The Open UniversitySkip to content

3D stochastic bicontinuous microstructures: Generation, topology and elasticity

Soyarslan, Celal; Bargmann, Swantje; Pradas, Marc and Weissmüller, Jörg (2018). 3D stochastic bicontinuous microstructures: Generation, topology and elasticity. Acta Materialia, 149 pp. 326–340.

Full text available as:
PDF (Version of Record) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (3MB) | Preview
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


Motivated by recent experimental investigations of the mechanical behavior of nanoporous metal we explore an efficient and robust method for generating 3D representative volume elements (RVEs) with strikingly similar behavior. Our approach adopts Cahn's method of generating a Gaussian random field by taking a superposition of standing sinusoidal waves of fixed wavelength but random in direction and phase. In its theory part, our study describes closed-form expressions for how the solid volume fraction affects the binarization level, mean structure size, specific surface area, averages of mean and Gaussian curvature, and the scaled topological genus. Based on numerical studies we report on criteria for achieving representative realizations of the structure by proper choice of the number of waves and element size. We also show that periodic structures are readily created. We analyze the mechanical properties considering linear and infinitesimal elasticity and evaluate the residual anisotropy (which can be made small) and the effective values of the Young's modulus and Poisson's ratio. The numerical results are in excellent agreement with experimental findings for the variation of stiffness with solid fraction of nanoporous gold made by dealloying. We propose scaling relations that achieve naturally a perfect agreement with the numerical and experimental data. The scaling relation for the stiffness accounts for a percolation-to-cluster transition in the random field microstructure at a finite solid fraction. We propose that this transition is the origin of the previously reported anomalous compliance of nanoporous gold.

Item Type: Journal Item
Copyright Holders: 2018 Acta Materialia Inc.
ISSN: 1359-6454
Keywords: RVE generation; nanoporous gold; topology; elastic scaling relations; homogenization
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 54038
Depositing User: Marc Pradas
Date Deposited: 03 Apr 2018 14:45
Last Modified: 23 Mar 2020 08:36
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU