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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Z. Hashin and S. Shtrikman, J. Appl. Phys. 33, 3125 (1962).
K.A. Lurie and A.V. Cherkaev, J. Opt. Theor. Appl. 46, 571 (1985).
A.N. Norris, Mech. Mater. 4, 1 (1985).
G.W. Milton, in Homogenization and Effective Moduli of Materials and Media, edited by J.L. Eriksen, D. Kinderlehrer, R. Kohn, and J.L. Lions (Springer-Verlag, New York, 1986).
G.A. Francfort and F. Murat, Arch. Rat. Mech. Anal. 94, 307 (1986).
S.B. Vigdergauz, Mech. Solids 24, 57 (1989); S.B. Vigdergauz, J. Appl. Mech. 3, 300 (1994).
S. Hyun and S. Torquato, J. Mater. Res. 15, 1985 (2000).
M.P. Bendsoe and N. Kikuchi, Comp. Meth. Appl. Mech. Eng. 71, 197 (1988).
O. Sigmund and S. Torquato, J. Mech. Phys. Solids 45, 1037 (1997).
C. Kittel, Introduction to Solid State Physics, 2nd ed. (John Wiley & Sons, New York, 1956).
S. Torquato, L.V. Gibiansky, M.J. Silva, and L.J. Gibson, Int. J. Mech. Sci. 40, 71 (1998).
R.M. Christensen, Int. J. Solids Struc. 37, 93 (2000).
M.P. Bendsoe and O. Sigmund, Arch. Appl. Mech. 69, 635 (1999).
S. Hyun and S. Torquato, J. Mater. Res. 16, 280 (2001).
N. Karmarkar, Combinatoria 4, 373 (1984).
S. Vigdergauz (unpublished).
I. Syozi, Prog. Theor. Phys. VI, 306 (1951).
P.W. Anderson, Phys. Rev. 102, 1008 (1956).
G. Aeppli and P. Chandra, Science 275, 177 (1997).
I.S. Hagemann, Q. Hunag, X.P.A. Gao, A.P. Ramirez, and R.J. Cava, Phys. Rev. Lett. 86, 894 (2001).
M.J. Higgins, Y. Xiao, S. Bhattacharya, P.M. Chaikin, S. Sethuraman, R. Bojko, and D. Spencer, Phys. Rev. Lett. 61, R894 (2000).
S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer-Verlag, New York, 2002).
J. Chen, M.F. Thorpe, and L.C. Davis, J. Appl. Phys. 77, 4349 (1995).
L.J. Gibson and M. Ashby, Cellular Solids, 2nd ed. (Pergamon Press, New York, 1997).
D.J. Sypeck and H.N.G. Wadley, J. Mater. Res. 16, 890 (2001).
S. Chiras, D.R. Mumm, A.G. Evans, N. Wicks, J.W. Hutchinson, K. Dharmasena, H.N.G. Wadley, and S. Fichter, Int. J. Solids Struct. (in press).
S. Hyun, A.M. Karlsson, S. Torquato, and A.G. Evans (unpublished).
S. Gu, T.J. Lu, and A.G. Evans (unpublished).
M. Zhang, Y. Nakayama, and L. Pan, Jpn. J. Appl. Phys. 39, L1242 (2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hyun, S., Torquato, S. Optimal and Manufacturable Two-dimensional, Kagomé-like Cellular Solids. Journal of Materials Research 17, 137–144 (2002). https://doi.org/10.1557/JMR.2002.0021
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/JMR.2002.0021