Modeling and homogenization of foams

Abstract

The mechanical modeling of foams is discussed on a microscopic, mesoscopic and macroscopic scale. A homogenization procedure is proposed to relate the models and to give detailed insight into the deformation behavior of foams. The mesoscopic model of open-cell foams is based on beam elements and evaluated for regular hexagonal structures considering small deformations. This approach gives rise to a Cosserat continuum on the macroscopic scale. Especially the misfit in the parameters governing the standard macroscopic model can be explained by the proposed homogenization procedure. This misfit results from the neglect of the rotations of the cell walls, see Diebels and Steeb [6, 7].