The crushable foam model in Abaqus comes from the work of Depshande & Fleck :
Deshpande, V. S., and N. A. Fleck, “Isotropic Constitutive Model for Metallic Foams,” Journal of the Mechanics and Physics of Solids, vol. 48, pp. 1253–1276, 2000
It is an elasto-plastic model with pressure-dependent yield surface. While first developed based on work for metallic foams, it is also used for polymer foams such as expanded polystyrene foams.
Polymeric Foams
Benchmark Manual 3.2.7 - Dytherm phenolic foam
Expanded Polystyrene foam (EPS)
Metallic Foams (under construction)
Aluminum foams - Deshpande & Fleck (2000)
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