Mechanical Behavior of Elastomeric Foams
Cellular solids are made up of interconnected networks of solid struts or plates that form the edges and faces of cells. Foams are made up of polyhedral cells that pack in three dimensions. The foam cells can be either open (e.g., sponge) or closed (e.g., flotation foam). Common examples of elastomeric foam materials are cellular polymers such as cushions, padding, and packaging materials that utilize the excellent energy absorption properties of foams: the energy absorbed by foams is substantially greater than that absorbed by ordinary stiff elastic materials for a certain stress level.
Another class of foam materials is crushable foams, which undergo permanent (plastic) deformation. Crushable foams are discussed in Crushable Foam Plasticity Models.
Foams are commonly loaded in compression. Figure 1 shows a typical compressive stress-strain curve.
Three stages can be distinguished during compression:
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At small strains (< 5%) the foam deforms in a linear elastic manner due to cell wall bending.
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The next stage is a plateau of deformation at almost constant stress, caused by the elastic buckling of the columns or plates that make up the cell edges or walls. In closed cells the enclosed gas pressure and membrane stretching increase the level and slope of the plateau.
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Finally, a region of densification occurs, where the cell walls crush together, resulting in a rapid increase of compressive stress. Ultimate compressive nominal strains of 0.7 to 0.9 are typical.
The tensile deformation mechanisms for small strains are similar to the compression mechanisms, but they differ for large strains. Figure 2 shows a typical tensile stress-strain curve.
There are two stages during tension:
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At small strains the foam deforms in a linear, elastic manner as a result of cell wall bending, similar to that in compression.
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The cell walls rotate and align, resulting in rising stiffness. The walls are substantially aligned at a tensile strain of about 1/3. Further stretching results in increased axial strains in the walls.
At small strains for both compression and tension, the average experimentally observed Poisson's ratio, ν, of foams is 1/3. At larger strains it is commonly observed that Poisson's ratio is effectively zero during compression: the buckling of the cell walls does not result in any significant lateral deformation. However, ν is nonzero during tension, which is a result of the alignment and stretching of the cell walls.
The manufacture of foams often results in cells with different principal dimensions. This shape anisotropy results in different loading responses in different directions. However, the hyperfoam model does not take this kind of initial anisotropy into account.