Computing elastic moduli on 3-D X-ray computed tomography image stacks

Published

December 10, 2014

Author(s)

Edward Garboczi, Volodymyr Kushch

Abstract

A common numerical task is to compute the effective elastic properties of a random composite material based on its microstructure by operating on a 3D digital image of the microstructure obtained via X-ray computed tomography (CT). The 3-D image is usually sub-sampled since an X-ray CT image is typically of order 1000^3 voxels or larger, which is considered to be a very large finite element problem. Two main questions are then: is the sub-sample size sufficiently large to capture enough of the important details of the random microstructure so that the computed moduli are accurate, and what boundary conditions should be chosen for this sub-sample? This paper gives contributions to the answer of both questions. A new hybrid numerical method is introduced, which makes use of finite element solutions coupled with exact solutions for elastic moduli of square arrays of parallel cylindrical fibers. The new method allows, in principle, for all of the microstructural data to be used when the image is in the form of a cylinder, which is often the case in X-ray CT. The appendix describes a similar algorithm for spherical sub-samples, which may be of use when examining the mechanical properties of particles. A simulated X-ray CT cylindrical microstructure with three phases is taken from a known random system, with two choices of the phase elastic moduli, and cubic sub-samples are taken from this cylindrical structure. Two different choices of boundary conditions for the cubic sub-samples are investigated: forced periodic and fixed displacements. It is found that using forced periodic displacements on the non-periodic (geometrically) sub-samples always gave better results than using fixed displacements, and using the complete cylindrical sample with the new method gave still better results in terms of accuracy and precision. Fortran 90 programs for the analytical solutions are made available on-line, along with the parallel finite element codes used.

Citation

Journal of the Mechanics and Physics of Solids

Volume

76

Pub Type

Journals

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DOI Link

Keywords

composite, analytical solutions, boundary conditions, X-ray computed tomography, elastic moduli, finite element

Citation

Garboczi, E. and Kushch, V. (2014), Computing elastic moduli on 3-D X-ray computed tomography image stacks, Journal of the Mechanics and Physics of Solids, [online], https://doi.org/10.1016/j.jmps.2014.12.003 (Accessed September 26, 2024)