Modeling In Engineering Using Innovative Numerical Methods For Solids And Fluids

The book examines innovative numerical methods for computational solid and fluid mechanics that can be used to model complex problems in engineering. It also presents innovative and promising simulation methods, including the fundamentals of these methods, as well as advanced topics and complex applications. Further, the book explores how numerical simulations can significantly reduce the number of time-consuming and expensive experiments required, and can support engineering decisions by providing data that would be very difficult, if not impossible, to obtain experimentally. It also includes chapters covering topics such as particle methods addressing particle-based materials and numerical methods that are based on discrete element formulations; fictitious domain methods; phase field models; computational fluid dynamics based on modern finite volume schemes; hybridizable discontinuous Galerkin methods; and non-intrusive coupling methods for structural models.

Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies related to the modeling of the complex phenomena occurring in materials processing. It is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics, and for engineering professionals or researchers.

The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict. The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations.

This book highlights the work of several world-class researchers on smart modeling of complex systems. The contributions are grouped into the four main categories listed below. · Numerical schemes construction for the solution of partial differential equations. · Numerical methods in continuum media mechanics problems. · Mathematical modeling in aerodynamics, plasma physics, deformable body mechanics, and geological hydrocarbon exploration. · Mathematical modeling in medical applications. The book offers a valuable resource for theoreticians and application scientists and engineers, as well as postgraduate students, in the fields of computational methods, numerical experiments, parallel algorithms, deformable solid bodies, seismic stability, seismic prospecting, migration, elastic and acoustic wave investigation, gas dynamics, astrophysics, aerodynamics, fluid dynamics, turbulent flows, hypersonic flows, detonation waves, composite materials, fracture mechanics, melting of metals, mathematical economics, medicine, and biology.

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling analysis of elasto-plastic structures engineering optimization and design, global optimization and related algorithms The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.

The first international symposium on mathematical foundations of the finite element method was held at the University of Maryland in 1973. During the last three decades there has been great progress in the theory and practice of solving partial differential equations, and research has extended in various directions. Full-scale nonlinear problems have come within the range of nu merical simulation. The importance of mathematical modeling and analysis in science and engineering is steadily increasing. In addition, new possibili ties of analysing the reliability of computations have appeared. Many other developments have occurred: these are only the most noteworthy. This book is the record of the proceedings of the International Sympo sium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics, held in Yamaguchi, Japan from 29 September to 3 October 2000. The topics covered by the symposium ranged from solids to fluids, and in cluded both mathematical and computational analysis of phenomena and algorithms. Twenty-one invited talks were delivered at the symposium. This volume includes almost all of them, and expresses aspects of the progress mentioned above. All the papers were individually refereed. We hope that this volume will be a stepping-stone for further developments in this field.

The idea of the book is to provide a comprehensive overview of computational physics methods and techniques, that are used for materials modeling on different length and time scales. Each chapter first provides an overview of the basic physical principles which are the basis for the numerical and mathematical modeling on the respective length-scale. The book includes the micro-scale, the meso-scale and the macro-scale, and the chapters follow this classification. The book explains in detail many tricks of the trade of some of the most important methods and techniques that are used to simulate materials on the perspective levels of spatial and temporal resolution. Case studies are included to further illustrate some methods or theoretical considerations. Example applications for all techniques are provided, some of which are from the author’s own contributions to some of the research areas. The second edition has been expanded by new sections in computational models on meso/macroscopic scales for ocean and atmosphere dynamics. Numerous applications in environmental physics and geophysics had been added.

This book provides readers with a detailed insight into diverse and exciting recent developments in computational solid mechanics, documenting new perspectives and horizons. The topics addressed cover a wide range of current research, from computational materials modeling, including crystal plasticity, micro-structured materials, and biomaterials, to multi-scale simulations of multi-physics phenomena. Particular emphasis is placed on pioneering discretization methods for the solution of coupled non-linear problems at different length scales. The book, written by leading experts, reflects the remarkable advances that have been made in the field over the past decade and more, largely due to the development of a sound mathematical background and efficient computational strategies. The contents build upon the 2014 IUTAM symposium celebrating the 60th birthday of Professor Michael Ortiz, to whom this book is dedicated. His work has long been recognized as pioneering and is a continuing source of inspiration for many researchers. It is hoped that by providing a "taste" of the field of computational mechanics, the book will promote its popularity among the mechanics and physics communities.

The prediction and understanding of physical systems is largely divided into two camps, those based on data, and those based on the numerical models. These two approaches have long been developed independently of each other. This work shows further improvements of the modeling of physical systems and also presents a new way to inject the data from simulations into deep learning architecture to aid in the engineering design process. In this thesis the computational mechanics technique, the Material Point Method (MPM) is extended to model the mixed-failure of damage propagation and plasticity in the aggregate materials commonly found deep underground. To achieve this, the Grady-Kipp damage model and the pressure dependent Drucker-Prager plasticity model are coupled to allow for mixed-mode failure to develop in the material. This is tested against analytical results for brittle materials, as well as a series of experimental results. In addition, the brittle fracture in thin silicon wafers is also modeled to better understand the tolerances in manufacturing loads on these delicate objects. Finally, in a novel approach to combine the results of a numerical simulation and the power of a deep neural network, biomedical device design is studied. Here the simulation of the acoustofluidics of a microchip is performed to generate a large dataset of boundary conditions and solved pressure fields. This dataset is then used to train a neural network so that the inverse relationship between the boundary condition and the pressure field can be obtained. Once this training is complete, the network is used as a design tool for a specified pressure field and the results are fabricated and tested.

The MIT mission - "to bring together Industry and Academia and to nurture the next generation in computational mechanics is of great importance to reach the new level of mathematical modeling and numerical solution and to provide an exciting research environment for the next generation in computational mechanics." Mathematical modeling and numerical solution is today firmly established in science and engineering. Research conducted in almost all branches of scientific investigations and the design of systems in practically all disciplines of engineering can not be pursued effectively without, frequently, intensive analysis based on numerical computations. The world we live in has been classified by the human mind, for descriptive and analysis purposes, to consist of fluids and solids, continua and molecules; and the analyses of fluids and solids at the continuum and molecular scales have traditionally been pursued separately. Fundamentally, however, there are only molecules and particles for any material that interact on the microscopic and macroscopic scales. Therefore, to unify the analysis of physical systems and to reach a deeper understanding of the behavior of nature in scientific investigations, and of the behavior of designs in engineering endeavors, a new level of analysis is necessary. This new level of mathematical modeling and numerical solution does not merely involve the analysis of a single medium but must encompass the solution of multi-physics problems involving fluids, solids, and their interactions, involving multi-scale phenomena from the molecular to the macroscopic scales, and must include uncertainties in the given data and the solution results. Nature does not distinguish between fluids and solids and does not ever repeat itself exactly. This new level of analysis must also include, in engineering, the effective optimization of systems, and the modeling and analysis of complete life spans of engineering products, from design to fabrication, to possibly multiple repairs, to end of service.