Effective elastic properties of 3D stochastic bicontinuous composites. (October 2019) - Soyarslan, Celal; Pradas, Marc; Bargmann, Swantje
Highlights: Compliant phase impregnation in metal-polymer bicontinuous nanocomposites compensates for the stiffness loss due to topological changes in the stiffer phase with reduction in its phase volume fraction. This results in a distinct scaling law for bicontinuous gold-epoxy nanocomposite. Analytical bounds fall short to accurately predict the effective response of high contrast bicontinuous composites with volume fraction bias towards the weaker phase. Finite element-based asymptotic homogenization with periodic boundary conditions is an efficient and accurate tool to this end. Abstract: 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 Cahn (1965) and Soyarslan et al. (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 from its nanoporous counterpart as determined by scrutinized macroscopic responses of gold-epoxy nanocomposites of various phase volume fractions. This is due to the fact that, in space-filling nanocomposites 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 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.