A critical evaluation of micromechanical models for syntactic foams

Lorenzo Bardella, Alessandro Sfreddo, Carlo Ventura

DICATA, Faculty of Engineering, University of Brescia, Via Branze, 4325123, Brescia, Italy

Maurizio Porfiri, Nikhil Gupta

Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University, Six MetroTech Center, Brooklyn, NY 11201, USA

Abstract

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 fifty 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 the theoretical models available in the literature. In particular, we compare the Composite Sphere-based Self-Consistent estimate originally proposed by Herve' and Pellegrini (1995 Arch. Mech. 47, 223-246) and further developed by Bardella and Genna (2001 Int. J. Solids Struct. 38, 7235-7260) with the Hollow Inclusion-based Differential Self-Consistent estimate recently proposed by Porfiri and Gupta (2009 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.

Author Keywords: Effective Elastic Properties; Finite element method; Morphologically Representative Pattern; Numerical Homogenization; Self-Consistent Scheme; Syntactic Foam