Effect of polydispersivity and porosity on the elastic properties of hollow particle filled composites

Hollow particle filled composites are characterized by a variety of properties of interest to marine structural applications, including low density, high specific modulus, and low moisture absorption. Usually, dispersed microspheres exhibit widely different geometric characteristics, such as wall thickness and outer radius. In this paper, we develop a homogenization technique based on the differential scheme that accounts for polydispersivity in geometry of inclusion phases in hollow particle reinforced composites. We find manageable differential expressions to predict the composite effective moduli in terms of a variety of concurrent factors, including matrix and particle elastic constants, geometrical properties of hollow particles, volume fractions, and void content in the matrix. Theoretical findings are validated by experimental data and are compared with results of several published models. We find that accounting for polydispersion in the model allows for a closer agreement with experimental results than monodisperse schemes. In particular, qualitatively different predictions are observed in syntactic foams containing thin walled particles when accounting for polydispersivity.