Effective elastic properties of 3D stochastic bicontinuous composites

(2019). Effective elastic properties of 3D stochastic bicontinuous composites. Mechanics of Materials, 137, article no. 103098.

DOI: https://doi.org/10.1016/j.mechmat.2019.103098


We study effective elastic properties of 3D bicontinuous random composites (such as, e.g., nanoporous gold filled with polymer) considering linear and infinitesimal elasticity and using asymptotic homogenization along with the finite element method. For the generation of the microstructures, a leveled-wave model based on the works of J. W. Cahn [J.W. Cahn. Phase separation by spinodal decomposition in isotropic systems. The Journal of Chemical Physics, 42(1):93-99, 1965.] and Soyarslan et al. [C. Soyarslan, S. Bargmann, M. Pradas, and J. Weissmüller. 3D stochastic bicontinuous microstructures: generation, topology and elasticity. Acta Materialia, 149: 326-340, 2018.] is used. The influences of volume element size, phase contrast, relative volume fraction of phases and applied boundary conditions on computed apparent elastic moduli are investigated. The nanocomposite behaves distinctly different than its nanoporous counterpart without any filling as determined by scrutinized macroscopic responses of gold-epoxy nanocomposites of various phase volume fractions. This is due to the fact that, in the space-filling nanocomposite the force transmission is possible in all directions whereas in the nanoporous gold the load is transmitted along ligaments, which hinges upon the phase topology through network connectivity. As a consequence, we observe a distinct elastic scaling law for bicontinuous metal-polymer composites. A comparison of our findings with the Hashin-Shtrikman, the three-point Beran-Molyneux and the Milton-Phan-Tien analytical bounds for the same composites show that computational homogenization using periodic boundary conditions is justified to be the only tool in accurate and efficient determination of the effective properties of 3D bicontinuous random composites with high contrast and volume fraction bias towards the weaker phase.

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