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Item type:Publication, Access status: with files , 3D stochastic bicontinuous microstructures: generation, topology and elasticity(2018-02-07); ; ; 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 xpressions for how the solid volume fraction affects the binarization evel, 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.Publicationtype: Journal ArticleScopus© Citations 148 391 876 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Surface excess elasticity of gold: ab initio coefficients and impact on the effective elastic response of nanowiresPredicting the influence of the surface on the effective elastic properties of nanoscale structures and nanomaterials remains a challenge, which we here address on both levels, continuum and atomic. Density Functional Theory (DFT) computation at the atomic level yields the first reliable surface excess elastic parameters for the (111) and (001) surfaces of gold. At the continuum level, we derive closed-form expressions for the effective elastic behavior that can be combined with the DFT-derived excess elastic parameters to obtain the effective axial, torsion, and bending stiffness of circular nanowires with surface excess elasticity. The two approaches use different reference frames, and we emphasize the need for consistent stress definitions and for conversion between the separate stress measures when transferring results between the approaches. We present excess elastic parameters separately for Cauchy and 2nd Piola-Kirchhoff stresses, demonstrating that the conversion substantially modifies their numerical value and may even invert their sign. The results afford an assessment of the contribution of the surface excess elastic parameters to the effective elastic response of nanoscale beams or wires. This assessment sheds doubt on earlier suggestions relating experimental observations of an effective stiffening or softening at small size to the excess elasticity of clean surfaces.Publicationtype: Journal ArticleScopus© Citations 33 438 850 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Elastic and plastic poisson’s ratios of nanoporous gold(2015-08-19); ; ; ; We explore the elastic and plastic Poisson’s ratios, mE and mP, of nanoporous gold, using digital image correlation during compression experiments including load/unload segments. The two coefficients differ significantly, with mE independent of the ligament size, L, and with a trend for mP / L at not too large L. Disorder in the network of ligaments may explain why mE is smaller than predicted by lattice-based models. Finite element simulations, based on the Deshpande–Fleck constitutive law, validate the data analysis. The constitutive law captures work-hardening and transverse flow of nanoporous gold in good agreement with the experiment.Publicationtype: Journal ArticleScopus© Citations 64 478 545