Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales. - Synthesizes available UQ methods for materials modeling - Provides practical tools and examples for problem solving in modeling material behavior across various length scales - Demonstrates UQ in density functional theory, molecular dynamics, kinetic Monte Carlo, phase field, finite element method, multiscale modeling, and to support decision making in materials design - Covers quantum, atomistic, mesoscale, and engineering structure-level modeling and simulation

Due to efficacy and optimization potential of genetic and evolutionary algorithms, they are used in learning and modeling especially with the advent of big data related problems. This book presents the algorithms and strategies specifically associated with pertinent issues in materials science domain. It discusses the procedures for evolutionary multi-objective optimization of objective functions created through these procedures and introduces available codes. Recent applications ranging from primary metal production to materials design are covered. It also describes hybrid modeling strategy, and other common modeling and simulation strategies like molecular dynamics, cellular automata etc. Features: Focuses on data-driven evolutionary modeling and optimization, including evolutionary deep learning. Include details on both algorithms and their applications in materials science and technology. Discusses hybrid data-driven modeling that couples evolutionary algorithms with generic computing strategies. Thoroughly discusses applications of pertinent strategies in metallurgy and materials. Provides overview of the major single and multi-objective evolutionary algorithms. This book aims at Researchers, Professionals, and Graduate students in Materials Science, Data-Driven Engineering, Metallurgical Engineering, Computational Materials Science, Structural Materials, and Functional Materials.

Anomalous rheology is a material behavior that presents the fingerprint of power-laws, arising from anomalous diffusion in microstructures, and observed in a range of complex materials. Such microstructures often display a fractal nature with sub-diffusive dynamics, e.g., of entangled polymer chains, and defect interactions such as dislocation avalanches, cracks, and voids. The corresponding macroscopic non-exponential behavior makes integer-order models to lack a compact representation of the small-scale physics. Furthermore, classical linear viscoelastic models require arbitrary arrangements of Hookean/Newtonian elements, introducing a limited number of exponential relaxation modes that, at most, represent a truncated power-law approximation. While this may be satisfactory for short times at engineering accuracy, such models often yield high-dimensional parameter spaces and lack predictability for multiple time/length-scales. In this scenario, Fractional Calculus (FC) becomes an attractive modeling alternative since it naturally accounts for power-law kernels in its integro-differential operators. This allows accurate and predictive modeling of soft materials for multiple timescales, in which most standard models fail or become impractical.In this work, a data-driven framework for efficient, multi-scale fractional modeling and failure of anomalous materials is proposed. The overarching goal is to identify/construct efficient fractional rheological models, especially for soft materials, undergoing nonlinear response and failure. To this purpose, a fractional linear and nonlinear viscoelastic existence study is developed and employed for the first time to urinary bladder tissues undergoing large strains. The framework is extended to account for power-law viscoplastic behavior, and aiming for applications to larger systems, the resulting models are solved through a new approach called fractional return-mapping algorithm, that generalizes existing predictor-corrector schemes of classical elastoplasticity. Regarding the effects of fractional constitutive laws on structural dynamics, a few developed models are incorporated to beam and truss structures, where the effects of evolving constitutive laws on the anomalous dynamics of systems are analyzed. Although FC became an effective modeling tool in the last few decades, it requires careful considerations to satisfy basic thermodynamic conservation/dissipation laws. To this end, the thermodynamic consistency of the developed visco-elasto-plastic models with the addition of damage effects is proved. Furthermore, the associated energy release rate due to crack/void formation is consistent with the employed fractional rheological elements, which naturally introduces memory effects on damage evolution.Fractional differential equations (FDEs) inherently carry a functional nonlocal dependency and near-singular behaviors at bounded domains, which increases the computational complexity and degenerates the global accuracy of many existing numerical schemes. Therefore, two numerical contributions are proposed in the last part of the framework. The first one is a data-driven singularity-capturing approach that automatically addresses the low solution regularity and yields high accuracy for long time-integration. In the second contribution, fast implicit-explicit (IMEX) schemes are developed for stiff/nonlinear FDEs, which are shown to have larger stability regions than existing approaches.

This open access book discusses advances in semantic interoperability for materials modelling, aiming at integrating data obtained from different methods and sources into common frameworks, and facilitating the development of platforms where simulation services in computational molecular engineering can be provided as well as coupled and linked to each other in a standardized and reliable way. The Virtual Materials Marketplace (VIMMP), which is open to all service providers and clients, provides a framework for offering and accessing such services, assisting the uptake of novel modelling and simulation approaches by SMEs, consultants, and industrial R&D end users. Semantic assets presented include the EngMeta metadata schema for research data infrastructures in simulation-based engineering and the collection of ontologies from VIMMP, including the ontology for simulation, modelling, and optimization (OSMO) and the VIMMP software ontology (VISO).

Predicting polymeric material behavior during processing and predicting final part properties continues to be a strong research focus within the scientific community as it involves taking into consideration a wide range of time-dependent variables. By use of data-driven modeling, the materials development process can be accelerated, and the highly predictive modeling techniques can facilitate the development of smart manufacturing systems. This dissertation worked on solving polymer engineering problems by use of data-driven modeling techniques. The first strategy was using data-driven modeling to provide a predictive model with statistical insights of the injection molding process to ensure part quality is maximized for a highly viscoelastic material blend. By injection molding highly viscoelastic materials, the probability of part defects is increased, therefore, it was crucial to use advanced computational techniques to understand the nuances of this highly non-linear process and to predict the outcome before creating material waste from faulty trials. The second strategy was in the use of data-driven modeling for reverse engineering purposes, specifically within materials development. By combining experimental characterization and data-driven modeling, algorithms were developed and compared to prove how highly predictive models can be used as reverse engineering toolboxes. This ultimately informed users of the optimal formulation which would reach the specified target material properties. The final strategy explored using data-driven modeling to validate the high influence of viscous heating within the pressure melt removal process, therefore, work was done in implementing a viscous heating system within a fused filament fabrication (FFF) 3D printer to accelerate the 3D printing process. The instrumented FFF 3D printer proved capable of accelerating print speeds and improving mechanical performance of 3D printed parts, working towards solving two of the largest bottlenecks within additive manufacturing: lead times and part quality. Given the unique capabilities of the data-driven modeling, the novel 3D printer was tested and evaluated via data-driven modeling to provide statistical information regarding which processing parameters were the most influential for improving overall performance of the 3D printing system. The results of this work provide a basis for future research endeavors related to combining data-driven modeling and polymer science, such as in optimizing the newly developed viscous heating 3D printer.

This book addresses the current status, challenges and future directions of data-driven materials discovery and design. It presents the analysis and learning from data as a key theme in many science and cyber related applications. The challenging open questions as well as future directions in the application of data science to materials problems are sketched. Computational and experimental facilities today generate vast amounts of data at an unprecedented rate. The book gives guidance to discover new knowledge that enables materials innovation to address grand challenges in energy, environment and security, the clearer link needed between the data from these facilities and the theory and underlying science. The role of inference and optimization methods in distilling the data and constraining predictions using insights and results from theory is key to achieving the desired goals of real time analysis and feedback. Thus, the importance of this book lies in emphasizing that the full value of knowledge driven discovery using data can only be realized by integrating statistical and information sciences with materials science, which is increasingly dependent on high throughput and large scale computational and experimental data gathering efforts. This is especially the case as we enter a new era of big data in materials science with the planning of future experimental facilities such as the Linac Coherent Light Source at Stanford (LCLS-II), the European X-ray Free Electron Laser (EXFEL) and MaRIE (Matter Radiation in Extremes), the signature concept facility from Los Alamos National Laboratory. These facilities are expected to generate hundreds of terabytes to several petabytes of in situ spatially and temporally resolved data per sample. The questions that then arise include how we can learn from the data to accelerate the processing and analysis of reconstructed microstructure, rapidly map spatially resolved properties from high throughput data, devise diagnostics for pattern detection, and guide experiments towards desired targeted properties. The authors are an interdisciplinary group of leading experts who bring the excitement of the nascent and rapidly emerging field of materials informatics to the reader.

The Institute for Mathematical Sciences at the National University of Singapore hosted a two-month research program on "Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design" from 1 July to 31 August 2009. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects four expanded lecture notes with self-contained tutorials. They cover a number of aspects on multiscale modeling, analysis and simulations for problems arising from materials science including some critical components in computational prediction of materials properties such as the multiscale properties of complex materials, properties of defects, interfaces and material microstructures under different conditions, critical issues in developing efficient numerical methods and analytic frameworks for complex and multiscale materials models. This volume serves to inspire graduate students and researchers who choose to embark into original research work in these fields.