Continuum Mechanics Through the Twentieth Century A Concise Historical Perspective

320 Pages·2013·1.543 MB·English

by  Maugin, Gřard A

Solid Mechanics and Its Applications
Volume 196
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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
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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