Gibson-Ashby & Deshpande-Fleck Models for Cellular Foams

⚠️ Important Disclaimer

The Gibson-Ashby model describes the three-stage compression behavior of cellular foams: elastic, plateau, and densification. The Deshpande-Fleck extension adds isotropic hardening to the plateau region, where the slope is controlled by hardening coefficient H.

References: Gibson, L.J., Ashby, M.F., "Cellular Solids: Structure and Properties", 2nd edition, Cambridge University Press, 1997. Deshpande, V.S., Fleck, N.A., "Isotropic constitutive models for metallic foams", Journal of the Mechanics and Physics of Solids, 2000.

Note: This interactive calculator shows typical foam behavior patterns. Use experimentally determined parameters for design calculations.

Gibson-Ashby & Deshpande-Fleck Models

E*/Es = C₁(ρ*/ρs)²
σ*/σs = C₃(ρ*/ρs)^1.5
σ(ε) = σpl[1 + H(ε - εy)]
where: E* - foam elastic modulus, Es - solid elastic modulus, σ* - foam plateau stress, σs - solid yield strength, ρ*/ρs - relative density, C₁, C₃ - material constants
Deshpande-Fleck: H - hardening coefficient (0 = pure plateau, >0 = hardening slope)

🔧 Units Settings

kg/m³
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