Modeling macroscopic extended continua with the aid of numerical homogenization schemes

While macroscopic material parameters are generally unknown for foams the macroscopic properties are derived from the microscale where the parameters are assumed to be known. After evaluation of the microscopic constitutive equations, which are also considered to be known, the quantities are mappped back to the macroscale by a homogenization procedure. This approach is known from literature as FE2 model, see e.g. [V. Kouznetsova, Computational homogenization for the multi-scale analysis of multi-phase materials, PhD-thesis, Technical University of Eindhoven, 2002], [Int. J. Numer. Meth. Eng., 54 (2002) 1235] or [Arch. Appl. Mech., 72 (2002) 300]. It is shown that the Cosserat continuum and the FE2 model are able to describe the same effects qualitatively.