Three-dimensional Voronoi models are developed to investigate the mechanical behavior of linearly elastic open cellfoams. Dependence of the Young_s modulus, Poisson_s ratio and bulk modulus of the foams on the relative density isevaluated through finite element analysis. Obtained results show that in the low density regime the Young_s modulusand bulk modulus of random Voronoi foams can be well represented by those of Kelvin foams, and are sensitive to thegeometric imperfections inherent in the microstructure of foams. In contrast, the compressive plateau stress of thefoams is less sensitive to the imperfections. Failure surface of the foams subject to multi-axial compression is determinedand is found to comply with the maximum compressive principal stress criterion, consistent with available experimentalobservations on polymer foams. Numerical results also show that elastic buckling of cell edges at microscopiclevel is the dominant mechanism responsible for the compressive failure of elastic open cell foams.

The constrained deformation of an aluminium alloy foam sandwiched between steel substrateshas been investigated. The sandwich plates are subjected to through-thickness shear and normalloading, and it is found that the face sheets constrain the foam against plastic deformation andresult in a size e$ect: the yield strength increases with diminishing thickness of foam layer.The strain distribution across the foam core has been measured by a visual strain mappingtechnique, and a boundary layer of reduced straining was observed adjacent to the face sheets.The deformation response of the aluminium foam layer was modelled by the elastic-plastic6nite element analysis of regular and irregular two dimensional honeycombs, bonded to rigidface sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elementswas set to zero to simulate full constraint from the rigid face sheets. It is found that the regularhoneycomb under-estimates the size e$ect whereas the irregular honeycomb provides a faithfulrepresentation of both the observed size e$ect and the observed strain pro6le through the foamlayer. Additionally, a compressible version of the Fleck–Hutchinson strain gradient theory wasused to predict the size e$ect; by identifying the cell edge length as the relevant microstructurallength scale the strain gradient model is able to reproduce the observed strain pro6les across thelayer and the thickness dependence of strength.

A Dugdale-type cohesive zone model is used to predict the mode I crack growth resistance(R-curve) of metallic foams, with the fracture process characterised by an idealised tractionseparationlaw that relates the crack surface traction to crack opening displacement. A quadraticyield function, involving the von Mises effective stress and mean stress, is used to accountfor the plastic compressibility of metallic foams. Finite element calculations are performed forthe crack growth resistance under small scale yielding and small scale bridging in plane strain,with K-field boundary conditions. The following effects upon the fracture process are quantified:material hardening, bridging strength, T-stress (the non-singular stress acting parallel tothe crack plane), and the shape of yield surface. To study the failure behaviour and notchsensitivity of metallic foams in the presence of large scale yielding, a study is made for panelsembedded with either a centre-crack or an open hole and subjected to tensile stressing. Forthe centre-cracked panel, a transition crack size is predicted for which the fracture responseswitches from net section yielding to elastic-brittle fracture. Likewise, for a panel containinga centre-hole, a transition hole diameter exists for which the fracture response switches fromnet section yielding to a local maximum stress criterion at the edge of the hole.

A unifed framework of constructing phenomenological constitutive models for a broad class of elasto-plastic materials exhibiting either plastical incompressibility (e.g., grey cast iron) or plastical compressibility (e.g., metal foams) is proposed. The constitutive framework also enables the di.erent yielding behaviours under tension and compression as well as di.erential hardening along di.erent loading paths to be accounted for in a relatively simple manner. The resulting plasticity model does not require the diffcult task of experimentally probing the initial yield surface and its subsequent evolution; it is completely determined from a set of as few as two distinctive stress

The infuence of each of the six di.erent types of morphological imperfection