### Abstract

The concept of representative volume element (RVE) is widely used to determine the effective material properties of random heterogeneous materials. In the present work, the RVE is investigated for the viscoelastic response of particle-reinforced polymer nanocomposites in the frequency domain. The smallest RVE size and the minimum number of realizations at a given volume size for both structural and mechanical properties are determined for a given precision using the concept of margin of error. It is concluded that using the mean of many realizations of a small RVE instead of a single large RVE can retain the desired precision of a result with much lower computational cost (up to three orders of magnitude reduced computation time) for the property of interest. Both the smallest RVE size and the minimum number of realizations for a microstructure with higher volume fraction (VF) are larger compared to those of one with lower VF at the same desired precision. Similarly, a clustered structure is shown to require a larger minimum RVE size as well as a larger number of realizations at a given volume size compared to the well-dispersed microstructures.

Original language | English (US) |
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Pages (from-to) | 55-74 |

Number of pages | 20 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 114 |

DOIs | |

State | Published - May 2018 |

### Keywords

- Polymer nanocomposites
- Representative volume elements
- Viscoelasticity

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

*Journal of the Mechanics and Physics of Solids*,

*114*, 55-74. https://doi.org/10.1016/j.jmps.2018.02.013