A continuum plasticity model for the constitutive and indentation behaviour of foamed metals

A yield surface is proposed that can be fitted to the plastic flow properties of a broad class of solids exhibiting plastic compressibility and different yield points in tension and compression. The yield surface is proposed to describe cellular solids, including foamed metals, and designed to be fitted to three experimental results: (1) the compressive stress–strain response (including densification), (2) the difference between the tensile and compressive yield points and (3) the degree of compressibility of the foam, as measured by the lateral expansion during a uniaxial stress compression test. The model is implemented using finite elements and used to study the effects of plastic compressibility on two problems: the compression of a doubly notched specimen and indentation by a spherical indenter. The model is then fitted to the properties of a typical closed cell aluminum foam and used to study indentation into a dense aluminum face sheet on a foam foundation. The dependence of the indentation load–displacement curve on the relevant material and geometric parameters is determined, and a single load–displacement relation is presented which approximates the behaviour of a wide range of practical designs. These results can be used to design against indentation failure of sandwich panels.