The Rational Spirit in Modern Continuum Mechanics

846 Pages·2005·4.706 MB·English

by  Man C.-S., Fosdick R.L. (eds.)

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
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PortraitbyJosephSheppard
Table of Contents
PortraitbyJosephSheppard v
ForewordbyChi-SingManandRogerFosdick xi
PublishedWorksofCliffordAmbroseTruesdellIII xiii
SerialsEditedbyCliffordAmbroseTruesdellIII xli
EulogiumbyRogerFosdick xliii
Photograph:Bloomington,Indiana,1959 xlv
BERNARDD.COLEMAN/MemoriesofCliffordTruesdell 1–13
ENRICOGIUSTI/CliffordTruesdell(1919–2000),HistorianofMathematics 15–22
WALTER NOLL / The Genesis of Truesdell’s Nonlinear Field Theories of
Mechanics 23–30
JAMESSERRIN/AnAppreciationofCliffordTruesdell 31–38
D. SPEISER / Clifford A. Truesdell’s Contributions to the Euler and the
BernoulliEdition 39–53
Photograph:Baltimore, Maryland, 1978
STUART S. ANTMAN / Invariant Dissipative Mechanisms for the Spatial
MotionofRodsSuggestedbyArtificialViscosity 55–64
MILLARDF.BEATTY/AnAverage-StretchFull-NetworkModelforRubber
Elasticity 65–86
MICHELEBUONSANTIandGIANNIROYER-CARFAGNI/From3-DNon-
linearElasticityTheoryto1-DBarswithNonconvexEnergy 87–100
GIOVANNIBURATTI,YONGZHONGHUOandINGOMÜLLER/Eshelby
TensorasaTensorofFreeEnthalpy 101–112
SANDRO CAPARRINI and FRANCO PASTRONE / E. Frola (1906–1962):
AnAttemptTowardsanAxiomaticTheoryofElasticity 113–125
GIANFRANCOCAPRIZandPAOLOMARIAMARIANO/Symmetriesand
HamiltonianFormalismforComplexMaterials 127–140
DONALD E. CARLSON, ELIOT FRIED and DANIEL A. TORTORELLI /
Geometrically-basedConsequencesofInternalConstraints 141–149
vii
viii
YI-CHAO CHEN / Second Variation Condition and Quadratic Integral In-
equalitieswithHigher OrderDerivatives 151–167
ELENACHERKAEVandANDREJCHERKAEV/PrincipalComplianceand
RobustOptimalDesign 169–196
JOHN C. CRISCIONE/Rivlin’sRepresentationFormulaisIll-Conceivedfor
theDeterminationofResponseFunctionsviaBiaxialTesting 197–215
CESARE DAVINI and ROBERTO PARONI / Generalized Hessian and Ex-
ternalApproximationsinVariationalProblemsofSecondOrder 217–242
F. DELL’ISOLA,G.SCIARRA andR.C. BATRA /Static Deformationsofa
LinearElasticPorousBodyFilledwithanInviscidFluid 243–264
GIANPIETRODELPIERO/AClassofFitRegionsandaUniverseofShapes
forContinuumMechanics 265–285
LUCA DESERI and DAVID R. OWEN / Toward a Field Theory for Elastic
BodiesUndergoingDisarrangements 287–326
MARCELOEPSTEINandIOANBUCATARU/ContinuousDistributionsof
DislocationsinBodieswithMicrostructure 327–344
MARCELOEPSTEINandMAREKELZ˙ANOWSKI/AModeloftheEvolu-
tionofaTwo-dimensionalDefectiveStructure 345–355
J.L.ERICKSEN/OntheTheoryofRotationTwinsinCrystalMultilattices 357–373
MAUROFABRIZIOandMURROUGHGOLDEN/MinimumFreeEnergies
forMaterialswithFiniteMemory 375–397
ROGER FOSDICK and LEV TRUSKINOVSKY / About Clapeyron’s The-
oreminLinearElasticity 399–426
M.FOSS,W.HRUSAandV.J.MIZEL/TheLavrentievPhenomenoninNon-
linearElasticity 427–435
GIOVANNIP. GALDI/SteadyFlow ofa Navier–StokesFluidarounda Ro-
tatingObstacle 437–467
TIMOTHYJ.HEALEYandERROLL.MONTES-PIZARRO/GlobalBifurc-
ationinNonlinearElasticitywithanApplicationtoBarrellingStates
ofCylindricalColumns 469–494
MOJIAHUANGandCHI-SINGMAN/ConstitutiveRelationofElasticPoly-
crystalwithQuadraticTextureDependence 495–524
MASARU IKEHATAandGEN NAKAMURA / ReconstructionFormulafor
IdentifyingCracks 525–538
R.J.KNOPSandPIEROVILLAGGIO/AnApproximateTreatmentofBlunt
BodyImpact 539–554
I-SHIH LIU / On the Transformation Property of the Deformation Gradient
underaChangeofFrame 555–562
ix
KONSTANTINA.LURIE/SomeNewAdvancesintheTheoryofDynamic
Materials 563–573
GERARDA.MAUGIN/Pseudo-plasticityandPseudo-inhomogeneityEffects
inMaterialsMechanics 575–597
A.IANMURDOCH/OntheMicroscopicInterpretationofStressandCouple
Stress 599–625
PABLOV.NEGRÓN-MARRERO/TheHangingRopeofMinimumElonga-
tionforaNonlinearStress–StrainRelation 627–649
MARIOPITTERI/OnCertainWeakPhaseTransformationsinMultilattices 651–671
PAOLOPODIO-GUIDUGLI/ANewQuasilinearModelforPlateBuckling 673–698
G.RODNAYandR.SEGEV/Cauchy’sFluxTheoreminLightofGeometric
IntegrationTheory 699–719
U. SARAVANAN and K.R. RAJAGOPAL / A Comparison of the Response
ofIsotropicInhomogeneousElasticCylindricalandSphericalShells
andTheirHomogenizedCounterparts 721–749
M.ŠILHAVÝ/OnSO(n)-InvariantRank1ConvexFunctions 751–762
K.WILMAN´SKI/OnThermodynamicsofNonlinearPoroelasticMaterials 763–777
WAN-LEEYIN/AnisotropicElasticityandMulti-MaterialSingularities 779–808
Foreword
Through his voluminous and influential writings, editorial activities, organiza-
tional leadership, intellectual acumen, and strong sense of history, Clifford Am-
brose Truesdell III (1919–2000) was the main architect for the renaissance of ra-
tionalcontinuum mechanicssincethemiddleofthetwentiethcentury.Thepresent
collectionof42essaysandresearchpaperspaystributetothismanofmathematics,
science, andnaturalphilosophy aswellastohislegacy.
The first five essays by B.D. Coleman, E. Giusti, W. Noll, J. Serrin, and
D.SpeiserweretextsofaddressesgivenbytheirauthorsattheMeetinginmemory
ofCliffordTruesdell,whichwasheldinPisainNovember2000.Intheseessaysthe
reader willfindpersonal reminiscences ofCliffordTruesdell themanandofsome
ofhisactivitiesasscientist,author,editor,historianofexactsciences,andprincipal
founding memberoftheSocietyforNaturalPhilosophy.
The bulk of the collection comprises 37 research papers which bear witness to
theTruesdellian legacy.Thesepaperscoverawiderangeoftopics; whattiesthem
together is the rational spirit. Clifford Truesdell, in his address upon receipt of a
BirkhoffPrizein1978,puttheessenceofmoderncontinuummechanicssuccinctly
as “conceptual analysis, analysis not in the sense of the technical term but in the
root meaning: logical criticism, dissection, and creative scrutiny.” It is in celebra-
tion of this spirit and this essence that these research papers are dedicated to the
memoryoftheir bearer, driving force, andmainpromoter forhalf acentury. Most
of these papers were presented at the Symposium on Recent Advances and New
Directions in Mechanics, Continuum Thermodynamics, and Kinetic Theory – In
Memory of Clifford A. Truesdell III, held in Blacksburg, Virginia, in June 2002;
partsoftwopapersweredeliveredatthemeetingRememberingCliffordTruesdell,
heldinTurininNovember2002;andtherestwaswrittenespeciallyforthepresent
collection.
The portrait, a photo of which serves as the frontispiece of this collection,
adorns the Clifford A. Truesdell III Room of History of Science in the library of
theScuolaNormaleSuperiore(Pisa,Italy),whichwasinauguratedinOctober2003
andpermanentlyhousesCliffordTruesdell’spreviouslyprivatecollectionofbooks,
papers,andcorrespondence.WearegratefultoMrs.CharlotteTruesdellforhelping
ussecure adigital fileof thisphoto andfor providing uswiththe listofpublished
worksofCliffordTruesdell.
CHI-SING MAN ROGER FOSDICK
UniversityofKentucky UniversityofMinnesota
Lexington Minneapolis
xi
Published Works of
Clifford Ambrose Truesdell III(cid:1)
Theyearofpublication isomittedfromtheentryunless itdiffersfromtheyear
under which the entry is listed. Letters following a number indicate subsidiary
separatepublications, asfollows:
P Preliminaryreportorpreprint,
A Abstract,separately published oronlypublished version,
C Condensed orextracted version,
L Lectureconcerning partorallofthecontents ofmainentry,
R Reprint,entire,
RE Reprintofanextract,
T Translation, entire,
TC Translation, condensed,
TE Translation ofanextract.
Thelistexcludessome600reviewspublishedbetween1949and1971inMath-
ematical Reviews, Applied Mechanics Reviews, Zentralblatt für Mathematik, In-
dustrialLaboratories, andMathematicsofComputation butincludes reviewspub-
lishedinotherjournals.
1943
1. (Co-author P. NEMÉNYI) Astressfunction forthemembranetheory ofshells
of revolution, Proceedings of the National Academy of Sciences (U.S.A.)29,
159–162.
Otherpublication in1943:No.3A1.
1944
2. ALONZO CHURCH, Introduction to Mathematical Logic, Part I, Notes by
C.A. TRUESDELL, Annals of Mathematics Studies No. 13, Princeton, Uni-
versityPress,vi+118pp.
(cid:1) Notebytheeditors:Thislistandthelistonp.29areslightlyeditedversionsofthosethatwe
received fromMrs. C.Truesdell, towhomweareheartilygrateful. Inour editorial workwehave
addedafewentries,updatedseveralitems,andmadeasmallnumberofotherminorcorrections.To
G.P.Galdi,K.Hutter,R.G.Muncaster,F.Pastrone,andD.Speiser,wearebeholdenfortheirhelpin
trackingdownarticletitlesandnumbersofjournalvolumes.Inwhatfollows,explanatoryremarks
setoffbysquarebracketsweremadebyCliffordTruesdellhimself.
xiii
xiv PUBLISHEDWORKSOFC.A.TRUESDELL
1945
3. The membrane theory of shells of revolution, Transactions of the American
MathematicalSociety 58,96–166.
3A1. The differential equations of the membrane theory of shells of revolu-
tion, Bulletin of the American Mathematical Society 49 (1943), 863–
864.
3A2. Themembrane theory of shells of revolution, Bulletin of theAmerican
Mathematical Society51,225.
4. Onafunction whichoccursinthetheoryofthestructure ofpolymers, Annals
of Mathematics 46,144–157. (cid:1) (cid:1)
5. GeneralizationsofEuler’ssummationsoftheseries ∞ n−2m, ∞ (−)n×
n=1 n=0
(2n+1)−2m−1,etc.,AnnalsofMathematics46,194–195.
Otherpublication in1945:No.12A1.
1946
6. (Co-author R.C. PRIM) On Linearized Axially Symmetric Flow of a Com-
pressibleFluid,U.S.NavalOrdnanceLaboratoryMemorandum8885,16De-
cember,4pp.
7. On Behrbohm and Pinl’s linearization of the equation of two-dimensional
steady polytropic flow of a compressible fluid, Proceedings of the National
Academy of Sciences (U.S.A.)32, 289–293 = U.S.Naval Ordnance Labora-
toryMemorandum 8888,18December,6pp.
7A. On Behrbohm and Pinl’s linearization of the two dimensional steady
flowofacompressible adiabaticfluid,BulletinoftheAmericanMathe-
maticalSociety 53(1947), 59.
Otherpublications in1946:Nos.8Aand12A2.
1947
8. OnSokolovsky’s “Momentless shells”, Transactions ofthe American Mathe-
maticalSociety61,128–133.
8A. Same title, Bulletin of the American Mathematical Society 52 (1946),
240.
9. (Co-author R.N. SCHWARTZ) The Newtonian mechanics of continua, U.S.
NavalOrdnanceLaboratory Memorandum 9223,18July,25pp.
9A. (Co-author R. SCHWARTZ)OntheNewtonianMechanics ofContinua,
BulletinoftheAmericanMathematical Society53,1125.
10. A note on the Poisson–Charlier functions, Annals of Mathematical Statistics
18,450–454.
11. ReviewofL.Brand’s“VectorandTensorAnalysis”, Science106,623.
Otherpublications in1947:Nos.7A,12A3,13P,14P,16P,16A,23P,48P.
1948
12. An Essay toward a Unified Theory of Special Functions, based on the Func-
tional Equation ∂F(z,α)/∂z = F(z,α+1),Annals ofMathematics Studies
No.18,Princeton,Princeton UniversityPress,iv+182pp.