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TECHNICAL PAPERS

High Strain Extension of Open-Cell Foams

[+] Author and Article Information
N. J. Mills, A. Gilchrist

School of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham B15 2IT, U.K.

J. Eng. Mater. Technol 122(1), 67-73 (Apr 22, 1999) (7 pages) doi:10.1115/1.482767 History: Received August 20, 1998; Revised April 22, 1999
Copyright © 2000 by ASME
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References

Kelvin,  Lord, Thompson,  W.), 1887, “On the Division of Space with Minimum Partitional Area,” Philos. Mag., 24, pp. 503–514.
Zhu,  H. X., Mills,  N. J., and Knott,  J. F., 1997, “Analysis of the High Strain Compression of Open-Cell Foams,” J. Mech. Phys. Solids, 45, pp. 1875–1904.
Warren,  W. E., and Kraynik,  A. M., 1997, “Linear Elastic Behavior of a Low-Density Kelvin Foam with Open Cells,” ASME J. Appl. Mech., 64, pp. 787–794.
Gent,  A. N., and Thomas,  A. G., 1959, “The Deformation of Foamed Elastic Materials,” J. Appl. Polym. Sci., 1, pp. 107–113.
Lederman,  J. M., 1971, “The Prediction of the Tensile Properties of Flexible Foams,” J. Appl. Polym. Sci., 45, pp. 693–703.
Ko,  W. L., 1965, “Deformations of Foamed Elastomers,” J. Cell. Plast., 1, pp. 45–50.
Dement’ev,  A. G., and Tarakanov,  O. G., 1970, “Model Analysis of Plastics Foams of the Polyurethane Type,” Mekh. Polim., 6, pp. 859–865; [Polym. Mech., 6, pp. 744–749].
Warren,  W. E., and Kraynik,  A. M., 1991, “The Non-Linear Elastic Behavior of Open-Cell Foams,” ASME J. Appl. Mech., 58, pp. 376–3811.
Pajon, M., Backacha, M. et al., 1996, “Modelling of PU Foam Behavior-Applications in the Field of Automotive Seats,” SAE SP-1155, paper 960513.
El-Ratal,  W. H., and Mallick,  P. K., 1996, “Elastic Response of Flexible Polyurethane Foams in Uniaxial Tension,” ASME J. Eng. Mater. Technol., 118, pp. 157–161.
Dawson,  J. R. and Shortall,  J. B., 1982, “The Microstructure of Rigid Polyurethane Foam,” J. Mater. Sci., 17, pp. 220–224.
Zhu,  H., Knott,  J. P., and Mills,  N. J., 1997, “The Elastic Constants of Open Cell Foams Having Tetrakaidecahedral Cells,” J. Mech. Phys. Solids, 45, pp. 319–343.
Phelan,  R., Weaire,  D., Peters,  E. A. J. F., and Verbist,  G., 1996, “The Conductivity of a Foam,” J. Phys.: Condens. Matter, 8, pp. L475–L482.
Warren,  W. E., Neilsen,  M. K., and Kraynik,  A. M., 1997, “Torsional Rigidity of a Plateau Border,” Mech. Res. Commun., 24, pp. 667–672.
Schulmeister, V., 1998, “Modelling of the Mechanical Properties of Low Density Polymer Foams,” Ph.D. thesis, Technical University of Delfit.
Mills,  N. J., and Gilchrist,  A., 1997, “The Effect of Heat Transfer and Poisson’s Ratio on the Compressive Response of Closed Cell Polymer Foams,” Cell. Polym., 16, pp. 87–119
Kraynik, A. M., Neilsen, M. K., Reinhelt, R. A., and Warren, W. E., 1999, “Foam Micromechanics,” NATO Adv. Sci. Inst. Series E: Appl. Sci., Vol. 354, Foams and Emulsions, N. Rivier and J. F. Sadok, eds., Kluwer, pp. 187–204.
Zhu,  H. X., and Mills,  N. J., 1999, “Analysis of Creep in Open-Cell Foams,” J. Mech. Phys. Solids, 47, pp. 1437–1457.

Figures

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A uniaxial tensile stress σz applied in the [001] direction of a Kelvin open cell foam. Chains of edges, like those in bold, take the load.
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(a) The structural cell for [001] direction tension of the Kelvin foam, (b) the effective load on the half-edge BO. Its shape is shown for 20% foam strain.
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The predicted reduced stress-strain relation for the Kelvin foam loaded in the [001] and [111] directions, using Plateau border edges, plus Shulmeister’s 15 random cell prediction [[dashed_line]] with circular section edges, all for a relative density of 0.025
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The maximum edge tensile strain versus the foam tensile strain, for the Kelvin foam extended in the [001] and [111] directions, with the same parameters as Fig. 3
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Predicted variation of Poisson’s ratio with foam tensile strain, for the Kelvin foam loaded in the [001] and [111] directions as in Fig. 3, compared with El-Ratal and Mallick’s Poisson’s ratio data • 10 for a commercial PU foam (increased by 0.15 to make the comparison easier)
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(a) xy projection of a triangular prism showing two sloping edges and two half horizontal edges, in both the undeformed and deformed states, for [111] direction extension of the Kelvin foam by 20%. G lies beneath and R above the plane of the projection (b) a perspective view of the force and moments applied at G to the edge CG.
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Predicted Kelvin foam cell shape for 20% tensile strain in the [111] direction, seen in perspective with the stress axis vertical
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Stress strain curve for a PU uphoistery foam of relative density 0.021, loaded in the plane of the sheet, cycled three times to 25% strain at a nominal strain rate of 0.005 s−1 . The Kelvin foam [111] predictions are [[dotted_line]] for equiaxed cells and [[dashed_line]] for cells with edges initially at 45 deg to the stress, using E=100 MPa for the polyurethane.
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Lateral contraction in the rise – and in-plane [[dashed_line]] directions versus tensile strain for the same experiment as Fig. 8, for cycles 2 and 3

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