Keywords: sandwich sheets, aluminium foam, four points bending, analytical model, finite element method.

The aim of this paper is to compare different models for the evaluation of the stress state in aluminium foam sandwich panels [1,2] subjected to a four point bending, highlighting the effects of distance between the supports and of the core and plate thickness. Several arm distances between the rollers in the range of 25-60 mm have been considered. The opportunity to apply a laminated plate classical theory solution for determining the state of plane stress of flat symmetric laminates was studied in [3], in which Pagano affirmed that this theory can be applied on composites for width/thickness ratios greater than 4. In the case examined, this ratio is included between 2.5 and 4 for specimens having 32 and 20 mm thickness respectively.

The reliability of the analytical model has been compared with a numerical model of the different aluminium foam sandwiches. Finite element analysis was performed using the Abaqus 6.9 software, adopting a discretization using elements having 20 nodes and a quadratic reduced integration formulation. The simplest model considered isotropic elastic behaviour both for aluminium plate and foam. Elasto-plastic isotropic hardening and crushable foam models have been used for the aluminium foam. A comparison between numerical and analytical results calculated for each aluminium foam sandwich (AFS) geometry and loading configuration showed that the maximum stress values are localised in the core-skin interface. Values of maximum stress calculated using analytical and numerical models are greatly different. In particular, the analytical model gives stresses that are generally two to three times higher than those calculated using a numerical model. However, the analytical model, in which bending is the only acting stress, is often not acceptable since compressive stresses due to local application of the load have generally the same magnitude as the bending stress. In fact, better results of laminated plate classical theory are obtained especially for AFS characterised by a small foam/skin thickness ratio. For this reason, it is more appropriate to consider a Von Mises equivalent stress rather than the bending stress to describe the stress state in the foam.

1

M.F. Ashby, A.G. Evans, N.A. Fleck, L.J. Gibson, J.W. Hutchinson, H.N.G. Wadley, "Metal Foams: A Design Guide", Butterworth-Heinemann publications, 2000.

2

J. Banhart, "Manufacture, characterization and application of cellular metals and metal foams", Progress in Materials Science, 46, 559-632, 2001. doi:10.1016/S0079-6425(00)00002-5

3

N.J. Pagano, "Exact solutions for rectangular bidirectional composites and sandwich plates", Journal of Composite Materials, 4, 20-34, 1970. doi:10.1016/0010-4361(70)90076-5

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