Front Cover; Hierarchical Materials Informatics; Copyright Page; Contents; Acknowledgments; 1 Materials, Data, and Informatics; 1.1 PSP Linkages; 1.2 Material Internal Structure; 1.3 Inverse Problems in Materials and Process Design; 1.4 Data, Information, Knowledge, and Wisdom; 1.5 Digital Representations; 1.6 Hierarchical Materials Informatics; References; 2 Microstructure Function; 2.1 Length Scales; 2.2 Local States and Local State Spaces; 2.2.1 Local States and Local State Spaces in Polycrystalline Microstructures; 2.3 Microstructure Function; 2.4 Digital Representation of Functions.

2.5 Digital Representation of Microstructure Function2.6 Spectral Representations of Microstructure Function; References; 3 Statistical Quantification of Material Structure; 3.1 Spatial Correlations; 3.2 Computation and Visualization of 2-Point Spatial Correlations; 3.3 Higher Order Spatial Correlations; 3.4 Reconstructions of Microstructures from Spatial Correlations; 3.5 Reconstructions from Partial Sets of 2-Point Statistics; 3.6 Representative Microstructures; References; 4 Reduced-Order Representations of Spatial Correlations; 4.1 Principal Component Analyses.

7.2 Case Study: Microstructure Evolution Using Phase-Field Models7.3 Case Study: DFT Databases for Crystal Plasticity Computations; References; 8 Materials Innovation Cyberinfrastructure; References; Index.

Custom design, manufacture, and deployment of new high performance materials for advanced technologies is critically dependent on the availability of invertible, high fidelity, structure-property-processing (SPP) linkages. Establishing these linkages presents a major challenge because of the need to cover unimaginably large dimensional spaces. Hierarchical Materials Informatics addresses objective, computationally efficient, mining of large ensembles of experimental and modeling datasets to extract this core materials knowledge. Furthermore, it aims to organize and present this high value kno

6.3 Case Study: Microstructure-Property Relationships in Porous Transport Layers6.4 Case Study: Structure-Property Linkages in Inclusions/Steel Composites; 6.5 MKS: Data-Driven Framework for Localization Linkages; 6.6 Case Study: MKS for Elastic Response of Composites; 6.7 Case Study: MKS for Elastic Response of Higher Contrast Composites; 6.8 Case Study: MKS for Elastic Response of Polycrystals; 6.9 Case Study: MKS for Perfectly Plastic Response of Composites; References; 7 Process-Structure Linkages; 7.1 Mathematical Framework.

4.2 Application to Spatial Correlations4.3 Case Study: α-β Ti Micrographs; 4.4 Case Study: Nonmetallic Inclusions/Steel Composite System; 4.5 Case Study: MD Simulation Datasets; References; 5 Generalized Composite Theories; 5.1 Conventions and Notations; 5.2 Review of Continuum Mechanics; 5.3 Concept of Homogenization; 5.4 Higher Order Homogenization Theory; References; 6 Structure-Property Linkages; 6.1 Data-Driven Framework for Homogenization Linkages; 6.2 Main Steps of the Data-Driven Framework for Homogenization Linkages.