Human history shows evidence of epochs defined by new material discovery and deployment, which in turn have led to technology innovation and industrial revolutions. Discovery and development of new and improved materials has accelerated with the availability of computational modeling and simulation tools. Integrated Computational Materials Engineering has been widely pursued over the past decade to understand and establish the processe structuree property relationships of new materials. Yet the deployment of computational tools for materials discovery and design is limited by the reliability and robustness of simulation predictions owing to various sources of uncertainty.
This is an introductory book which presents various uncertainty quantification (UQ) methods and their applications to materials simulation at multiple scales. The latest research on UQ for materials modeling is introduced. The book reflects a range of perspectives on material UQ issues from over 50 researchers at universities and research laboratories worldwide. The target audience includes materials scientists and engineers who want to learn the basics of UQ methods, as well as statistical scientists and applied mathematicians who are interested in solving problems related to materials.
The book is organized as follows. Chapter 1 provides an overview of various UQ methods, both nonintrusive and intrusive, the sources of uncertainty in materials modeling, and the existing research work of UQ in materials simulation and design at different length scales. Chapters 2e5 describe the existing research efforts on model error quantification for quantum mechanical simulation to predict material properties via density functional theory. Chapters 6e7 provide state-of-the-art examples of Bayesian model calibration of interatomic potentials, the major source of errors in molecular dynamics simulation, and sensitivity analyses of their effects on physical property predictions. Chapters 8e10 provide examples of UQ methods developed for mesoscale simulations of materials, including kinetic Monte Carlo and phase field simulations. Chapters 11e13 discuss recent research of random fields and their applications to materials modeling in the higher length scale (mesoscopic) continuum regime, such as uncertainty propagation between scales in composites for mechanical property prediction and damage detection. Chapters 14 and 15 illustrate some of the unique UQ issues in multiscale materials modeling, including Bayesian model calibration based on information obtained from different scales, and reliability assessment based on stochastic reduced-order models with samples obtained using multifidelity simulations. Chapter 16 provides insight regarding materials design and optimization under uncertainty for cases in which Bayesian optimization and surrogate models can play a major role. Chapter 17 highlights the challenges in metamaterial property and behavior predictions, where the variability induced by additive manufacturing processes needs to be quantified in simulations and incorporated in the material database.
We would like to thank all authors of the chapters for their contributions to this book and their efforts to advance the frontiers of the emerging field of UQ for materials. We are also in debt to our reviewers who rigorously examined the submissions, provided helpful feedback during manuscript selection, and improved the quality of the included chapters. This volume would not have been possible without the tireless efforts and devotion of Ms. Ana Claudia Abad Garcia, our Elsevier publishing editor and project manager, as well as the encouragement from the book series editor-in-chief Prof. Dr. Vadim Silberschmidt.
Uncertainty quantification in materials modeling 1
Yan Wang, David L. McDowell
Georgia Institute of Technology, Atlanta, GA, United States
1.1 Materials design and modeling
New and improved materials have long fostered innovation. The discovery of new materials leads to new product concepts and manufacturing techniques. Historically, materials discovery emerges from exploratory research in which new chemical, physical, and biological properties of new materials become evident. Then their potential applications are identified. This discovery pathway is typically lengthy and has largely relied on serendipity. In contrast, intentional materials design is an application requirementedriven process to systematically search for solutions. In general, design involves iterative searching aimed at identifying optimal solutions in the design space, which is formed by the material composition and hierarchical structure (e.g., microstructure). The goal thus is to find compositions and structures that achieve the most suitable chemical and physical properties subject to various constraints, including cost, time, availability, manufacturability, and others.
A transformational trend in early 21st century is to incorporate computational modeling and simulation of material processestructure and structureeproperty relations to reduce materials development cycle time and its reliance on costly and time-consuming empirical methods. The Integrated Computational Materials Engineering (ICME) initiative [1,2] has been embraced by various industry sectors as a viable path forward to accelerate materials development and insertion into products by employing more comprehensive management of data, process monitoring, and integrated computational modeling and simulation. This has led more recently to the development of the US Materials Genome Initiative (MGI) , as well as companion thrusts in Europe and Asia , which aim to accelerate discovery and development of new and improved materials via a strategy of fusing information from experiments, theory, and computational simulation, aided by the tools of uncertainty quantification (UQ) and data science with the emphasis on high throughput protocols.
An accurate measurement to evaluate the role of ICME is the extent that it principally provides decision support for materials design and development. In other words, a metric for measuring the success of ICME is the increase of the fraction of decisions made in the critical path of materials development, optimization, certification, and deployment, where decision makers are informed via modeling and simulation as opposed to experiments. The same is true for the discovery of new materials as per objectives of the MGI.
To design material systems  by tailoring the hierarchical material structure to deliver required performance requires that we go beyond the aims of basic science to explain phenomena and governing mechanisms, namely to understand and quantify these phenomena and mechanisms to the extent necessary to facilitate control and to manipulate structure at individual scales in a way that trends toward desired properties or responses. This change of emphasis toward connecting process to structure and structure to properties or responses undergirds much of the science base supporting ICME goals of materials design and development.