The size effect in foams and its theoretical and numerical investigation

Experimental data for foams lead to different values of the elastic moduli depending on the performed test, i.e. compression and tension tests give a different set of parameters than shear and bending tests. This may be explained by the size effect, which depends on the microstructure of the foams. Thus, in this paper, the behaviour of foams is investigated on the basis of both microscopic and macroscopic mechanical models. The microscopic approach is based on a lattice beam model. The solution of this model shows that the boundary-layer effect is strongly local but allows for the explanation of the size effect. Furthermore, the size effect can be included in the macroscopic continuum model by application-of a Cosserat formulation. The extended continuum model allows for the independent fit of material parameters to different load cases, i.e. to compression and shear. The solution of the macroscopic Cosserat model permits a relation of the internal length-scale to the average cell size of the microstructure.