Bentheimer networks

• https://doi.org/10.1007/s11075-007-9063-9

Abstract — Virtual material design is the microscopic variation of materials in the computer, followed by the numerical evaluation of the effect of this variation on the material’s macroscopic properties. The goal of this procedure is an in some sense improved material. Here, we give examples regarding the dependence of the effective elastic moduli of a composite material on the geometry of the shape of an inclusion. A new approach on how to solve such interface problems avoids mesh generation and gives second order accurate results even in the vicinity of the interface. The Explicit Jump Immersed Interface Method is a finite difference method for elliptic partial differential equations that works on an equidistant Cartesian grid in spite of non-grid aligned discontinuities in equation parameters and solution. Near discontinuities, the standard finite difference approximations are modified by adding correction terms that involve jumps in the function and its derivatives. This work derives the correction terms for two dimensional linear elasticity with piecewise constant coefficients, i.e. for composite materials. It demonstrates numerically convergence and approximation properties of the method.

• https://doi.org/10.1007/s10596-018-9768-y

Abstract — Three sets of synthetic images were created from two original datasets. A suite exhibiting greyscale contrast was produced from an 8.96-μm voxel size 3D X-ray microscopy image of a sandstone rock and a two suites (one showing greyscale contrast and one showing both greyscale and textural contrast) were produced from a 5 × 5 × 5 nm voxel size FIB-SEM image of a shale rock. The performance of three image segmentation algorithms (global multi-Otsu thresholding, seeded watershed region growing, and machine learning-based multivariant classification) was then assessed by their ability to recover their respective original segmented 3D images. While all algorithms performed well at low noise levels, machine learning-based classification proved significantly more noise tolerant than either of the traditional algorithms. It was also able to segment the non-greyscale (textural based) contrast, something the traditional completely failed to do, with voxel misclassification rates for the traditional techniques above 50% at a 0 noise level within the textural contrast regions. Machine learning-based classification, in contrast, achieved misclassification rates of less than 5% in the same regions.

• https://doi.org/10.1029/2019WR025171
• 10.1029/2019WR025171

Abstract — We statistically infer fluid flow and transport properties of porous materials based on their geometry and connectivity, without the need for detailed material properties and expensive physical simulations. Our predictions are consistent with traditional approaches. We summarize structure by persistent homology, then determines the similarity of structures using image analysis and statistics. Longer term, this may enable quick and automated categorization of rocks into known archetypes. We first compute persistent homology of binarized 3D images of material subvolume samples. The persistence parameter is the signed Euclidean distance from inferred material interfaces, which captures the distribution of sizes of pores and grains. Each persistence diagram is converted into an image vector. We infer structural similarity by calculating image similarity. For each image vector, we compute principal components to extract features. We fit statistical models to features estimates material permeability, tortuosity, and anisotropy. We develop a Structural SIMilarity index (SSIM) to determine Statistical Representative Elementary Volumes (sREV).