Irregular metallic foams have been simulated using Voronoi three-dimensional structures generated with a spatial uniform probabilistic distribution of germination nuclei.

A detailed finite element model has been created starting from the foam geometry and a probabilistic macroscopic or "equivalent" elasticity matrix has been deduced by means of the strain energy based homogenization approach.

The Bayesian approach has been used to perform a global sensitivity analysis of each parameter representing the foam cell geometry on the "equivalent" mechanical properties of the foam.

Afterwards, the information obtained has been used to perform a probabilistic optimization of a sandwich plate with a metallic foam core by means of a non-sorted genetic algorithm.

To better perform an optimization process, considering also the uncertainty in the equivalent foam mechanical properties, a meta-model based on a Gaussian process and an uncertainty propagation algorithm have been used.

The sensitivity analysis shows that all the considered geometric parameters influence the foam relative density. The most important parameter, obviously, is the cell wall thickness. Increasing the number of cells and fixing the representative volume element (RVE) dimensions, the relative density increases and at the same time, also the elastic constants values increase, this being due to the decreasing average volume of each cell. Also the RVE dimensions affect the values of the elastic constants; in particular, stretching the RVE in a selected direction influences the corresponding value of the elastic modulus.

Increasing the number of cells, the density rate variance decreases, as also the scattering of the elastic constants does; with a small number of cells the random nuclei germination selection process influences the mechanical properties, increasing the number of cells whereas their position is less important. At the same time, increasing the RVE dimensions the position of the cells becomes more important, and this causes a higher scattering in the mechanical properties. In the second part of this work a reliability based robust design optimization (RBRDO) of a sandwich panel with a foam core is performed.

During the optimization process the relative density of the foam tends to decrease. Generally, the y-length of the RVE is bigger than the x-length because the optimization process is attracted by an orthotropic foam core to better support the uniaxial compression load and to the increase the corresponding critical load.

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