Elastic properties of equilibrium foams

Abstract Stochastic equilibrium finite element (FE) foam models are used to study the influence of relative density and distribution of solid material between cell walls and edges on the elastic properties of foam materials. It is first established that the models contain a sufficient number of cells to ascertain isotropy and numerically and statistically robust results. It is then found that the elastic moduli are very weakly coupled to cell size variation in the models, when the latter is varied systematically. The influence from relative density and distribution of solid on the elastic parameters is considerably stronger. Analytical estimates from the literature, based on idealized cell models and dimension analysis, are matched by fitting coefficients to the FE results, providing good qualitative but relatively poor quantitative correlation. An expansion of the analytical coupling functions is then suggested in order to reduce their level of idealization. The expanded formulation shows virtually perfect agreement with the numerical results for almost the whole range of relative densities and distributions of solid in the FE parameter study. The presented analytical expression is believed to be general and provide accurate estimates of the elastic properties of a wide range of foam materials, provided that their bulk material properties and micro structure can be established.