Calculating effective material properties from 3D images: new solutions

Posted on 23 April 2015 by Wojciech Smigaj

Researchers and analysts working with 3D image data (CT, micro-CT, FIB-SEM…) of complex materials face a number of challenges when attempting to reconstruct and obtain information from scans. One particular challenge involves being able to compute material properties (such as solid, flow and electrical properties) from scanned samples without having to use significant computational resources, or without combining multiple types of software.

At Simpleware, we have worked on creating software tools that make it easier for analysts and researchers to get more out of their image data, and provide a number of different methods for visualising, processing and exporting data as models. To complement the ability to segment and compute statistics (pores, surface areas…) from image data in ScanIP and export FE/CFD models in +FE, our recently released Physics Modules offer a new solution for calculating the effective material properties of scanned samples.

The Physics Modules focus on calculating effective material properties using finite element-based homogenisation techniques, and extend the robust multi-domain meshing algorithms we have developed for our software. There are three modules available:

  • +SOLID for calculating effective stiffness tensor/elastic moduli of samples
  • +FLOW for calculating the absolute permeability tensor of porous materials
  • +LAPLACE for calculating the properties of materials whose physics is governed by the Laplace equation (such as electrical conductivity/permittivity, thermal conductivity, and molecular diffusivity)

Homogenisation Methodology

Homogenisation approximates a complex heterogeneous material with a homogeneous material

The homogenisation methods used by the modules are based on approximating a complex heterogeneous material (such as a multi-phase composite) by a homogeneous material with effective properties chosen so that its response to external loads resembles as closely as possible the original material. This simplifies the analysis of complex systems and has many potential industrial applications, including: the study of composites, soil and porous media, as well as digital rock physics and special core analysis, and industrial non-destructive testing of products and synthetics.

Our software solution offers two ways of retrieving the effective material properties. Most commonly, the built-in FE solver is used to calculate these properties by post-processing the fields induced in a cuboidal material sample by a sequence of appropriate boundary conditions. Alternatively, +SOLID and +LAPLACE are able to calculate upper and lower bounds for the effective properties directly from image data. The FE-based approach we use has some major advantages over alternative methods. While homogenisation as a method is not new, our use of smoothed FE-based meshes and a built-in solver provides a strong alternative to existing grid or voxel-based methods that allows for much higher-quality final meshes.

Comparison of traditional voxel mesh with Simpleware mesh preserving segmented domains without decreasing data resolution

Our FE mesh surfaces for a given resolution are more accurate than voxel mesh surfaces and their area converges with increasing resolution to the actual surface area of the sample; rather than reducing the size of voxel meshes by decreasing image data resolution, the Physics Modules employ a decimation algorithm that preserves segmented domain accuracy whilst reducing mesh size. This improves on grid or voxel-based methods that produce stepped surfaces, which leads to an over-estimation of the surface area between material phases, significantly affecting the accuracy and convergence of results.

Interpreting Results

Interpreting results using a graph for displaying effective material properties and evaluating accuracy

We have developed tools to reduce the potential effects of boundary conditions on FE homogenisation, where the sample size needs to be large enough to produce meaningful results; this includes calculating the effective properties from field averages taken over a domain smaller than the region of interest used in simulations, thus mitigating the influence of near-boundary artefacts on the final result. A graph tool has also been created to display the effective material properties as a function of the domain size used for their calculation, indicating whether a sample is too small to be representative of the material or whether its size can be decreased to reduce solving time and memory usage.

Visualising fields produced by the FE solver

Doing More with Results

There is a lot the user can do with calculated effective properties; they can be displayed as tensors in the original coordinate system, as tensors in the coordinate system associated with the automatically determined principal axes, and as best-fit isotropic (all modules), orthotropic (+SOLID), and uniaxial (+LAPLACE, +FLOW) approximations. In addition, results from FE simulations can be visualised and animated, as well as exported as text files and images.

The Physics Modules were developed with the goal of making it straightforward to calculate the effective properties of materials starting from image data. By integrating image processing, analysis and mesh generation into a single software environment, it’s possible to rapidly extract information from scanned samples without a lot of intermediate steps that can reduce the accuracy of calculated properties.

We are happy to hear questions about what the Physics Modules can do, so please get in touch if you want to know more, or try them for yourself with a free trial.