Determination of the Local Stress-Strain Response of Foams

[+] Author and Article Information
T. Wierzbicki, M. Doyoyo

Impact and Crashworthiness Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139

J. Appl. Mech 70(2), 204-211 (Mar 27, 2003) (8 pages) doi:10.1115/1.1546242 History: Received September 27, 2001; Revised April 16, 2002; Online March 27, 2003
Copyright © 2003 by ASME
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Andrews,  E. W., Gioux,  G., Onck,  P., and Gibson,  L. J., 2001, “Size Effects in Ductile Cellular Foams. Part II: Experimental Results,” Int. J. Mech. Sci., 43, p. 701.
Wierzbicki, T., 1997, “Experimental, Numerical and Analytical Study of Honeycomb Material,” Report No. 1: Joint MIT/Industry Ultralight Consortium, Impact and Crashworthiness Laboratory, MIT, Cambridge, MA, Nov.
Hanssen, A. G., Hopperstad, O. S., Langseth, M., and Ilstad, H., 2000, “Validation of Constitutive Models Applicable to Aluminum Foams,” Ph.D. thesis, Norwegian University of Science and Technology.
Wierzbicki, T., Doyoyo, M., and Markaki, A., 2001, “Redefining the Concept of Stress-Strain Curve for Foams,” Cellular Metals and Metal Foaming Technology, Ed.: J. Banhart, M. Ashby, and N. Fleck, eds., Verlag MIT Publishing, Germany, pp. 449–453.
Bastawros,  A. F., and Evans,  A. G., 2000, “Deformation Heterogeneity in Cellular Al Alloys,” Adv. Eng. Mat., 4 , p. 210.
Doyoyo, M., and Wierzbicki, T., 2000, “Fracture of Aluminum Honeycombs and Foams Under Hemi-spherical Punch Indentation,” Report No. 38: Joint MIT/Industry Ultralight Consortium, Impact and Crashworthiness Laboratory, MIT, Cambridge, MA, June.
Marciniak, 1965, private communication.
McClintock,  F. A., and Zheng,  Z. M., 1993, “Ductile Fracture in Sheets Under Transverse Strain Gradients,” Int. J. Fract., 64, p. 321.
Doyoyo, M., and Wierzbicki, T., 2002, “Measurement of the Failure Surface for Ductile and Brittle Foams,” Plasticity, Damage and Fracture at Macro, Micro and Nano Scales, A. Khan and O. Lopez-Pamies, eds., Neat Press, pp. 114–116.
Doyoyo, M., and Wierzbicki, T., 2002, “Experimental Studies on Yield Behavior of Ductile and Brittle Aluminum Foams Under a Biaxial State of Stress,” Int. J. Plast., in press.
Gibson, L. J., and Ashby, M. F., 1997, Cellular Solids: Structure and Properties, 2nd Ed., Cambridge University Press, Cambridge, UK.
Malvern, L. E., 1969, Introduction to the Mechanics of a Continuous Media, Prentice-Hall, Englewood Cliffs, NJ.


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The variation of load with crushing displacement during compression of foam trapezoids. The load increases linearly with crushing displacement beyond the initial plateau load.
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(a) Photographs of the 80 deg tapered specimen at subsequent stages of uniaxial compression. (b) The photograph of the original 75 deg tapered specimen and the deformed tapered specimen after compression down to a height of 130 mm. The specimen develops new lateral shapes during compression.
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(a) Final shapes of the crushed regions of the tapered specimens obtained from digitized photographs. (b) The evaluation of the power-type function, which describes the lateral shape of the deformed specimens.
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(a) Foam block crushed to 80 times the initial peak load is compared photographically to the uncrushed block. (b) The conventional stress-strain curve corresponding to the crushing of the foam block to densification and locking.
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The variation of local plastic Poisson’s ratio with local engineering strain during crushing of the 257 kg/m3 dense Alporas foam trapezoid
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Local stress-strain response in foams for different values of n, according to Eq. (17) for zero plastic Poisson’s ratio. The pattern is similar for the variable Poisson’s ratio case in Eq. (23) as the values of n are the same for the two cases.
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The effect of specimen size in conventional stress-strain curves obtained by compressing the 257 kg/m3 dense Alporas foam cubes
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The local versus conventional stress-strain responses in the 257 kg/m3 dense Alporas foam
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A typical stress-strain curve of a closed-cell metallic foam cube under uniaxial compression. The plastic regime is characterized by a plateau stress, followed by a hardening region, which eventually leads to densification and locking.
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A section through a block of Cymat aluminum alloy foam, which was indented by a hemi-spherical punch (Doyoyo and Wierzbicki 6). A distinct boundary/interface separates the crushed and uncrushed regions.
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(a) A schematic of the original tapered specimen (dotted line) and the deformed specimen (solid line). The crushing front propagates down the specimen, separating the crushed cells (shaded region) from the uncrushed cells ahead of the front. The effect of the plastic Poisson’s ratio is shown when point A moves vertically (v) and horizontally (u) to point A1 during loading. (b) A schematic showing how the original points A and B in the undeformed specimen travel to their current positions A1 and B1 in the deformed specimen during loading.



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