Three-Dimensional Heterogeneous Material Microstructure Reconstruction from Limited Morphological Information via Stochastic Optimization

Jiao Yang; Jiao Yang

doi:10.3934/matersci.2014.1.28

AIMS Materials Science

2014, Volume 1, Issue 1: 28-40. doi: 10.3934/matersci.2014.1.28

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Three-Dimensional Heterogeneous Material Microstructure Reconstruction from Limited Morphological Information via Stochastic Optimization

Jiao Yang ^,

Materials Science and Engineering, Arizona State University, 411 N Central Ave, Tempe, Arizona, USA

Received: 04 December 2013 Accepted: 09 January 2014 Published: 22 January 2014

We present a general computational framework that enables one to generate realistic 3D microstructure models of heterogeneous materials from limited morphological information via stochastic optimization. In our framework, the 3D material microstructure is represented as a 3D array, whose entries indicate the local state of that voxel. The limited structural data obtained in various experiments correspond to different mathematical transformations of the 3D array. Reconstructing the 3D material structure from such limited data is formulated as an inverse problem, originally proposed by Yeong and Torquato [Phys. Rev. E 57, 495 (1998)], which is solved using the simulated annealing procedure. The utility, versatility and robustness of our general framework are illustrated by reconstructing a polycrystalline microstructure from 2D EBSD micrographs and a binary metallic alloy from limited angle projections. Our framework can be also applied in the reconstructions based on small-angle x-ray scattering (SAXS) data and has ramifications in 4D materials science (e.g., charactering structural evolution over time).
- Heterogeneous materials,
- 3D microstructure,
- Reconstruction,
- Optimization
Citation: Jiao Yang. Three-Dimensional Heterogeneous Material Microstructure Reconstruction from Limited Morphological Information via Stochastic Optimization[J]. AIMS Materials Science, 2014, 1(1): 28-40. doi: 10.3934/matersci.2014.1.28

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Abstract

We present a general computational framework that enables one to generate realistic 3D microstructure models of heterogeneous materials from limited morphological information via stochastic optimization. In our framework, the 3D material microstructure is represented as a 3D array, whose entries indicate the local state of that voxel. The limited structural data obtained in various experiments correspond to different mathematical transformations of the 3D array. Reconstructing the 3D material structure from such limited data is formulated as an inverse problem, originally proposed by Yeong and Torquato [Phys. Rev. E 57, 495 (1998)], which is solved using the simulated annealing procedure. The utility, versatility and robustness of our general framework are illustrated by reconstructing a polycrystalline microstructure from 2D EBSD micrographs and a binary metallic alloy from limited angle projections. Our framework can be also applied in the reconstructions based on small-angle x-ray scattering (SAXS) data and has ramifications in 4D materials science (e.g., charactering structural evolution over time).

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