Definition of a unified material model for cellular materials with high morphological and topological dispersion: Application to an AA7075-T6 aluminium foam

The compression behaviour in quasi-static and dynamic conditions of cellular materials is crucial for their applications both for ensuring structural strength and high energy absorption capability. Despite the recent progress made in understanding the experimental observations, analytical and numerical modelling still requires improvements in the Representative Volume Element (RVE) identification that can be uncertain due to the limited dimensions of the investigated specimens and to the cell inhomogeneity. The objective of this paper is to implement a material model able to consider the statistical distribution so that its effect can be quantitatively highlighted, mitigating uncertainty of the RVE identification. The applied methodology started with morphological and topological analyses on samples extracted from an ingot of AA7075T6 foam, which was manufactured by compact powder technology. Quasi-static and dynamic experimental compression tests have been carried out and compared with 3D mesoscale numerical simulations in order to correlate the mechanical behaviour of the foam to the cell characteristics. Finally, an equivalent material model, which is a function of the statistical distributions of cells morphology and topology, has been proposed and analytically verified.