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Elastomeric foam

For elastomeric cellular solids, as the foam is compressed, first it behaves elastically as the cell walls bend, then as the cell walls buckle there is yielding and breakdown of the material until finally the cell walls crush together and the material ruptures. This is seen in a stress-strain curve as a steep linear elastic regime, a linear regime with a shallow slope after yielding (plateau stress), and an exponentially increasing regime. The stiffness of the material can be calculated from the linear elastic regime where the modulus for open celled foams can be defined by the equation:

(E ∗ E s) f = C f (ρ ∗ ρ s) 2 {\displaystyle \left({\frac {E^{*}}{E_{s}}}\right)_{f}=C_{f}\left({\frac {\rho ^{*}}{\rho _{s}}}\right)^{2}}

where E s {\displaystyle E_{s}} is the modulus of the solid component, E ∗ {\displaystyle E^{*}} is the modulus of the honeycomb structure, C f {\displaystyle C_{f}} is a constant having a value close to one, ρ ∗ {\displaystyle \rho ^{*}} is the density of the honeycomb structure, and ρ s {\displaystyle \rho _{s}} is the density of the solid. The elastic modulus for closed cell foams can be described similarly by:

(E ∗ E s) f = C f (ρ ∗ ρ s) 3 {\displaystyle \left({\frac {E^{*}}{E_{s}}}\right)_{f}=C_{f}\left({\frac {\rho ^{*}}{\rho _{s}}}\right)^{3}}

where the only difference is the exponent in the density dependence. However, in real materials, a closed-cell foam has more material at the cell edges which makes it more closely follow the equation for open-cell foams. The ratio of the density of the honeycomb structure compared with the solid structure has a large impact on the modulus of the material. Overall, foam strength increases with density of the cell and stiffness of the matrix material.