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TECHNICAL PAPERS

The Deformation Habits of Compressed Open-Cell Solid Foams

[+] Author and Article Information
Y. Wang, G. Gioia, A. M. Cuitiño

Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854

J. Eng. Mater. Technol 122(4), 376-378 (Apr 15, 2000) (3 pages) doi:10.1115/1.1288923 History: Received January 04, 2000; Revised April 15, 2000
Copyright © 2000 by ASME
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References

Artavia, L. D., and Macosko, C. W., 1994, “Polyurethane flexible foam formation,” Low Density Cellular Plastics: Physical Basis of Behavior, Hilyard, N. C., and Cunningham, A., eds., Chapter 2, pp. 22–55, Chapman & Hall, United Kingdom.
Gibson, L. J., and Ashby, M. F., 1997, Cellular Solids, 2nd ed., Cambridge University, United Kingdom.
Fatı́ma Vaz,  M., and Fortes,  M. A., 1993, “Characterization of deformation bands in the compression of cellular materials,” J. Mater. Sci. Lett., 12, pp. 1408–1410.
Wang,  Y., and Cuitiño,  A. M., 2000, “Three dimensional modeling of open cell foams with large deformations,” J. Mech. Phys. Solids, 48, p. 961.
Ericksen, J. L., 1998, Introduction to the Thermodynamics of Solids, 2nd ed., Chapter 3, Springer-Verlag, New York.
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Sutton,  M. A., Cheng,  M. Q., Peters,  W. H., Chao,  Y. J., and McNeill,  S. R., 1986, “Application of an optimized digital correlation method to planar deformation analysis,” Image Vis. Comput., 4, pp. 143–151.
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Figures

Grahic Jump Location
(a) Microstructure of an open-cell polyurethane solid foam in the vicinity of a pore. (b) This view of the surface of a specimen, where the foam was severed across a plane, reveals the nearly regular microstructure which prevails in most of the foam. (c) Simple model of the microstructure as a regular, three-dimensional network of bars. The four-bar structure in the upper right corner of the figure is the basic unit of the network. The direction indicated in the upper left corner of the figure is the rise direction of the foam 1. (d) Mechanical response of the foam (a-b) subject to uniaxial compressive stretch along the rise direction.
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(a) When the foam is subject to a uniaxial stretch in the rise direction, the four-bar basic unit of Figure 1(c) can be reduced to a two-bar basic unit. The bars are linear elastic of Young’s modulus E and circular cross section of radius r(A=πr2); they are ruled by Von Kármán’s theory of beams. The tilted bar is in actuality three bars, each with the same cross-sectional radius as the vertical bar. (b) Predicted strain energy density of the foam as a function of the applied uniaxial stretch. We have used L1/L=1.5,δ=cos−1(2/7), and the r/L ratio which corresponds to a foam of relative density ρr=0.01.
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(a) For an overall applied stretch λ̄ the total strain energy can be minimized by a straightforward nonconvex analysis. The mechanical response of the foam is governed by ϕ̄(λ). Thus the stress for a given λ̄ is σ=−dϕ̄/dλ|λ=λ̄. (b) Inhomogeneous distribution of stretch in the specimen. The high- and low-density phases may not be connected, as shown here, but mixed with each other, see Section 2; the volume fraction α is always given by the compatibility condition, Eq. (1). (c) Microstructure of the low-density phase (before snap-through buckling). (d) Microstructure of the high-density phase (after snap-through buckling).
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Experimental (light gray, same curve as in Fig. 1(d)) and predicted stress-stretch curves for the foam of Fig. 1(a)–(b). The predictions are those of the reduced model of Fig. 2(a), properly convexified, with L1/L=1.5,δ=cos−1 (2/7), and the r/L ratio which corresponds to a foam of relative density ρr=0.01. To fit the curves we have used E=68 MPa and ρ=730 Kgm−3 for the bars (the apparent density of the foam is ρ=21.9 Kgm−3); these are reasonable values, within a factor of 2 of the expected ones (perhaps E=50 MPa and ρ=1000 Kgm−3, see 2). The resulting characteristic stretches are λL=0.91 and λH=0.60.
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Displacement field measured by the Digital Image Correlation (DIC) technique. The specimen is subject to an overall stretch in the y direction. v is the displacement along the y direction (y is measured in the original configuration). The units of x,y, and v are pixels. (a) Contour plot of the displacement field v(x,y) on the surface of the specimen. The plot consists of lines of equal v at regular intervals Δv. (b) Plot of the displacement v along the dotted line of (a), and the characteristic slopes which correspond to λL=0.91 and λH=0.60 (from Fig. 4).

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