Three dimensional modelling of closed-cell aluminium foams with predictive macroscopic behaviour

This study presents an efficient approach to generate a realistic micromechanical model for closed-cell foams using irregular Voronoi models. Starting with a reference microstructure consisting of regular Kelvin cells, the nucleating points underlying each reference unit cell is subjected to a random displacement, the magnitude of which depends on the pore size and a misalignment parameter. For convenience, the misalignment parameter is calibrated from available statistical data on unit cell geometries for the commercially available closed-cell aluminium foam, and a common value is utilised for all cases considered. Numerical analyses with the irregular 3D micromechanical models are done using ABAQUS/Explicit. Considering both uniaxial and hydrostatic compressive loading cases, the numerical responses compare well with the experimental data in literature, over a wide range of relative densities. The deformation mechanism is next elaborated. In uniaxial compression, the deformation initiates at the weaker regions induced by the geometrical irregularities, before evolving into a localized deformation band through the coalescence between neighbouring regions of local weakness. This localized deformation band forms an irregular 3D relief in space, a phenomenon which cannot be captured by regular periodic microstructures. In hydrostatic compression, the irregular geometry also induces deformation through cell wall bending. In tension, a stretching mode induces a shift in the yield surface towards the positive mean stress quadrant, which is consistent with experimental observations. The proposed approach thus generates the irregular 3D microstructures efficiently through a single calibrated misalignment parameter, leading to realistic deformation mechanisms, with good predictions on the macroscopic behaviour, over a wide range of relative densities and different loading conditions.