### Abstract

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.

Original language | English (US) |
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Article number | 103548 |

Journal | International Journal of Non-Linear Mechanics |

Volume | 126 |

DOIs | |

State | Published - Nov 2020 |

### Keywords

- Fillers
- Finite deformation
- Homogenization
- Internal variables
- Pores

### ASJC Scopus subject areas

- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics

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## Cite this

*International Journal of Non-Linear Mechanics*,

*126*, [103548]. https://doi.org/10.1016/j.ijnonlinmec.2020.103548