Numerical and analytical solutions for anisotropic yield surfaces of the open-cell Kelvin foam

• An efficient method for elastic–plastic homogenisation is presented.
• The method is applied to the Kelvin cell and the anisotropic initial and subsequent yield/failure surfaces are determined.
• An analytical solution for the initial yield/failure surface for the Kelvin cell is presented.

An analytical solution for the effective yield surface of the Kelvin cell is presented. Several local strength and yield criteria are applied like von Mises, maximum principal normal stress with and without tension/compression asymmetry. These criteria are representative for the yielding or failure of different ductile or brittle materials. Their influence on the effective failure behaviour of foams is investigated. An efficient numerical method is derived to determine anisotropic initial and subsequent yield surfaces for open-cell foams. It is applied to the Kelvin cell model and used to verify the analytical solution. The results are used to determine the conservative, isotropic minimum yield surface for the Kelvin cell. The properties of the different effective yield surfaces are evaluated and discussed.