Stress and couple stress in foams

Even in the range of small elastic deformations the behavior of foams is not well described by only two elastic constants. Usually the manufacturers give values of the material parameters depending on the loading conditions. This problem is investigated on a microscopic scale by a simple beam model. It has been found that this approach shows the size effect that cannot be described within the framework of the standard continuum mechanical setting. The size effect within this model can be explained by independent rotations which do not scale with the displacement field. genization procedure is proposed that allows for the determination of macroscopic quantities like stress and couple stress in terms of volumetrical averages. The homogenized results of the microscopic model are compared to the results obtained by an enhanced macroscopic model, namely a Cosserat model. Both approaches show good agreement.