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TECHNICAL PAPERS

On the Crushing Stress of Open Cell Foams

[+] Author and Article Information
Lixin Gong

Research Center for Mechanics of Solids, Structures & Materials, The University of Texas at Austin, WRW 110, Austin, TX 78712

Stelios Kyriakides1

Research Center for Mechanics of Solids, Structures & Materials, The University of Texas at Austin, WRW 110, Austin, TX 78712skk@mail.utexas.edu

1

To whom correspondence should be addressed.

J. Appl. Mech 73(5), 807-814 (Apr 25, 2005) (8 pages) doi:10.1115/1.2047608 History: Received December 16, 2004; Revised April 25, 2005

The compressive response of many foams is characterized by an initial linearly elastic regime which is terminated by instability. For open cell foams instability leads to localized buckling and collapse of zones of cells. Local collapse in these zones is terminated by contact between cell ligaments. In the process collapse spreads to neighboring cells hitherto intact. The spreading of collapse occurs at a well-defined load plateau and continues until most of the cells are thus affected when the material response regains stiffness once more. This type of three-regime compressive response was reproduced numerically by idealizing such foams to be assemblages of space-filling Kelvin cells. The onset of instability involves a long wavelength mode. It has been established by considering a fully periodic column of cells tall enough to accommodate this mode. The crushing response has been evaluated by considering finite size microsections which allow localized deformation to develop. This paper shows that the crushing stress can also be established from the local response of the fully periodic column of cells through an energy argument leading to a Maxwell-type construction.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 6

(a) Stress-displacement responses of a finite size foam microsection. (b) Sequence of deformed configurations corresponding to response in (a).

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Figure 7

(a) Response of a fully periodic column of cells and the Maxwell construction. (b) Sequence of deformed configurations corresponding to response in (a).

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Figure 8

Comparison of crushed configurations from the finite width domain (a) and the fully periodic domain (b)

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Figure 9

(a) Fully periodic domain responses for various imperfection amplitudes. (b) Fully periodic domain responses for various contact parameter ψ values.

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Figure 10

Critical stress, limit stress, and crushing stress as a function of the foam geometric parameter ro∕ℓ

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Figure 11

Fully periodic domain stress-displacement responses for foams of three different anisotropy values

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Figure 1

(a) Compressive stress-displacement response of polyester-urethane foam. (b) Sequence of deformed configurations of crushed foam.

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Figure 2

Cluster of anisotropic Kelvin cells

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Figure 3

Geometry of foam ligaments

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Figure 4

The Kelvin foam characteristic cell

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Figure 5

(a) Calculated prebuckling and postbuckling responses in rise direction. (b) Deformed configurations of periodic column of cells.

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