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Effective elastic and transport properties of regular honeycombs for all densities

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
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Abstract

The effective planar elastic moduli and planar conductivity (or dielectric constant) of regular hexagonal and triangular honeycombs were investigated for the entire range of volume fractions. Only the extreme limits of the volume fraction have been studied in the past. We studied the effective properties both numerically, via finite elements, and analytically, via rigorous three-point bounds, three-point approximations, and cross-property bounds. We show here that the three-point bounds and approximations are generally in excellent agreement with the simulation data and are superior to the two-point Hashin–Shtrikman bounds. Therefore, the three-point estimates provide accurate analytical predictions of the effective properties for all densities. Both the effective bulk modulus and effective conductivity are nearly extremal in the case of hexagonal honeycombs for the entire volume-fraction range, in contrast to the effective shear modulus. In the case of triangular honeycombs, all of the property values are relatively close to being optimal. Thus, the triangular honeycomb has desirable multifunctional performance for all densities in so far as the elastic moduli, conductivity, and dielectric constant are concerned.

Type
Articles
Information
Journal of Materials Research , Volume 15 , Issue 9 , September 2000 , pp. 1985 - 1993
Copyright
Copyright © Materials Research Society 2000

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References

REFERENCES

1.Gibson, L.J. and Ashby, M., Cellular Solids (Pergamon Press, New York, 1988).Google Scholar
2.Christensen, R.M., Angew, Z.. Math. Phys. 46, S506 (1995).Google Scholar
3.Torquato, S., Gibiansky, L.V., Silva, M.J., and Gibson, L.J., Int. J. Mech. Sci. 40, 71 (1998).CrossRefGoogle Scholar
4.Jasiuk, I., Chen, J., and Thorpe, M.F., Appl. Mech. Rev. 47, S18 (1994).CrossRefGoogle Scholar
5.Thorpe, M.F., Proc. R. Soc. London, Ser. A 437, 215 (1992).Google Scholar
6.Hashin, Z. and Shtrikman, S., J. Mech. Phy. Solids 11, 127 (1963).CrossRefGoogle Scholar
7.Hashin, Z., J. Mech. Phys. Solids 13, 119 (1965).CrossRefGoogle Scholar
8.Gibiansky, L.V. and Torquato, S., J. Mech. Phys. Solids 43, 1587 (1995).CrossRefGoogle Scholar
9.Torquato, S., J. Mech. Phys. Solids 46, 1411 (1998).CrossRefGoogle Scholar
10.Eischen, J.W. and Torquato, S., J. Appl. Phys. 74, 159 (1993).CrossRefGoogle Scholar
11.Gibiansky, L.V. and Torquato, S., Phys. Rev. Lett. 71, 2927 (1993).CrossRefGoogle Scholar
12.Lurie, K.A. and Cherkaev, A.V., J. Opt. Theor. Appl. 46, 571 (1985).CrossRefGoogle Scholar
13.Francfort, G.A. and Murat, F., Arch. Ration. Mech. Anal. 94, 307 (1986).CrossRefGoogle Scholar
14.Milton, G.W., J. Mech. Phys. Solids 30, 177 (1982).CrossRefGoogle Scholar
15.Prevost, J.H., DYNAFLOW version 99 finite element solver (1999).Google Scholar
16.Day, A.R., Snyder, K.A., Garboczi, E.J., and Thorpe, M.F., J. Mech. Phys. Solids 40, 1031 (1992).CrossRefGoogle Scholar
17.Cherkaev, A.V., Lurie, K.A., and Milton, G.W., Proc. R. Soc. London, Ser. A 438, 519 (1992).Google Scholar
18.Vigdergauz, S.B., Mech. Solids 24, 57 (1989).Google Scholar
19.Vigdergauz, S.B., J. Appl. Mech. 3, 300 (1994).Google Scholar
20.Sigmund, O., J. Mech. Phys. Solids 48, 397 (1999).CrossRefGoogle Scholar
21.Hyun, S. and Torquato, S. (unpublished).Google Scholar