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Microstructure Sensitive Design for Performance Optimization

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TLDR
This review presents the MSD framework in the context of both the engineering advances that have led to its creation, and those that complement or provide alternative methods for design of materials (meaning ‘optimization of material structure’ in this context).
Abstract
The accelerating rate at which new materials are appearing, and transforming the engineering world, only serves to emphasize the vast potential for novel material structure, and related performance. Microstructure-sensitive design (MSD) aims at providing inverse design methodologies that facilitate design of material internal structure for performance optimization. Spectral methods are applied across the structure, property and processing design spaces in order to compress the computational requirements for linkages between the spaces and enable inverse design. Research has focused mainly on anisotropic, polycrystalline materials, where control of local crystal orientation can result in a broad range of property combinations. This review presents the MSD framework in the context of both the engineering advances that have led to its creation, and those that complement or provide alternative methods for design of materials (meaning ‘optimization of material structure’ in this context). A variety of definitions for the structure of materials are presented, with an emphasis on correlation functions; and spectral methods are introduced for compact descriptions and efficient computations. The microstructure hull is defined as the design space for structure in the spectral framework. Reconstruction methods provide invertible links between statistical descriptions of structure, and deterministic instantiations. Subsequently, structure–property relations are reviewed, and again subjected to representation via spectral methods. The concept of a property closure is introduced as the design space for performance optimization, and methods for moving between the closures and hulls are presented as the basis for the subsequent discussion on microstructure design. Finally, the spectral framework is applied to deformation processes, and methodologies that facilitate process design are reviewed.

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Citations
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Calibrated localization relationships for elastic response of polycrystalline aggregates

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Quantification and classification of microstructures in ternary eutectic alloys using 2-point spatial correlations and principal component analyses

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Materials Knowledge Systems in Python—a Data Science Framework for Accelerated Development of Hierarchical Materials

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Improving stochastic reconstructions by weighting correlation functions in an objective function

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A reduced multiscale model for nonlinear structural topology optimization

TL;DR: In this article, a reduced multiscale model for macroscopic structural design considering microscopic material nonlinear microstructures is presented, which reduces the computational effort for solving the microscopic boundary value problems.
References
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Equation of state calculations by fast computing machines

TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Book

Table of Integrals, Series, and Products

TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
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Eigenfaces for recognition

TL;DR: A near-real-time computer system that can locate and track a subject's head, and then recognize the person by comparing characteristics of the face to those of known individuals, and that is easy to implement using a neural network architecture.
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An algorithm for the machine calculation of complex Fourier series

TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
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The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems

TL;DR: In this paper, it is shown that to answer several questions of physical or engineering interest, it is necessary to know only the relatively simple elastic field inside the ellipsoid.
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