DOCSLIB.ORG

Continuum Mechanics and Thermodynamics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Continuum Mechanics and Thermodynamics Continuum Mechanics and Thermodynamics Continuum mechanics and thermodynamics are foundational theories of many fields of science and engineering. This book presents a fresh perspective on these important subjects, exploring their fundamentals and connecting them with micro- and nanoscopic theories. Providing clear, in-depth coverage, the book gives a self-contained treatment of topics di- rectly related to nonlinear materials modeling with an emphasis on the thermo-mechanical behavior of solid-state systems. It starts with vectors and tensors, finite deformation kine- matics, the fundamental balance and conservation laws, and classical thermodynamics. It then discusses the principles of constitutive theory and examples of constitutive models, presents a foundational treatment of energy principles and stability theory, and concludes with example closed-form solutions and the essentials of finite elements. Together with its companion book, Modeling Materials (Cambridge University Press, 2011), this work presents the fundamentals of multiscale materials modeling for graduate students and researchers in physics, materials science, chemistry, and engineering. A solutions manual is available at www.cambridge.org/9781107008267, along with a link to the authors’ website which provides a variety of supplementary material for both this book and Modeling Materials. Ellad B. Tadmor is Professor of Aerospace Engineering and Mechanics, University of Minnesota. His research focuses on multiscale method development and the microscopic foundations of continuum mechanics. Ronald E. Miller is Professor of Mechanical and Aerospace Engineering, Carleton University. He has worked in the area of multiscale materials modeling for over 15 years. Ryan S. Elliott is Associate Professor of Aerospace Engineering and Mechanics, University of Minnesota. An expert in stability of continuum and atomistic systems, he has received many awards for his work. Continuum Mechanics and Thermodynamics From Fundamental Concepts to Governing Equations ELLAD B. TADMOR University of Minnesota, USA RONALD E. MILLER Carleton University, Canada RYAN S. ELLIOTT University of Minnesota, USA CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao˜ Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9781107008267 C E. Tadmor, R. Miller and R. Elliott 2012 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2012 Printed in the United Kingdom at the University Press, Cambridge A catalog record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Tadmor, Ellad B., 1965– Continuum mechanics and thermodynamics : from fundamental concepts to governing equations / Ellad B. Tadmor, Ronald E. Miller, Ryan S. Elliott. p. cm. Includes bibliographical references and index. ISBN 978-1-107-00826-7 1. Continuum mechanics. 2. Thermodynamics – Mathematics. I. Miller, Ronald E. (Ronald Earle) II. Elliott, Ryan S. III. Title. QA808.2.T33 2012 531 – dc23 2011040410 ISBN 978-1-107-00826-7 Hardback Additional resources for this publication at www.cambridge.org/9781107008267 Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface page xi Acknowledgments xiii Notation xvii 1Introduction 1 Part I Theory 7 2 Scalars, vectors and tensors 9 2.1 Frames of reference and Newton’s laws 9 2.2 Tensor notation 15 2.2.1 Direct versus indicial notation 16 2.2.2 Summation and dummy indices 17 2.2.3 Free indices 18 2.2.4 Matrix notation 19 2.2.5 Kronecker delta 19 2.2.6 Permutation symbol 20 2.3 What is a tensor? 22 2.3.1 Vector spaces and the inner product and norm 22 2.3.2 Coordinate systems and their bases 26 2.3.3 Cross product 29 2.3.4 Change of basis 31 2.3.5 Vector component transformation 33 2.3.6 Generalization to higher-order tensors 34 2.3.7 Tensor component transformation 36 2.4 Tensor operations 38 2.4.1 Addition 38 2.4.2 Magnification 38 2.4.3 Transpose 39 2.4.4 Tensor products 39 2.4.5 Contraction 40 2.4.6 Tensor basis 44 2.5 Properties of tensors 46 2.5.1 Orthogonal tensors 46 2.5.2 Symmetric and antisymmetric tensors 48 2.5.3 Principal values and directions 48 2.5.4 Cayley–Hamilton theorem 51 v t vi Contents 2.5.5 The quadratic form of symmetric second-order tensors 52 2.5.6 Isotropic tensors 54 2.6 Tensor fields 55 2.6.1 Partial differentiation of a tensor field 56 2.6.2 Differential operators in Cartesian coordinates 56 2.6.3 Differential operators in curvilinear coordinates 60 2.6.4 Divergence theorem 64 Exercises 66 3 Kinematics of deformation 71 3.1 The continuum particle 71 3.2 The deformation mapping 72 3.3 Material and spatial field descriptions 74 3.3.1 Material and spatial tensor fields 75 3.3.2 Differentiation with respect to position 76 3.4 Description of local deformation 77 3.4.1 Deformation gradient 77 3.4.2 Volume changes 79 3.4.3 Area changes 80 3.4.4 Pull-back and push-forward operations 82 3.4.5 Polar decomposition theorem 83 3.4.6 Deformation measures and their physical significance 87 3.4.7 Spatial strain tensor 90 3.5 Linearized kinematics 91 3.6 Kinematic rates 93 3.6.1 Material time derivative 93 3.6.2 Rate of change of local deformation measures 96 3.6.3 Reynolds transport theorem 100 Exercises 101 4 Mechanical conservation and balance laws 106 4.1 Conservation of mass 106 4.1.1 Reynolds transport theorem for extensive properties 109 4.2 Balance of linear momentum 110 4.2.1 Newton’s second law for a system of particles 110 4.2.2 Balance of linear momentum for a continuum system 111 4.2.3 Cauchy’s stress principle 113 4.2.4 Cauchy stress tensor 115 4.2.5 An alternative (“tensorial”) derivation of the stress tensor 117 4.2.6 Stress decomposition 119 4.2.7 Local form of the balance of linear momentum 119 4.3 Balance of angular momentum 120 4.4 Material form of the momentum balance equations 122 4.4.1 Material form of the balance of linear momentum 122 4.4.2 Material form of the balance of angular momentum 124 4.4.3 Second Piola–Kirchhoff stress 125 Exercises 127 t vii Contents 5 Thermodynamics 129 5.1 Macroscopic observables, thermodynamic equilibrium and state variables 130 5.1.1 Macroscopically observable quantities 131 5.1.2 Thermodynamic equilibrium 133 5.1.3 State variables 133 5.1.4 Independent state variables and equations of state 136 5.2 Thermal equilibrium and the zeroth law of thermodynamics 137 5.2.1 Thermal equilibrium 137 5.2.2 Empirical temperature scales 138 5.3 Energy and the first law of thermodynamics 139 5.3.1 First law of thermodynamics 139 5.3.2 Internal energy of an ideal gas 143 5.4 Thermodynamic processes 147 5.4.1 General thermodynamic processes 147 5.4.2 Quasistatic processes 147 5.5 The second law of thermodynamics and the direction of time 148 5.5.1 Entropy 149 5.5.2 The second law of thermodynamics 150 5.5.3 Stability conditions associated with the second law 152 5.5.4 Thermal equilibrium from an entropy perspective 153 5.5.5 Internal energy and entropy as fundamental thermodynamic relations 156 5.5.6 Entropy form of the first law 159 5.5.7 Reversible and irreversible processes 161 5.6 Continuum thermodynamics 168 5.6.1 Local form of the first law (energy equation) 170 5.6.2 Local form of the second law (Clausius–Duhem inequality) 175 Exercises 177 6 Constitutive relations 180 6.1 Constraints on constitutive relations 181 6.2 Local action and the second law of thermodynamics 184 6.2.1 Specific internal energy constitutive relation 184 6.2.2 Coleman–Noll procedure 186 6.2.3 Onsager reciprocal relations 190 6.2.4 Constitutive relations for alternative stress variables 191 6.2.5 Thermodynamic potentials and connection with experiments 192 6.3 Material frame-indifference 195 6.3.1 Transformation between frames of reference 196 6.3.2 Objective tensors 200 6.3.3 Principle of material frame-indifference 202 6.3.4 Constraints on constitutive relations due to material frame-indifference 203 6.3.5 Reduced constitutive relations 207 6.3.6 Continuum field equations and material frame-indifference 213 6.3.7 Controversy regarding the principle of material frame-indifference 213 6.4 Material symmetry 215 6.4.1 Simple fluids 218 6.4.2 Isotropic solids 221 t viii Contents 6.5 Linearized constitutive relations for anisotropic hyperelastic solids 225 6.5.1 Generalized Hooke’s law and the elastic constants 229 6.6 Limitations of continuum constitutive relations 236 Exercises 237 7 Boundary-value problems, energy principles and stability 242 7.1 Initial boundary-value problems 242 7.1.1 Problems in the spatial description 243 7.1.2 Problems in the material description 245 7.2 Equilibrium and the principle of stationary potential energy (PSPE) 247 7.3 Stability of equilibrium configurations 249 7.3.1 Definition of a stable equilibrium configuration 250 7.3.2 Lyapunov’s indirect method and the linearized equations of motion 251 7.3.3 Lyapunov’s direct method and the principle of minimum potential energy (PMPE) 255 Exercises 259 Part II Solutions 263 8 Universal equilibrium
Load more

Recommended publications
  • The Scientific Life and Influence of Clifford Ambrose Truesdell
    Arch. Rational Mech. Anal. 161 (2002) 1–26 Digital Object Identifier (DOI) 10.1007/s002050100178 The Scientific Life and Influence of Clifford Ambrose Truesdell III J. M. Ball & R. D. James Editors 1. Introduction Clifford Truesdell was an extraordinary figure of 20th century science. Through his own contributions and an unparalleled ability to absorb and organize the work of previous generations, he became pre-eminent in the development of continuum mechanics in the decades following the Second World War. A prolific and scholarly writer, whose lucid and pungent style attracted many talented young people to the field, he forcefully articulated a view of the importance and philosophy of ‘rational mechanics’ that became identified with his name. He was born on 18 February 1919 in Los Angeles, graduating from Polytechnic High School in 1936. Before going to university he spent two years at Oxford and traveling elsewhere in Europe. There he improved his knowledge of Latin and Ancient Greek and became proficient in German, French and Italian.These language skills would later prove valuable in his mathematical and historical research. Truesdell was an undergraduate at the California Institute of Technology, where he obtained B.S. degrees in Physics and Mathematics in 1941 and an M.S. in Math- ematics in 1942. He obtained a Certificate in Mechanics from Brown University in 1942, and a Ph.D. in Mathematics from Princeton in 1943. From 1944–1946 he was a Staff Member of the Radiation Laboratory at MIT, moving to become Chief of the Theoretical Mechanics Subdivision of the U.S. Naval Ordnance Labo- ratory in White Oak, Maryland, from 1946–1948, and then Head of the Theoretical Mechanics Section of the U.S.
    [Show full text]
  • Accomplishments
    REPORT TO THE CommunityVancouver Public Schools JULY 2006 • VOLUME 16, ISSUE 4 accomplishmentsCelebrating alumni, staff and students Ann Kao is saving the world, one person at a time In a remote refuge camp in the hills of northeast Kao’s mission to improve the world began when and I don’t have any money,’ she said. ‘Where is Rwanda, Dr. Ann Kao is doing what she can to save a she was a young girl growing up in Vancouver. She your money?’ I ask and she tells me, ‘I gave it away.’” two-year-old child. The baby lies motionless, other attended the Challenge program at Truman Elemen- than a slight twitching of his arms. His breathing is tary and Shumway Middle School. At the age of Following the deadly tsunami that hit Southeast shallow. 16, she graduated from Hudson’s Bay High School Asia on Dec. 26, 2004, Kao joined Project HOPE as both a Washington Scholar and a National Merit (Health Opportunities for People Everywhere) Kao works in a tent. She has no running water Scholar. and the U.S. Navy in the relief mission. She was and only a few basic medical supplies. This young in the forefront, doctor, who has not yet reached her 30th birthday, Ann Koa’s parents, Annie and Ken Kao, have saved providing urgent is the only physician for 5,000 Congolese Tutsi mementos from their daughter’s childhood—her medical care from Obviously refugees. She is helping survivors of the 1994 poem that won a national contest when she was 13, the USNS hos- “we’re here for a genocide.
    [Show full text]
  • Commencement1978.Pdf (5.368Mb)
    Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://archive.org/details/commencement1978 ORDER OF PROCESSION MARSHALS JOHN BARTH FRANCIS E. ROURKE PAUL DANIELS THOMAS W. SIMPSON ARCHIE S. GOLDEN CHARLES R. WESTGATE GERALD S. GOTTERER J. WENDELL WIGGINS JAMES H. HUSTIS III KENNETH T. WILBURN MARGARET E. KNOPF M. GORDON WOLMAN ROBERT A. LYSTAD JOHN P. YOUNG THE GRADUATES * MARSHALS ROGER A. HORN PAUL R. OLSON THE DEANS MEMBERS OF THE SOCIETY OF SCHOLARS OFFICERS OF THE UNIVERSITY THE TRUSTEES * MARSHALS OWEN M. PHILLIPS OREST RANUM THE FACULTIES CHIEF MARSHAL EDYTH H. SCHOENRICH THE CHAPLAINS THE HONORARY DEGREE CANDIDATES THE PROVOST OF THE UNIVERSITY THE CHAIRMAN OF THE BOARD OF TRUSTEES THE PRESIDENT OF THE UNIVERSITY * ORDER OF EVENTS STEVEN MULLER President of the University, presiding * * # FANFARE PROCESSIONAL The audience is requested to stand as the Academic Procession moves into the area and to remain standing after the Invocation. " Trumpet Voluntary " Henry Purcell The Peabody Wind Ensemble Richard Higgins, Director * INVOCATION REV. CHESTER W1CK.WIRE Chaplain, The Johns Hopkins University * THE NATIONAL ANTHEM * GREETINGS ROBERT D. H. HARVEY Chairman of the Board of Trustees * PRESENTATION OF NEW MEMBERS OF THE SOCIETY OF SCHOLARS ARTHUR ADEL WILLARD E. GOODWIN ROBERT AUSTRIAN SAMIR S. NAJJAR JOHN HOWIE FLINT BROTHERSTON KENNETH L. PICKRELL DORLAND JONES DAVIS OSCAR D. RATNOFF RAY E. TRUSSELL SCHOLARS PRESENTED BY RICHARD LONGAKER Provost of the University " Sonata From Die Bankelsangerlieder ANONYMOUS (c. 1684) * CONFERRING OF HONORARY DEGREES ALEXANDER DUNCAN LANGMUIR FRANCIS JOHN PETTIJOHN VIRGIL THOMSON JOHN ROBERT EVANS PRESENTED BY RICHARD LONGAKER ADDRESS JOHN ROBERT EVANS President, University of Toronto CONFERRING OF DEGREES ON CANDIDATES BACHELORS OF ARTS Presented by SIGMUND R.
    [Show full text]
  • Three Facets of Modern Liquid Crystal Science
    Three facets of modern liquid crystal science The complex phase behavior of chiral thermotropic smectics Electrospinning of nano-/microfibers with liquid crystals Dispersing and aligning carbon nanotubes in lyotropic liquid crystals Jan Lagerwall January 27, 2011 2 Curiosity is one of the permanent and certain characteristics of a vigorous intellect. Samuel Johnson 3 Three facets of modern liquid crystal science Habilitationsschrift zur Erlangung des akademischen Grades doctor rerum naturalium habilitatus (Dr. rer. nat. habil.) vorgelegt der Naturwissenschaftlichen Fakult¨atII der Martin-Luther-Universit¨atHalle-Wittenberg von Herrn Tekn. Dr. Jan P. F. Lagerwall geb. am 28.05.1970 in G¨oteborg, Schweden Gutachter: 1. Herr Prof. Dr. H. Kitzerow (Universit¨atPaderborn) 2. Herr Prof. Dr. E. Samulski (University of North Carolina at Chapel Hill) 3. Herr Prof. Dr. C. Tschierske (Martin-Luther-Universit¨atHalle-Wittenberg) Halle (Saale), verteidigt am 23.11.2010. 4 Preface This habilitation thesis summarizes my research during the almost eight years that have passed since I gained my Ph.D. The common denominator of this work is liquid crystals, which have played a central role in almost all my research work. During the last five-six years I have however combined liquid crystal research with aspects, materials and techniques from quite different research areas. Therefore, of the three main chapters of this thesis only the first deals purely with liquid crystals. The two latter are devoted to polymer fibers containing liquid crystals| produced by the technique of coaxial electrospinning|and composites of liquid crystals and carbon nanotubes, respectively. Considering this quite broad scope I hope that a readership comprising also non-liquid crystal researchers can find the thesis interesting.
    [Show full text]
  • Commencement1983.Pdf (5.239Mb)
    VT THE CLOSE OF THE 107th ACADEMIC YEAR The Johns Hopkins University May 27, 1983 Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://archive.org/details/commencement1983 ORDER OF PROCESSION MARSHALS Arthur Doak Barnett Roger A. Horn Arthur Bushel William H. Huggins Russ B. Corotis Warner E. Love Milton Cummings, Jr. Margaret M. Murphy Frederic Davidson Lee Joyce Richmond Sidney S. Forrest Henry M. Seidel Richard L. Higgins Charles R. Westgate. THE GRADUATES MARSHALS Richard E. Flathman James C. Walker THE DEANS MEMBERS OF THE SOCIETY OF SCHOLARS OFFICERS OF THE UNIVERSITY THE TRUSTEES MARSHALS Hans Goedicke George W. Fisher THE FACULTIES * CHIEF MARSHAL M. Gordon Wolman THE CHAPLAINS THE HONORARY DEGREE CANDIDATES THE PROVOST OF THE UNIVERSITY THE CHAIRMAN OF THE BOARD OF TRUSTEES THE PRESIDENT OF THE UNIVERSITY ORDER OF EVENTS STEVEN MULLER President of the University, presiding PRELUDE PROCESSIONALS The audience is requested to stand as the Academic Procession moves into the area and to remain standing after the Invocation. Marches from Belshazzar, Floridante, Ezio, Saint Cecilia's Day, Rinaldo and Scipione Georg Frederich Handel (1685-1759) THE PRESIDENT'S PROCESSION Fanfare Walter Piston (1894-1976) March from Judas Maccabaeus Georg Frederich Handel (1685-1759) INVOCATION CLYDE R. SHALLENBERGER Director, Chaplaincy Service Johns Hopkins Medical Institutions * THE NATIONAL ANTHEM GREETINGS ROBERT D. H. HARVEY Chairman of the Board of Trustees PRESENTATION OF NEW MEMBERS OF THE SOCIETY OF SCHOLARS MORDHAY AVRON RlCHARD B. HORNICK Ross J. Baldessarini Julius R. Krevans Shao-Chiung Cheng Dwight C. McGoon Malcolm Andrew Ferguson-Smith David L.
    [Show full text]
  • Continuum Mechanics Through the Ages - from the Renaissance to the Twentieth Century from Hydraulics to Plasticity Solid Mechanics and Its Applications
    Solid Mechanics and Its Applications Gérard A. Maugin Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century From Hydraulics to Plasticity Solid Mechanics and Its Applications Volume 223 Series editors J.R. Barber, Ann Arbor, USA Anders Klarbring, Linköping, Sweden Founding Editor G.M.L. Gladwell, Waterloo, ON, Canada Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is to the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity. More information about this series at http://www.springer.com/series/6557 Gérard A. Maugin Continuum Mechanics
    [Show full text]
  • Continuum Mechanics Through the Twentieth Century a Concise Historical Perspective Solid Mechanics and Its Applications
    Solid Mechanics and Its Applications Series Editor: G.M.L. Gladwell Gérard A. Maugin Continuum Mechanics Through the Twentieth Century A Concise Historical Perspective Solid Mechanics and Its Applications Volume 196 Series Editor G. M. L. Gladwell Department of Civil Engineering University of Waterloo Waterloo, ON Canada For further volumes: http://www.springer.com/series/6557 Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity. Gérard A. Maugin Continuum Mechanics Through the Twentieth Century A Concise Historical Perspective 123 Gérard A. Maugin Institut Jean Le Rond d’Alembert Université Pierre et Marie Curie Paris Cedex 05 France ISSN 0925-0042 ISBN 978-94-007-6352-4 ISBN 978-94-007-6353-1 (eBook) DOI 10.1007/978-94-007-6353-1 Springer Dordrecht Heidelberg New York London Library of Congress Control Number: 2013931199 Ó Springer Science+Business Media Dordrecht 2013 This work is subject to copyright.
    [Show full text]
  • Notices of the American Mathematical Society
    Notices of the American Mathematical Society June 1983, Issue 226 Volume 30, Number 4, Pages 385-472 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of th~ meet· ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions.
    [Show full text]
  • Springer Science+ Business Media, LLC Ronald S
    Collected Papers of R.S. Rivlin Volume I Springer Science+ Business Media, LLC Ronald S. Rivlin. Photo by Fella Studios, Inc. G.I. Barenblatt D.D. Joseph Editors Collected Papers of R.S. Rivlin Volume I With 323 Illustrations Springer Grigori Isaakovich Barenblatt G.l. Taylor Professor of Fluid Mechanics, Emeritus Department of Applied Mathematics and Theoretical Physics University of Cambridge Silver Street Cambridge CB3 9EW United Kingdom Daniel D. Joseph Department of Aerospace Engineering 107 Ackerman Hali University of Minnesota Il O Union Street, SE Minneapolis, MN 55455, USA Collected Papers of R.S. Rivlin Volume 1: 1-1424 Volume II: 1425-2828 Library of Congress Cataloging-in-Publication Data Rivlin, Ronald S. [Works. 1996] Collected papers of R.S. Rivlin 1 G.!. Barenblatt and D.D. Joseph, editors. p. cm. Includes bibliographical references. ISBN 978-1-4612-7530-5 ISBN 978-1-4612-2416-7 (eBook) DOI 10.1007/978-1-4612-2416-7 1. Continuum mechanics. 2. Nonlinear theories. 1. Barenblatt, G.l. II. Joseph, Daniel D. III. Title. QA3.R588 1996 531-cd20 96-22080 Printed on acid-free paper. © 1997 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc. in 1997 Softcover reprint of the hardcover 1st edition 1997 Ali rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
    [Show full text]
  • Front Matter
    Cambridge University Press 978-0-521-40598-0 - The Mechanics and Thermodynamics of Continua Morton E. Gurtin, Eliot Fried and Lallit Anand Frontmatter More information THE MECHANICS AND THERMODYNAMICS OF CONTINUA The Mechanics and Thermodynamics of Continua presents a unified treatment of con- tinuum mechanics and thermodynamics that emphasizes the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behavior. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and ther- modynamics for graduates and advanced undergraduates in engineering, physics, and mathematics. The chapters on plasticity discuss the standard isotropic theories and crys- tal plasticity and gradient plasticity. Morton E. Gurtin is the Alumni Professor Emeritus of Mathematics at Carnegie Mellon University. His research concerns nonlinear continuum mechanics and thermodynam- ics, with recent emphasis on applications to problems in materials science. Among his many awards are the 2004 Timoshenko Medal of the American Society of Mechani- cal Engineers (ASME) “in recognition of distinguished contributions to the field of ap- plied mechanics”; the Agostinelli Prize (an annual prize in pure and applied mathemat- ics and mathematical physics); Accademia Nazionale dei Lincei, Italy; Dottore Honoris Causa, Civil Engineering, University of Rome; Distinguished Graduate School Alumnus Award, Brown University; and the Richard Moore Education Award, Carnegie Mel- lon University. In addition to his numerous archival research publications, Professor Gurtin is the author of Configurational Forces as Basic Concepts in Continuum Physics, An Introduction to Continuum Mechanics, Thermomechanics of Evolving Phase Bound- aries in the Plane, Topics in Finite Elasticity, The Linear Theory of Elasticity, Handbuch der Physik, Volume VIa/2, and Wave Propagation in Dissipative Materials (with B.
    [Show full text]
  • Aerospace Engineering and Mechanics
    DEPARTMENT OF AEROSPACE ENGINEERING AND MECHANICS Department Update - Summer 2021 Welcome Professors Kirsten Strandjord and Melissa Green The Department of Aerospace En- Green joins the fluid dynamics fac- gineering and Mechanics is pleased ulty as an Associate Professor. Her to welcome Kirsten Strandjord and research focuses on lift generated Melissa Green as the newest addi- by flapping wings, thrust generated tions to the faculty. Both Strandjord by oscillating fins, drag generated by and Green will start in Fall 2021. struts and cables, moments gener- ated by a gust hitting an aircraft Strandjord’s joins the aerospace wing. In all of these scenarios, the systems group as an Assistant Profes- interaction of fluid (air, water) with sor. Her area of research is in Global the surface generates coherent What’s Inside... Positioning System (GPS) and Global structures or motions in the fluid, -of Navigation Satellite System (GNSS) ten in the form of vorticity or distinct technology and applications for posi- vortices. These in turn are often p.2 Letter from Department Head tioning, navigation and timing (PNT). associated with pressure and forces Strandjord’s research involves char- on the surface. In some cases, these p.3 Faculty News & Awards acterizing the phenomena of GNSS interactions are desired and need to p.5 Student News & Awards multipath and the effects on position be augmented, while in others, they p.8 Senior Design solutions. She is also active in the need to be mitigated. Fundamental p.10 Student Teams area of urban navigation, where she investigation and visualization of investigates the use of long-term how these interactions play out is p.12 Research evolution (LTE) signals typically used key to predicting future forces or p.14 Congratulations Graduates for communication purposes as sig- moments, and to designing appropri- p.15 Alumni News nals of opportunity for navigation.
    [Show full text]
  • THE RATIONAL SPIRIT in MODERN CONTINUUM MECHANICS the Rational Spirit in Modern Continuum Mechanics
    See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/227194505 E. Frola (1906–1962): An Attempt Towards an Axiomatic Theory of Elasticity Chapter in Journal of Elasticity · January 2006 DOI: 10.1007/1-4020-2308-1_10 CITATIONS READS 0 602 2 authors: Sandro Caparrini Franco Pastrone Università degli Studi di Torino Accademia delle Scienze di Torino 1 PUBLICATION 0 CITATIONS 84 PUBLICATIONS 515 CITATIONS SEE PROFILE SEE PROFILE All content following this page was uploaded by Franco Pastrone on 19 December 2013. The user has requested enhancement of the downloaded file. THE RATIONAL SPIRIT IN MODERN CONTINUUM MECHANICS The Rational Spirit in Modern Continuum Mechanics Essays and Papers Dedicated to the Memory of Clifford Ambrose Truesdell III Edited by CHI-SING MAN University of Kentucky, Lexington, U.S.A. and ROGER L. FOSDICK University of Minnesota, Minneapolis, U.S.A. Reprinted from Journal of Elasticity: The Physical and Mathematical Science of Solids, Vols. 70, 71, 72 (2003) KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 1-4020-2308-1 Print ISBN: 1-4020-1828-2 ©2005 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: http://ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Portrait by Joseph Sheppard Table of Contents Portrait by Joseph Sheppard v Foreword by Chi-Sing Man and Roger Fosdick xi Published Works of Clifford Ambrose Truesdell III xiii Serials Edited by Clifford Ambrose Truesdell III xli Eulogium by Roger Fosdick xliii Photograph: Bloomington, Indiana, 1959 xlv BERNARD D.
    [Show full text]