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Continuum Mechanics in the Earth Sciences

Author: William I. Newman

Publisher: Cambridge University Press

Published: 2012-03-15

Total Pages: 195

ISBN-13: 1107078679

Continuum mechanics underlies many geological and geophysical phenomena, from earthquakes and faults to the fluid dynamics of the Earth. This interdisciplinary book provides geoscientists, physicists and applied mathematicians with a class-tested, accessible overview of continuum mechanics. Starting from thermodynamic principles and geometrical insights, the book surveys solid, fluid and gas dynamics. In later review chapters, it explores new aspects of the field emerging from nonlinearity and dynamical complexity and provides a brief introduction to computational modeling. Simple, yet rigorous, derivations are used to review the essential mathematics. The author emphasizes the full three-dimensional geometries of real-world examples, enabling students to apply this in deconstructing solid earth and planet-related problems. Problem sets and worked examples are provided, making this a practical resource for graduate students in geophysics, planetary physics and geology and a beneficial tool for professional scientists seeking a better understanding of the mathematics and physics within Earth sciences.

Mechanics in the Earth and Environmental Sciences

Author: Gerard V. Middleton

Publisher: Cambridge University Press

Published: 1994-08-26

Total Pages: 480

ISBN-13: 9780521446693

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The study of the Earth and the environment requires an understanding of the physical processes within and at the surface of the Earth. This book will allow the student to develop a broad working knowledge of mechanics and its application to the earth and environmental sciences. The mathematics are introduced at a level that assumes only an understanding of first-year calculus. The concepts are then developed to allow an understanding of the basic physics for a wide range of natural processes. These are illustrated by examples from many real situations, such as the application of the theory of flow through porous media to the study of groundwater, the viscosity of fluids to the flow of lava, and the theory of stress to the study of faults. The breadth of topics will allow students and professionals to gain an insight into the workings of many aspects of the Earth's systems.

Continuum Mechanics in Environmental Sciences and Geophysics

Author: K. Hutter

Publisher: Springer

Published: 2014-05-04

Total Pages: 533

ISBN-13: 3709126002

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Modern continuum mechanics is the topic of this book. After its introduction it will be applied to a few typical systems arising in the environmental sciences and in geophysics. In large lake/ocean dynamics peculiar effects of the rotation of the Earth will be analyzed in linear/nonlinear processes of a homogenous and inhomogenous water body. Strong thermomechanical coupling paired with nonlinear rheology affects the flow of large ice sheets (such as Antarctica and Greenland) and ice shelves. Its response to the climatic forcing in an environmental of greenhouse warming may significantly affect the life of future generations. The mechanical behavior of granular materials under quasistatic loadings requires non-classical mixture concepts and encounters generally complicated elastic-plastic-type constitutive behavior. Creeping flow of soils, consolidation processes and ground water flow are described by such theories. Rapid shearing flow of granular materials lead to constitutive relations for the stresses which incorporate rate independent behavior of Mohr-Coulomb type together with dispersive stress contributions due to particle collisions. Rockfalls, sturzstroms, snow and ice avalanches, but also debris flow and sea ice drifting can be described with such formulations.

Continuum Mechanics in the Earth Sciences

Author: William I. Newman

Publisher: Cambridge University Press

Published: 2012-03-15

Total Pages: 195

ISBN-13: 0521562899

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This interdisciplinary book provides graduate students in geophysics, planetary physics and geology with a class-tested, accessible overview of continuum mechanics.

Stress and Strain

Author: W.D. Means

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 343

ISBN-13: 146139371X

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This is an elementary book on stress and strain theory for geologists. It is written in the belief that a sound introduction to the mechanics of continu ous bodies is essential for students of structural geology and tectonics, just as a sound introduction to physical chemistry is necessary for students of petrology. This view is shared by most specialists in structural geology, but it is not yet reflected in typical geology curricula. Undergraduates are still traditionally given just a few lectures on mechanical fundamentals, and there is rarely any systematic lecturing on this subject at the graduate level. The result is that many students interested in structure and tectonics finish their formal train ing without being able to understand or contribute to modem literature on rocks as mechanical systems. The long-term remedy for this is to introduce courses in continuum mechanics and material behavior as routine parts of the undergraduate curriculum. These subjects are difficult, but no more so than optical mineralogy or thermo dynamics or other rigorous subjects customarily studied by undergraduates. The short-term remedy is to provide books suitable for independ ent study by those students and working geologists alike who wish to improve their understanding of mechanical topics relevant to geology. This book is intended to meet the short-term need with respect to stress and strain, two elementary yet challenging concepts of continuum mechanics.

Mechanics of Electromagnetic Solids

Author: J.S. Yang

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 289

ISBN-13: 1461302439

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The mechanics of electromagnetic materials and structures has been developing rapidly with extensive applications in, e. g. , electronics industry, nuclear engineering, and smart materials and structures. Researchers in this interdisciplinary field are with diverse background and motivation. The Symposium on the Mechanics of Electromagnetic Materials and Structures of the Fourth International Conference on Nonlinear Mechanics in Shanghai, China in August 13-16, 2002 provided an opportunity for an intimate gathering of researchers and exchange of ideas. This volume contains papers based on most of the presentations at the symposium, and articles from a few invited contributors. These papers reflect some of the recent activities in the mechanics of electromagnetic materials and structures. The first twelve papers are in the order in which they were listed in the program of the conference. These are followed by six invited papers in alphabetical order of the last names of the first authors. We would like to extend our sincere thanks to Professor David Y. Gao of Virginia Tech for suggesting the symposium, and to the authors for their time and effort invested in preparing their manuscripts. We are also grateful to Professor Daining Fang of Tsinghua University for co-chairing the symposium with J. S. Yang. Our special thanks belong to Kluwer for preparing this book for publication. J. S. Yang G. A. Maugin PIEZOELECTRIC VIBRATORY GYROSCOPES J. S.

Continuum Mechanics Modeling of Material Behavior

Author: Martin H. Sadd

Publisher: Academic Press

Published: 2018-03-31

Total Pages: 432

ISBN-13: 0128116498

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Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries; kinematics of motion and deformation; force and stress measures; and mass, momentum and energy balance principles. The book then moves beyond other books by dedicating the last chapter to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity, as well as linear and nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Offers a thorough, concise and organized presentation of continuum mechanics formulation Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study Features extensive use of exercises, providing more material for student engagement and instructor presentation

Continuum and Computational Mechanics for Geomechanical Engineers

Author: Ömer Aydan

Publisher: CRC Press

Published: 2021-04-20

Total Pages: 345

ISBN-13: 1000367827

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The field of rock mechanics and rock engineering utilizes the basic laws of continuum mechanics and the techniques developed in computational mechanics. This book describes the basic concepts behind these fundamental laws and their utilization in practice irrespective of whether rock/rock mass contains discontinuities. This book consists of nine chapters and six appendices. The first four chapters are concerned with continuum mechanics aspects, which include the basic operations, definition of stress and strain tensors, and derivation of four fundamental conservation laws in the simplest yet precise manner. The next two chapters are the preparation for computational mechanics, which require constitutive laws of geomaterials relevant to each conservation law and the procedures for how to determine required parameters of the constitutive laws. Computational mechanics solves the resulting ordinary and partial differential equations. In Chapter 7, the methods of exact (closed-form) solutions are explained and they are applied to ordinary/partial differential equations with solvable boundary and initial conditions. In Chapter 8, the fundamentals of approximate solution methods are explained for one dimension first and then how to extend them to multi-dimensional problems. The readers are expected to learn and clearly understand how they are derived and applied to various problems in geomechanics. The final chapter involves the applications of the approximate methods to the actual problems in practice for geomechanical engineers, which cover the continuum to discontinuum, including the stress state of the earth as well as the ground motions induced by earthquakes. Six appendices are provided to have a clear understanding of continuum mechanics operations and procedures for how to deal with discontinuities/interfaces often encountered in rock mechanics and rock engineering.

Continuum Methods of Physical Modeling

Author: Kolumban Hutter

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 645

ISBN-13: 3662064022

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The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.

A First Course in Continuum Mechanics

Author: Oscar Gonzalez

Publisher: Cambridge University Press

Published: 2008-01-17

Total Pages: 5

ISBN-13: 0521886805

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The modeling and simulation of fluids, solids and other materials with significant coupling and thermal effects is becoming an increasingly important area of study in applied mathematics and engineering. Necessary for such studies is a fundamental understanding of the basic principles of continuum mechanics and thermodynamics. This book is a clear introduction to these principles. It is designed for a one- or two-quarter course for advanced undergraduate and beginning graduate students in the mathematical and engineering sciences, and is based on over nine years of teaching experience. It is also sufficiently self-contained for use outside a classroom environment. Prerequisites include a basic knowledge of linear algebra, multivariable calculus, differential equations and physics. The authors begin by explaining tensor algebra and calculus in three-dimensional Euclidean space. Using both index and coordinate-free notation, they introduce the basic axioms of continuum mechanics pertaining to mass, force, motion, temperature, energy and entropy, and the concepts of frame-indifference and material constraints. They devote four chapters to different theories of fluids and solids, and, unusually at this level, they consider both isothermal and thermal theories in detail. The book contains a wealth of exercises that support the theory and illustrate various applications. Full solutions to odd-numbered exercises are given at the end of each chapter and a complete solutions manual for all exercises is available to instructors upon request. Each chapter also contains a bibliography with references covering different presentations, further applications and numerical aspects of the theory. Book jacket.