Book•
Microstructure Sensitive Design for Performance Optimization
09 Oct 2012-
TL;DR: 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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TL;DR: In this paper, the authors review recent advances in overcoming this tradeoff, by purposely deploying heterogeneous nanostructures in an otherwise single-phase metal, and advocate this broad vision to help guide future innovations towards a synergy between high strength and high ductility.
611 citations
Cites methods from "Microstructure Sensitive Design for..."
...The digitally reconstructed microstructure can be used for further analysis by microstructure sensitive computational models [70,71]....
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TL;DR: Computational and information aspects of design of materials with hierarchical microstructures are explored and key underdeveloped elements essential to supporting ICME are identified.
Abstract: Designing materials for targeted performance requirements as required in Integrated Computational Materials Engineering (ICME) demands a combined strategy of bottom-up and top-down modeling and simulation which treats various levels of hierarchical material structure as a mathematical representation, with infusion of systems engineering and informatics to deal with differing model degrees of freedom and uncertainty. Moreover, with time, the classical materials selection approach is becoming generalized to address concurrent design of microstructure or mesostructure to satisfy product-level performance requirements. Computational materials science and multiscale mechanics models play key roles in evaluating performance metrics necessary to support materials design. The interplay of systems-based design of materials with multiscale modeling methodologies is at the core of materials design. In high performance alloys and composite materials, maximum performance is often achieved within a relatively narrow window of process path and resulting microstructures. Much of the attention to ICME in the materials community has focused on the role of generating and representing data, including methods for characterization and digital representation of microstructure, as well as databases and model integration. On the other hand, the computational mechanics of materials and multidisciplinary design optimization communities are grappling with many fundamental issues related to stochasticity of processes and uncertainty of data, models, and multiscale modeling chains in decision-based design. This paper explores computational and information aspects of design of materials with hierarchical microstructures and identifies key underdeveloped elements essential to supporting ICME. One of the messages of this overview paper is that ICME is not simply an assemblage of existing tools, for such tools do not have natural interfaces to material structure nor are they framed in a way that quantifies sources of uncertainty and manages uncertainty in representing physical phenomena to support decision-based design.
297 citations
Cites background from "Microstructure Sensitive Design for..."
...A number of different measures of the spatial correlations in the microstructure have been proposed and utilized in literature [19,20]....
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TL;DR: A comprehensive review of representative approaches for MCR and elaborate on their algorithmic details, computational costs, and how they fit into the PSP mapping problems is provided.
252 citations
Cites background from "Microstructure Sensitive Design for..."
..., an evolving microstructure) over a long period of time would provide the same statistical measures as taking many independent realizations of that system over time [7]....
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...SDF generally takes a simple parametric form; enabling materials design by considerably reducing the microstructure design space (aka microstructure hull [7])....
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...The significance of this task is highlighted by the Materials Genome Initiative [1–4] and the emergence of computational tools and frameworks such as materials by design [5,6], microstructure sensitive design [7], and integrated computational materials engineering (ICME) [8]....
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TL;DR: This work designs and implements a deep learning approach to model an elastic homogenization structure-property linkage in a high contrast composite material system and demonstrates that this end-to-end framework can predict the effective stiffness of high contrast elastic composites with a wide of range of microstructures, while exhibiting high accuracy and low computational cost for new evaluations.
225 citations
Additional excerpts
...of desired property combinations [4,26,27])....
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TL;DR: A comprehensive review on the development of evolutionary structural optimization (ESO) type methods, in particular the latest convergent and mesh-independent BESO method is highlighted by Huang and Xie as mentioned in this paper.
Abstract: The evolutionary structural optimization (ESO) method developed by Xie and Steven (Comput Struct 49(5):885–896, 162), an important branch of topology optimization, has undergone tremendous development over the past decades. Among all its variants, the convergent and mesh-independent bi-directional evolutionary structural optimization (BESO) method developed by Huang and Xie (Finite Elem Anal Des 43(14):1039–1049, 48) allowing both material removal and addition, has become a widely adopted design methodology for both academic research and engineering applications because of its efficiency and robustness. This paper intends to present a comprehensive review on the development of ESO-type methods, in particular the latest convergent and mesh-independent BESO method is highlighted. Recent applications of the BESO method to the design of advanced structures and materials are summarized. Compact Malab codes using the BESO method for benchmark structural and material microstructural designs are also provided.
217 citations
Cites background from "Microstructure Sensitive Design for..."
...Meanwhile, the fast progress made in the field of material science allows us to control the material microstructure composition to an unprecedented extent [35, 152]....
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References
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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.
Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.
35,161 citations
Book•
01 Jan 1943TL;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
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
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.
Abstract: We have developed 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. The computational approach taken in this system is motivated by both physiology and information theory, as well as by the practical requirements of near-real-time performance and accuracy. Our approach treats the face recognition problem as an intrinsically two-dimensional (2-D) recognition problem rather than requiring recovery of three-dimensional geometry, taking advantage of the fact that faces are normally upright and thus may be described by a small set of 2-D characteristic views. The system functions by projecting face images onto a feature space that spans the significant variations among known face images. The significant features are known as "eigenfaces," because they are the eigenvectors (principal components) of the set of faces; they do not necessarily correspond to features such as eyes, ears, and noses. The projection operation characterizes an individual face by a weighted sum of the eigenface features, and so to recognize a particular face it is necessary only to compare these weights to those of known individuals. Some particular advantages of our approach are that it provides for the ability to learn and later recognize new faces in an unsupervised manner, and that it is easy to implement using a neural network architecture.
14,562 citations
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.
Abstract: An efficient method for the calculation of the interactions of a 2' factorial ex- periment was introduced by Yates and is widely known by his name. The generaliza- tion to 3' was given by Box et al. (1). Good (2) generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series. In their full generality, Good's methods are 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, where m is proportional to log N. This results inma procedure requiring a number of operations proportional to N log N rather than N2. These methods are applied here to the calculation of complex Fourier series. They are useful in situations where the number of data points is, or can be chosen to be, a highly composite number. The algorithm is here derived and presented in a rather different form. Attention is given to the choice of N. It is also shown how special advantage can be obtained in the use of a binary computer with N = 2' and how the entire calculation can be performed within the array of N data storage locations used for the given Fourier coefficients. Consider the problem of calculating the complex Fourier series N-1 (1) X(j) = EA(k)-Wjk, j = 0 1, * ,N- 1, k=0
11,795 citations
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.
Abstract: It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material stresses will be present both inside and outside the region. The resulting elastic field may be found very simply with the help of a sequence of imaginary cutting, straining and welding operations. In particular, if the region is an ellipsoid the strain inside it is uniform and may be expressed in terms of tabulated elliptic integrals. In this case a further problem may be solved. An ellipsoidal region in an infinite medium has elastic constants different from those of the rest of the material; how does the presence of this inhomogeneity disturb an applied stress-field uniform at large distances? 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.
11,784 citations