Numerical prediction of the macroscopic material response for the design of solid foams with structural hierarchy

The present study is concerned with a scheme for numerical prediction of the macroscopic properties of hybrid foams as composite material consisting of two cellular constituents. For their numerical analysis, a hierarchical homogenization procedure has been established, consisting in repeated determination of the effective properties on different levels of structural hierarchy. The homogenization analysis is performed by means of an energy based approach which can be applied to both, mechanical and thermal problems as well as to infinitesimal and to finite strain problems, irrespectively of the materials constitutive behavior. In a comparison with experimental data for the example of a metal-ceramic hybrid foam, the numerical scheme proves to provide accurate results. In interaction with experimental characterization, the numerical approach enables an efficient design of complex materials by a reduction of the extensive experimental effort otherwise required for parameter studies. Furthermore, it enables the optimization and tailoring of the material to fit with prescribed requirements in structural application using mathematical optimization procedures.