3D image based stochastic micro-structure modelling of foams for simulating elasticity

TL;DR

The study presents a complete workflow to predict macroscopic elasticity of foams from 3D imaging by fitting random Laguerre tessellations to observed micro-structures and performing LS-FFT-based homogenization. By analyzing micro-CT data of open-cell aluminum foams, the authors estimate intrinsic-volume densities, segment the voxel structure, and fit a stochastic geometry model that can generate multiple synthetic realizations. The approach is validated against compression experiments and used to explore how strut cross-section shape and relaxation affect stiffness, demonstrating practical utility for material design and representative-volume-element sizing. This framework enables efficient generation of realistic micro-structures with tunable properties for micromechanics studies and optimization of foam geometries in engineering applications.

Abstract

Image acquisition techniques such as micro-computed tomography are nowadays widely available. Quantitative analysis of the resulting 3D image data enables geometric characterization of the micro-structure of materials. Stochastic geometry models can be fit to the observed micro-structures. By alteration of the model parameters, virtual micro-structures with modified geometry can be generated. Numerical simulation of elastic properties in realizations of these models yields deeper insight on the influence of particular micro-structural features. Ultimately, this allows for an optimization of the micro-structure geometry for particular applications. Here, we present this workflow at the example of open cell foams. Applicability is demonstrated using an aluminum alloy foam sample. The structure observed in a micro-computed tomography image is modeled by the edge system of a random Laguerre tessellation generated by a system of closely packed spheres. Elastic moduli are computed in the binarized micro-CT image of the foam as well as in realizations of the model. They agree well with the results of a compression test on the real material.

Figures (11)

• Figure 1: Visualizations of $500^3$ voxel sub-volumes from reconstructed CT images of rigid foams. From left to right: open polymer, partially closed ceramic, and closed polymer foams. All CT scans taken at ITWM with voxel sizes $49\,\micro$m for the open polymer foam, $34\,\micro$m for the ceramic foam, and $3\,\micro$m for the closed polymer foam. Samples provided by Vesuvius (ceramic) and Evonik (closed polymer foam).
• Figure 2: Morphological cell reconstruction, illustrated using 2D slices of the 3D image. Left: Binarized - solid foam structure appearing white, pore space black. Center, left: Inverted Euclidean distance map on the pore space, small values dark, high white. Center, right: Pore system generated by the watershed transform. Right: Pore system generated by the pre-flooded watershed transform.
• Figure 3: Left and middle: Realizations of Voronoi tessellations generated by a Poisson point process and a regular point process. Right: Laguerre tessellation generated by the same point pattern as in the middle.
• Figure 4: Application of boundary conditions for homogenization. Blue arrows indicate the forces applied.
• Figure 5: Left: Volume rendering of the reconstructed CT image. The CT image taken at ITWM has originally a voxel size of $29.9\,\micro$m and the sample is contained in a cube of edge length 1 500 voxels corresponding to 4.5 cm. Center: sub-volume of edge length 0.9 cm with blob like production leftover. Right: System of reconstructed cells.