Modelling of metal foams by a modified elastic law

• Multiscale modelling of metal foams: Microscale to macroscale.
• Development of a new and simple phenomenological constitutive continuum model.
• Rheological spring model for build-up of stress fluctuations in macromodel.
• Mesostructural simulation of RVE for validation.

Metal foams are bio-inspired microheterogeneous materials with great potential for application in lightweight construction or as kinetic energy absorbers. Based on their complex microstructure, the global properties depend strongly on the local properties of the microstructure. According to the compressible behaviour of metal foams, there is a localised damage in crushing zones with a thickness of several pores. Size effects are very important. The built-up of deformation bands with strain localisation and damage localisation causes stress-fluctuations in the macroscopic stress-strain curve.In this contribution, starting from a simplified microstructural motivated 1D rheological model, a RVE-based continuum model, which allows the explicit consideration of size effects, is developed by the projection of microstresses on the macroscale. For simplification, a one-pore model for the RVE is used. Different types of one-pore functions and discretisations were analysed. In a second step, the results are compared with fully resolved micromodels with different number of pores in order to find the right size for the RVE.

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