato, S., and Evans, A.G. (unpublished).Google Scholar
Gu, S., Lu, T.J., and Evans, A.G. (unpublished).Google Scholar