A critical evaluation of micromechanical models for syntactic foams

The purpose of this work is the accurate prediction of the effective elastic moduli of syntactic foams, for arbitrary selection of the volume fraction and material for the matrix and the filler (made up of hollow spheres called balloons). Hence, we develop a series of three-dimensional finite element models, each including 50 balloons, for a wide range of geometric and material properties. This allows us to garner accurate reference data to ascertain the quality of the predictions of theoretical models available in the literature. In particular, we compare the Composite Sphere-based Self-Consistent estimate originally proposed by Hervé and Pellegrini [Hervé, E., Pellegrini, O., 1995. The elastic constants of a material containing spherical coated holes. Arch. Mech. 47, 223–246] and further developed by Bardella and Genna [Bardella, L., Genna, F., 2001. On the elastic behaviour of syntactic foams. Int. J. Solids Struct. 38, 7235–7260] with the Hollow Inclusion-based Differential Self-Consistent estimate recently proposed by Porfiri and Gupta [Porfiri, M., Gupta, N., 2009. Effect of volume fraction and wall thickness on the elastic properties of hollow particle filled composites. Compos. Part B – Eng. 40, 166–173]. We also discuss the results on the basis of (i) a novel Composite Sphere-based Differential Self-Consistent estimate, (ii) both rigorous and Composite Sphere-based bounds, and (iii) a re-derivation of the Hollow Inclusion-based Differential Self-Consistent estimate coherent with classical and Morphologically Representative Pattern-based homogenisation procedures considered in this work.