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Continuum Mechanics Through the Twentieth Century A Concise Historical Perspective PDF

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Solid Mechanics and Its Applications Volume 196 Series Editor G. M. L. Gladwell Department of Civil Engineering University of Waterloo Waterloo, ON Canada For furthervolumes: http://www.springer.com/series/6557 Aims and Scope of the Series Thefundamentalquestionsarisinginmechanicsare:Why?,How?,andHowmuch? The aim of this series is to provide lucid accounts written by authoritative researchersgivingvisionandinsightinansweringthesequestionsonthesubjectof 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,kinematicsanddynamicsofrigidandelasticbodies: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 andmachine design. Themedianlevelofpresentationisthefirstyeargraduatestudent.Sometextsare monographsdefiningthecurrentstateofthefield;othersareaccessibletofinalyear undergraduates; butessentiallythe emphasis is onreadability andclarity. Gérard A. Maugin Continuum Mechanics Through the Twentieth Century A Concise Historical Perspective 123 GérardA.Maugin InstitutJean LeRond d’Alembert Université Pierre etMarieCurie 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 SpringerDordrechtHeidelbergNewYorkLondon LibraryofCongressControlNumber:2013931199 (cid:2)SpringerScience+BusinessMediaDordrecht2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. Duplication of this publication or parts thereof is permitted only under the provisions of theCopyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the CopyrightClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience?BusinessMedia(www.springer.com) Preface What is This Book About? ‘‘Youreasoneditoutbeautifully… Itissolongachain,andyeteverylinkringstrue’’ (Dr.WatsontoSherlockHolmes) The proposed conspectus of the development of continuum mechanics throughout the twentieth century seems to be unique in its scope and ambition. Althoughremindingthereaderoftheearlydevelopmentsofthedisciplinewiththe magisterial works of our elders (from Newton to the late nineteenth century or more precisely the advent of the First World War), the book concentrates on the twentieth century, and more particularly on its second half, as witnessed by the authorwhohasliveddirectlythroughthesedevelopments,andhashumblytriedto contributetothem.ButthemainreasonforthisdelineationisthatthepostWorld- WarTwoperiodsawanincredibleburgeoningandprogressintheenlargementof the field, its mathematization and its rational organization, i.e., both in its objec- tives and methods, tothe benefit offruitful applications to the mechanics of large classesofmaterialsandinreciprocalinteractionwithotherfields.Thishasbeena fruitful period thatsawaconsolidationofanalyticalworks, andadevelopmentof new aspects, both in modeling and mathematical approach. This is placed in a context where the marked interest of the author for the historyofScience,forEpistemology,andforPeopleisobvious,havingbeenmuch influenced by Pierre Duhem and Clifford Truesdell. Accordingly, this is also a studyaboutindividualsandscientificschoolsandinstitutionsinanevolvingsocial and historical context that experienced tragic events. We hope the book succeeds topresentwithobjectivityabalancedappraisalofcontributionsfromvariousparts of the world. The chosen approach emphasizes the importance of the role played by(i)organizedprofessionalgroups,e.g.,theA.S.M.Ewithitsspecificspiritinthe v vi Preface USA,(ii)traditionalstrongholdssuchastheUniversityofCambridgeintheUKor the Technical University of Hannover in Germany, (iii) remarkable individuals such as Clifford Truesdell in the USA, or Paul Germain in France, or still Leonid Sedov in the Soviet Union, and others in Poland, Germany, and Japan, and (iv) a well-structured network of teaching institutions and research units whether in countries that inherited from the Austro-Hungarian Empire, or in the original system of ‘‘grandes écoles’’ in France and their copies all over the world, or the Academies of Sciences in formerly communist-led countries such as the Soviet Union. That is, the development of modern continuum mechanics; in spite of its technical subtleties (effects of nonlinearity, thermodynamic irreversibility, microstructure, and singularities) that are carefully scrutinized, is shown to take placewithinatruehumanbackgroundwithitsgrandeursandpettiness,andnotas a purely abstract teleological evolution. This permeates an exposition which is, therefore,vividandbearswitnessofanepochmakingprocess,towhichtheauthor contributes both his technical expertize and his international experience. In order to fulfil this ambitious project and to satisfy the various needs of potential readers, a three-way strategy has been implemented. After two pre- liminarychaptersthattakethereadertopostWorldWarIandunderlinethenewly raised technical questions and the ongoing general reflections on the bases of continuummechanics,threechaptersaredevotedto:(i)newprogressinnonlinear aspects (in both elastic solids and the newly formulated rheology of non-Newto- nianfluids),(ii)aspecificspiritdistilledtocontinuummechanicsbytheinfluential organizedgrouprepresentedbytheAmericanSocietyofMechanicalEngineers(in particular with works in plasticity but also in coupled fields), and (iii) the aerial viewofcontinuummechanicsintroducedbytheTruesdellSchoolwithitseffortsat a true rationalization and axiomatization, as well as its construct of an efficient thermomechanics, and its positioning in a real historical perspective. Thesecondstrategiclineisimplementedinthenextsixchapterswhereamore per-country or regional view has been chosen for reasons that should be clear enough. This is due to the existence—still true at the time of most of the second half of the twentieth century—of national styles, peculiar teaching and research institutions inherited from the past, and the role played by some remarkable individuals.This isthecase inthe UK,France, Poland,andGermany. Therestof westernandsouthernEuropeancontributionsaredescribedinonelengthychapter together with some indications on some Asian countries. It is to repair an unjust toofrequentbelittlingoftheroleplayedbytheSovietUnionandRussiathatalong chapter is devoted to them. This allows for a more balanced view than usually given. The third line consists in the deeper and more technical examination of four special avenues of developments which the author estimates to be most emblematic-and original-of the last 50 years and to which he can devote a more thoughtful approach having been much involved in these. They are: (i) the interaction between continuum mechanics and electromagnetism, (ii) the mechanicsofgeneralizedcontinua,(iii)theso-calledconfigurationalmechanicsof continua, and (iv) relativistic continuum mechanics. These four avenues bring us Preface vii closer to other fields of physics in conjunction with typical twentieth century developments (exploitation of coupled fields, physical acoustics, solid-state physics, the ‘‘mechanics of materials’’, and relativistic physics). An epilogue providing a general summary and pointing to recent and future developments (going to smaller scales, influence of powerful computational means, and a true internationalization of science) is given by way of conclusion. An appendix pre- senting about one hundred short biographies of the most fruitful contributing mechaniciansintheconsideredperiodisgiveninencyclopedicformtothebenefit of all readers who can satisfy a legitimate curiosity by finding there useful, albeit brief, information. The bibliography given in different chapters is generous-in all, more than 900 entries. As it is conceived and written with an obvious generosity of information and a rather open mindedness to many styles and objects of works, the book, despiteitsinherentconcision,shouldsatisfythecuriosityandattracttheinterestof all those involved in the study and development of continuum mechanics as a general contemporary science. In writing this book, I admit to have benefited from a powerful memory of names,dates,andresearchpapers,onwhichisgraftedacertaininterestforforeign languages,atleastinreadingform.However,inthelineoftheteaching ofoneof mymentors,Paul GermaininParis,Ialways ponderedallcontributions, tryingto extract the best of each without prejudice, and being aware that scientific activity remains the product of human beings, with their qualities and deficiencies. But someenouncedappraisalsmaybethoughttoosevere,andotherstoolenient.Inall cases, the author takes the full responsibility of his judgment. For some largely unknownreasons,butperhapsbecauseoftheexceptionalqualityandegoofmany involved scientists in our field in the examined period of time, there have been vividdiscussionsonsomeprivilegedadvances,nottheleastinthealwaysdebated thermomechanics of continua. This is sometimesreflected in the book where I do nothesitatetogivemyownviewpointthatmightnotbesharedbyall.Informing my views, I also had the chance to be scientifically formed in two countries (FranceandtheUSA)andtohaveentertainedaprofessionalpositionthatallowed metobenefitfromcooperativescientificstaysinmanycountries.Iwasalsolucky, andhonored,todeliverseriesofgraduatelecturestostudentsandprofessorsfrom all over the world at the International Centre of Mechanical Sciences (so-called CISM) in Udine, Italy, and this for a record number of eight times between 1977 and 2011. All these opportunities were dutifully exploited, first to establish enrichingcontactsandbuildenduringfriendships,andnexttogetacquaintedwith other systems of higher education and research and their past history. These words should be enough to explain to the reader the frame of mind in which this book was written, as a mixture of plain scientific facts and personal recollections. The level of required knowledge is that of graduate studies and of professional researchers in continuum mechanics. I have avoided too many equations, keeping only a few representative ones. As to the rather rich bibliog- raphy,eitheritservestosubstantiateaspecificinformationoritprovidesanideaof workspublishedbysomeofthemostfruitfulscientists,oftenintheformofbooks. viii Preface Finally,veryclosetothespiritofautobiographicalnotes,fromtimetotimeIgive withinsquaredbrackets[..]whatIcalla‘‘personaltouch’’,whatmostlyconsistsin injecting some personal recollection to relax the reader from an obviously extre- mely serious reading of a dense text. I wish the reader an utmost pleasant and rewarding reading. Heart full thanks are due to my worldwide friends who contributed valuable information, and to my colleague, Dr. Martine Rousseau (Paris), for her critical reading of most chapters. Specialthanksgotothosewhohavebeenessentialintheeditingandproductionof this book, namely: Professor G.M.L. Gladwell, Editor-in-Chief, who unhesitat- ingly welcomed the book in his formidable series, Nathalie Jacobs and Cynthia Feenstra for their friendly editing at Springer in Dordrecht, and the production team at SPS in Chennai for their understanding and professional competence. Paris, February 2013 The Author Contents 1 The Land Clearers and the ‘‘Classics’’ . . . . . . . . . . . . . . . . . . . . 1 1.1 Analysis and Partial Differential Equations: 18th Century. . . . 1 1.2 Transition to the 19th Century. . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Finite Deformations: Piola, Kirchhoff, Boussinesq . . . . . . . . . 3 1.4 The French ‘‘Ingénieurs-savants’’. . . . . . . . . . . . . . . . . . . . . 5 1.5 The British Giants: Green, Kelvin, Stokes, Maxwell. . . . . . . . 7 1.6 The German School and its Giants: Kirchhoff, Clebsch, Voigt, Mohr, et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.7 Concluding Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Transition to the 20th Century . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1 Setting the Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Describing More Real Mechanical Behaviours. . . . . . . . . . . . 21 2.2.1 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.2 Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.3 Visco-Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3 New Interests of Investigation . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.1 Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.2 Internal Degrees of Freedom . . . . . . . . . . . . . . . . . 25 2.3.3 Elements of Homogenisation . . . . . . . . . . . . . . . . . 26 2.4 Pondering the Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 Concluding Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3 Rheology and Nonlinear Elasticity. . . . . . . . . . . . . . . . . . . . . . . . 31 3.1 Beyond Standard Linear Elasticity and Viscous Fluids . . . . . . 31 3.1.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 31 ix

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