Skeletonization, Geometrical Analysis, and Finite Element Modeling of Nanoporous Gold Based on 3D Tomography Data

Abstract

Abstract:Various modeling approaches simplify and parametrize the complex network structure of nanoporous gold (NPG) for studying the structure-property relationship based on artificially generated structures. This paper presents a computational efficient and versatile finite element method (FEM) beam model that is based on skeletonization and diameter information derived from the original 3D focused ion beam-scanning electron microscope (FIB-SEM) tomography data of NPG. The geometrical skeleton network is thoroughly examined for a better understanding of the NPG structure. A skeleton FEM beam model is derived that can predict the macroscopic mechanical behavior of the material. Comparisons between the mechanical response of this skeleton beam model and a solid FEM model are conducted. Results showed that the biggest-sphere diameter algorithm implemented in the open-source software FIJI, commonly used for geometrical analysis of microstructural data, overestimates the diameter of the curved NPG ligaments. The larger diameters lead to a significant overestimation of macroscopic stiffness and strength by the skeleton FEM beam model. For a parabolic shaped ligament with only 20% variation in its diameter, a factor of more than two was found in stiffness. It is concluded that improved algorithms for image processing are needed that provide accurate diameter information along the ligament axis.

Connections Between Topology and Macroscopic Mechanical Properties of Three-Dimensional Open-Pore Materials

“…By this approach, common issues with determining the percolation threshold p c and exponent could be avoided. For measuring the total cut fraction of a real structure, e.g., from a skeleton of a FIB tomography (Hu et al, 2016;Ziehmer et al, 2016;Hu, 2017;Richert and Huber, 2018), the related fully connected reference is required; however, this is unknown. Alternatively, the average coordination number z of a 3D network could be measured, because it is connected with the total cut fraction by the linear relationship, as given in Equation (12).…”

“…The first FEM models built from 3D FIB tomography data were presented independently by Hu et al (2016) and Mangipudi et al (2016). The model of Hu et al (2016) has been further refined by Richert and Huber (2018), who analyzed the detected ligament shapes and investigated the predictive capability of the FEM beam model in comparison to the 3D solid model of Hu et al (2016). Soyarslan et al (2018) used complex artificially generated structures and FEM solid modeling for validating an analytical solution that relates the solid fraction to the scaled genus density.…”

Computation of Thickness and Mechanical Properties of Interconnected Structures: Accuracy, Deviations, and Approaches for Correction

“…The algorithm is commonly used to estimate the mean trabecular thickness of trabecular bone (Day et al, 2000;Almhdie-Imjabber et al, 2014), or other bone structures (Witkowska et al, 2014), because it is a powerful and fast volume-based algorithm. In the context of NPG the Thickness algorithm has been applied for analyzing 3D tomography data or voxel models by Hu et al (2016), Mangipudi et al (2016), Richert and Huber (2018), and Soyarslan et al (2018a,b).…”

“…However, for the prediction of mechanical properties using FEM, the correct diameter distribution along the ligament axis is crucial. Richert and Huber (2018) showed that the Thickness algorithm reaches its limits when being applied to typical shapes of NPG ligaments, due to the strongly varying diameter along the ligament axis. The resulting overestimation in ligament radius up to 30% has a strong impact on the predicted mechanical stiffness, which can deviate by a factor of more than two.…”

“…The resulting overestimation in ligament radius up to 30% has a strong impact on the predicted mechanical stiffness, which can deviate by a factor of more than two. In their conclusions, Richert and Huber (2018) mentioned the need for a correction method for tracing back an identified ligament shape to the corresponding true geometry, which could be based on inverse methods, such as optimization or machine learning. This important finding has been ignored by Soyarslan et al (2018b) who used the diameter information as determined from the Thickness algorithm in their beam-FE model, without any local validation of the detected diameters or discussion of possible consequences for their mechanical prediction.…”