Institute of Fundamental Technological Research

Three kinds of cellular materials are considered. Depending on geometry and physical properties of the skeleton, these are metallic cellular materials with convex or reentrant open cell structure. To the third group belong alumina foams produced by gel casting method. Finite element computations are used to analyse mechanical properties of a material volume. Such an analysis is usually related with big computational costs. Therefore, it is important to keep the size of the considered cellular material volume as small as possible. On the other hand, the validity of the continuum model requires the proper size of the RVE. The aim of the study is to estimate the sufficient size of representative volume element (RVE) in order to assess the validity of the elastic model of the considered cellular material. An array of cubes of virtual cellular material is used to compute the particular deformation modes providing elastic moduli, Young modulus E, shear modulus G and bulk modulus K as well as the resulting Poisson's ratio. Also the results of the microtomography of alumina foams are used to create the „virtual cellular material” i.e. the numerical model reconstructing the structure of real foam skeleton. The numerical simulations of compression test are performed. The results are compared with experimental data of elastic moduli and failure strength. The numerical simulations of failure strength under compression for alumina foams are performed. The calculations with use of the numerical model are time consuming. Therefore, the simplified method of the assessment of failure strength is proposed. It is based on the energy-based hypothesis on the equivalence of of elastic moduli and the resulting equivalence of the values of failure strength of real alumina foam and the cellular material with regular structure (e.g. fcc type). The justification of the hypothesis based on experimental data of compression of alumina foam are discussed and the range of validity as regards porosity values is studied.

virtual cellular materials, convex skeleton, reentrant skeleton. representative volume element, numerical simulations