Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-14T09:38:57.825Z Has data issue: false hasContentIssue false
  • English
  • Français

Digital-Image-Based Study of Circular Holes in an Elastic Matrix

Published online by Cambridge University Press:  21 February 2011

A. R. Day,
M. F. Thorpe,
K. A. Snyder and
E. J. GarBoczi
A. R. Day
Affiliation:
Marquette University Dept. of Physics, Milwaukee, WI 53233
M. F. Thorpe
Affiliation:
Michigan State University, Dept. of Physics and Astronomy, East Lansing, MI 48824
K. A. Snyder
Affiliation:
National Institute of Standards and Technology, Building Materials Division, Bldg. 226, Room B348, Gaithersburg, MD 20899
E. J. GarBoczi
Affiliation:
National Institute of Standards and Technology, Building Materials Division, Bldg. 226, Room B348, Gaithersburg, MD 20899
Get access

Abstract

Using a digital-image-based representation of a continuum composite, we apply computer simulation techniques to obtain the elastic moduli of a matrix containing randomly-centered circular voids. As the area fraction of the voids increases, the elastic moduli of the composite decrease until they eventually vanish at the percolation threshold. We compare our results with an effective medium theory, which predicts that Poisson ratio tends to a fixed value as the percolation threshold is approached, independent of the values of the elastic moduli in the pure system. Our results are also compared with recent experimental results.

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.)

Article purchase

Temporarily unavailable

References

[1] For a review, see for example Watt, J.P., Davies, G.F., and O'Connell, R.J., Rev. Geoph. Space Phys. 14, 541 (1976).CrossRefGoogle Scholar
[2] Gawlinski, E.T. and Stanley, H.E., J. Phys. A: Math. Gen. 14, L291 (1981).Google Scholar
[3] Castleman, K.R., Digital Image Processing (Prentice-Hall, Englewood Cliffs, 1979).Google Scholar
[4] Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T., Numerical Recipes (Cambridge University Press, Cambridge, England, 1989).Google Scholar
[5] Cook, R.D., Malkus, D.S., and Plesha, M.E., Concepts and Applications of Finite Element Analysis. Third Edition (John Wiley and Sons, New York, 1989).Google Scholar
[6] Feng, S. and Sen, P.N., Phys. Rev. Letts. (1984).Google Scholar
[7] Feng, S., Thorpe, M.F., and Garboczi, E.J., Phys. Rev. B 31, 276 (1985).Google Scholar
[8] Thorpe, M.F. and Sen, P.N., J. Acoust. Soc. Am. 77, 1674 (1985).Google Scholar
[9] This algorithm was written by and can be obtained from Day, A.R., at the address given above.Google Scholar
[10] Xia, W. and Thorpe, M.F., Phys. Rev. A38, 2650 (1988).CrossRefGoogle Scholar
[11] Garboczi, E.J., Thorpe, M.F., deVries, M., and Day, A.R., “Universal Conductance Curve for a Plane Containing Random Holes”, submitted to Phys. Rev. A.Google Scholar
[12] Stauffer, Dietrich, Introduction to Percolation Theory (Taylor and Francis, London, 1985).Google Scholar
[13] Sofo, J., Lorenzana, J., and Martinez, E.N., Phys. Rev. B35, 3960 (1987).Google Scholar
[14] Lobb, C.J. and Forrester, M.G., Phys. Rev. B35, 1899 (1987).CrossRefGoogle Scholar
[15] Halperin, B.J., Feng, S., and Sen, P.N., Phys. Rev. Lett. 54, 2391 (1985).Google Scholar