Hierarchical n-point polytope functions for quantitative representation of complex heterogeneous materials and microstructural evolution

Pei En Chen, Wenxiang Xu, Nikhilesh Chawla, Yi Ren, Yang Jiao

Research output: Contribution to journalArticle

Abstract

Effective and accurate characterization and quantification of complex microstructure of a heterogeneous material and its evolution under external stimuli are very challenging, yet crucial to achieving reliable material performance prediction, processing optimization and advanced material design. Here, we address this challenge by developing a set of hierarchical statistical microstructural descriptors, which we call the “n-point polytope functions” Pn, for quantitative characterization, representation and modeling of complex material microstructure and its evolution. These polytope functions successively include higher-order n-point statistics of the features of interest in the microstructure in a concise, expressive, explainable, and universal manner; and can be directly computed from multi-modal imaging data. We develop highly efficient computational tools to directly extract the Pn functions up to n = 8 from multi-modal imaging data. Using simple model microstructures, we show that these statistical descriptors effectively “decompose” the structural features of interest into a set of “polytope basis”, allowing one to easily detect any underlying symmetry or emerging features during the structural evolution. We apply the Pn functions to quantify and model a variety of heterogeneous material systems, including particle-reinforced composites, metal-ceramic composites, concretes, porous materials; as well as the microstructural evolution in an aged lead-tin alloy. Our results indicate that the Pn functions can offer a practical set of basis for quantitative microstructure representation (QMR), for both static 3D complex microstructure and 4D microstructural evolution of a wide spectrum of heterogeneous material systems.

Original languageEnglish (US)
Pages (from-to)317-327
Number of pages11
JournalActa Materialia
Volume179
DOIs
StatePublished - Oct 15 2019

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Microstructural evolution
Microstructure
Particle reinforced composites
Tin alloys
Imaging techniques
Lead alloys
Cermets
Porous materials
Statistics
Concretes
Composite materials
Processing

Keywords

  • Heterogeneous materials
  • Microstructure evolution
  • Multi-modal imaging data
  • N-point polytope functions
  • Quantitative microstructure representation (QMR)

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Ceramics and Composites
  • Polymers and Plastics
  • Metals and Alloys

Cite this

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title = "Hierarchical n-point polytope functions for quantitative representation of complex heterogeneous materials and microstructural evolution",
abstract = "Effective and accurate characterization and quantification of complex microstructure of a heterogeneous material and its evolution under external stimuli are very challenging, yet crucial to achieving reliable material performance prediction, processing optimization and advanced material design. Here, we address this challenge by developing a set of hierarchical statistical microstructural descriptors, which we call the “n-point polytope functions” Pn, for quantitative characterization, representation and modeling of complex material microstructure and its evolution. These polytope functions successively include higher-order n-point statistics of the features of interest in the microstructure in a concise, expressive, explainable, and universal manner; and can be directly computed from multi-modal imaging data. We develop highly efficient computational tools to directly extract the Pn functions up to n = 8 from multi-modal imaging data. Using simple model microstructures, we show that these statistical descriptors effectively “decompose” the structural features of interest into a set of “polytope basis”, allowing one to easily detect any underlying symmetry or emerging features during the structural evolution. We apply the Pn functions to quantify and model a variety of heterogeneous material systems, including particle-reinforced composites, metal-ceramic composites, concretes, porous materials; as well as the microstructural evolution in an aged lead-tin alloy. Our results indicate that the Pn functions can offer a practical set of basis for quantitative microstructure representation (QMR), for both static 3D complex microstructure and 4D microstructural evolution of a wide spectrum of heterogeneous material systems.",
keywords = "Heterogeneous materials, Microstructure evolution, Multi-modal imaging data, N-point polytope functions, Quantitative microstructure representation (QMR)",
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T1 - Hierarchical n-point polytope functions for quantitative representation of complex heterogeneous materials and microstructural evolution

AU - Chen, Pei En

AU - Xu, Wenxiang

AU - Chawla, Nikhilesh

AU - Ren, Yi

AU - Jiao, Yang

PY - 2019/10/15

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N2 - Effective and accurate characterization and quantification of complex microstructure of a heterogeneous material and its evolution under external stimuli are very challenging, yet crucial to achieving reliable material performance prediction, processing optimization and advanced material design. Here, we address this challenge by developing a set of hierarchical statistical microstructural descriptors, which we call the “n-point polytope functions” Pn, for quantitative characterization, representation and modeling of complex material microstructure and its evolution. These polytope functions successively include higher-order n-point statistics of the features of interest in the microstructure in a concise, expressive, explainable, and universal manner; and can be directly computed from multi-modal imaging data. We develop highly efficient computational tools to directly extract the Pn functions up to n = 8 from multi-modal imaging data. Using simple model microstructures, we show that these statistical descriptors effectively “decompose” the structural features of interest into a set of “polytope basis”, allowing one to easily detect any underlying symmetry or emerging features during the structural evolution. We apply the Pn functions to quantify and model a variety of heterogeneous material systems, including particle-reinforced composites, metal-ceramic composites, concretes, porous materials; as well as the microstructural evolution in an aged lead-tin alloy. Our results indicate that the Pn functions can offer a practical set of basis for quantitative microstructure representation (QMR), for both static 3D complex microstructure and 4D microstructural evolution of a wide spectrum of heterogeneous material systems.

AB - Effective and accurate characterization and quantification of complex microstructure of a heterogeneous material and its evolution under external stimuli are very challenging, yet crucial to achieving reliable material performance prediction, processing optimization and advanced material design. Here, we address this challenge by developing a set of hierarchical statistical microstructural descriptors, which we call the “n-point polytope functions” Pn, for quantitative characterization, representation and modeling of complex material microstructure and its evolution. These polytope functions successively include higher-order n-point statistics of the features of interest in the microstructure in a concise, expressive, explainable, and universal manner; and can be directly computed from multi-modal imaging data. We develop highly efficient computational tools to directly extract the Pn functions up to n = 8 from multi-modal imaging data. Using simple model microstructures, we show that these statistical descriptors effectively “decompose” the structural features of interest into a set of “polytope basis”, allowing one to easily detect any underlying symmetry or emerging features during the structural evolution. We apply the Pn functions to quantify and model a variety of heterogeneous material systems, including particle-reinforced composites, metal-ceramic composites, concretes, porous materials; as well as the microstructural evolution in an aged lead-tin alloy. Our results indicate that the Pn functions can offer a practical set of basis for quantitative microstructure representation (QMR), for both static 3D complex microstructure and 4D microstructural evolution of a wide spectrum of heterogeneous material systems.

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