Continuum Mechanics in the Earth Sciences
Continuum Mechanics in the Earth Sciences

Author: William I. Newman

Publisher: Cambridge University Press

Published: 2012-03-15

Total Pages: 195

ISBN-13: 1107078679

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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.

Stress and Strain
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 in the Earth and Environmental 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
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 Methods of Physical Modeling
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.

Continuum Mechanics and Applications in Geophysics and the Environment
Continuum Mechanics and Applications in Geophysics and the Environment

Author: Brian Straughan

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 402

ISBN-13: 3662044390

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The topics covered include soil mechanics and porous media, glacier and ice dynamics, climatology and lake physics, climate change as well as numerical algorithms. The book, written by well-known experts, addresses researchers and students interested in physical aspects of our environment.

Continuum Micromechanics
Continuum Micromechanics

Author: Dazhi Jiang

Publisher: Springer Nature

Published: 2023-03-11

Total Pages: 431

ISBN-13: 3031233131

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The book integrates theory, numerical methods, and practical applications seamlessly. MATLAB and MathCad programs are provided for readers to master the theory, understand the approach, and to further develop and apply the methods to geological problems. Multiscale and multi-physics investigations of Earth and planetary processes have been an active trend of research in Earth Sciences, thanks to the development of scientific computation and computer software and hardware. Based on the author's research and teaching over the past 15 years, the book stands alone as the first comprehensive text in unifying fundamental continuum micromechanics theory, geometric/kinematic analysis, and applications. The book should appeal to a broad audience of students and researchers, particularly those in the fields of structural geology, tectonics, (natural and experimental) rock deformation, mineral physics and rheology, and numerical modeling of multiscale and coupling processes.

Continuum Mechanics Modeling of Material Behavior
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 general principles of mass, momentum and energy balance. The book then moves beyond other books by dedicating several chapters 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. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. 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 Mechanics Aspects of Geodynamics and Rock Fracture Mechanics
Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics

Author: P. Thoft-Christensen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 282

ISBN-13: 9401022682

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During a NATO Advanced Study Institute in Izmir, Tur key, July 1973 on Modern Developments in Engineering Seis mology and Earthquake Engineering it emerged that a debate on Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics would be very welcome. Therefore, it was decided to seek NATO sponsorship for an Advanced Study In stitute on this subject. The purpose of the new Advanced Study Institute was to provide a link between mechanics of continuum media and geo dynamic s. By bringing together a group of leading scientists from the above two fields and participants actively engaged in research and applications in the same fields, it was believed that fruitful discussions could emerge to facilitate an exchange of knowledge, experience and newly-conceived ideas. The Institute aimed primarily at the solution of such problems as connected with the study of stress and strain con ditions in the Earth, generic causes of earthquakes, energy release and focal mechanism and seismic wave propagation in troducing modern methods of continuum and rock fracture mechanics. Secondly to inspire scientists working in continuum mechanics to open new avenues of research connected with the above problems, and seismologists to adapt modern, advanced methods of continuum and rock fracture mechanics to their work.