A Simple Explicit Model Constructed from a Homogenization Solution for the Large-Strain Mechanical Response of Elastomeric Syntactic Foams

This paper introduces a homogenization-based constitutive model for the large-strain mechanical response of elastomeric syntactic foams subject to arbitrary quasistatic loading and unloading conditions. Based on direct observations
from experiments, this class of emerging foams are considered to be made of a nonlinear elastic matrix filled with a random isotropic distribution of hollow thin-walled spherical shells | commonly termed microspheres or microballoons |
each having the same mean diameter that are made of an elastic brittle material that is much stiffer than the elastomeric matrix, typically, either glass or a hard polymer. Accordingly, such underlying microballoons behave effectively as rigid
particles initially. Along a given loading path, however, they may fracture (in the case of glass microballoons) or buckle (in the case of polymer microballoons) at which point they abruptly transition to behave effectively as vacuous pores.
On that account, the proposed constitutive model corresponds to a homogenization solution for the nonlinear elastic response of particle-filled porous elastomers | precisely, elastomers embedding both rigid spherical particles and vacuous spherical pores of equal monodisperse size | wherein the volume fraction of pores corresponds to the volume fraction of
fractured or buckled microballoons and hence is not a fixed parameter but rather an internal variable of state that evolves as a function of the loading history. After the general presentation of the model, where its theoretical and practical features are discussed, its descriptive and predictive capabilities are showcased via comparisons with experimental data for silicone syntactic foams filled with glass microballoons.