Taylor averaging on heterogeneous foams

In this article we present a formulation to account for the effect of cell size distribution on the mechanical behavior of foams. The present approach averages the response of unit cells with different sizes via a Taylor averaging approach. This technique can be applied to different unit cell models where the cell size is explicitly given. In order to keep the averaging formulation analytically traceable, we select a unit cell model, bubble model (Ortiz, M., Gioia, G. and Cuitino, A.M. Manuscript in preparation), that considers the behavior of an homogeneous array of thin-walled spherical cells undergoing uniform finite deformation. This model relays on the computation of the strain energy density for the deformed configuration due to membrane stretching and bending. For this unit cell model, the effect of the cell size distribution is described only by the first three moments of the distribution, or the mean radius, variance and skeweness. The effect of these parameters on the foam behavior subjected to uniaxial compression is analyzed for two different values of the relative density of the foam. The model is compared against a unixial compression test of a ductile foam system with nearly spherical cells of different sizes. The cell size distribution is measured independenly and introduced to the model as a input. The prediction of load displacement response is in general good agreement with the experimental test.