Holdings: Understanding viscoelasticity

Understanding viscoelasticity: basics of rheology

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Bibliographic Details
Main Author:	Phan-Thien, Nhan 1952- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2002
Series:	Physics and astronomy online library
Subjects:	Viscoélasticité Viscoelasticity Viskoelastizität
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 145 S. Ill., graph. Darst.
ISBN:	3540433953

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MARC


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adam_text	CONTENTS 1. TENSOR NOTATION .......................................... 1 1.1 CARTESIANFRAMEOFREFERENCE............................ 1 1.1.1 POSITIONVECTOR .................................. 3 1.2 FRAMEROTATION........................................ 3 1.2.1 ORTHOGONALMATRIX ............................... 4 1.2.2 ROTATIONMATRIX.................................. 4 1.3 TENSORS ............................................... 4 1.3.1 ZERO-ORDERTENSORS............................... 4 1.3.2 FIRST-ORDERTENSOR ............................... 4 1.3.3 OUTERPRODUCTS .................................. 5 1.3.4 SECOND-ORDERTENSORS............................. 5 1.3.5 THIRD-ORDERTENSORS.............................. 5 1.3.6 TRANSPOSEOPERATION.............................. 6 1.3.7 DECOMPOSITION................................... 6 1.3.8 SOMECOMMONVECTORS............................ 7 1.3.9 GRADIENTOFASCALAR.............................. 7 1.3.10 SOMECOMMONTENSORS ........................... 7 1.4 TENSORANDLINEARVECTORFUNCTION ....................... 9 1.4.1 CLAIM........................................... 9 1.4.2 DYADICNOTATION ................................. 10 1.5 TENSOROPERATIONS...................................... 10 1.5.1 SUBSTITUTION..................................... 10 1.5.2 CONTRACTION...................................... 10 1.5.3 TRANSPOSE....................................... 11 1.5.4 PRODUCTSOFTWOTWO-TENSORS ..................... 11 1.6 INVARIANTS ............................................. 12 1.6.1 INVARIANTOFAVECTOR.............................. 12 1.6.2 INVARIANTSOFATENSOR............................. 12 1.7 DECOMPOSITIONS ........................................ 12 1.7.1 EIGENVALUEANDEIGENVECTOR........................ 12 1.7.2 SQUAREROOTTHEOREM............................. 13 1.7.3 POLARDECOMPOSITIONTHEOREM..................... 13 1.7.4 CAYLEYHAMILTONTHEOREM ........................ 13 X CONTENTS 1.8 DERIVATIVEOPERATIONS................................... 14 1.8.1 DERIVATIVEOFDET(A).............................. 15 1.8.2 DERIVATIVEOFTR(A) ............................... 15 1.8.3 DERIVATIVEOFTR(A 2 )............................... 15 1.9 GRADIENTOFAFIELD..................................... 16 1.9.1 FIELD ........................................... 16 1.9.2 CARTESIANFRAME ................................. 16 1.9.3 NON-CARTESIANFRAMES ............................ 18 1.9.4 SPHERICALCOORDINATES............................. 19 1.10INTEGRALTHEOREMS...................................... 21 1.10.1 GAUSSDIVERGENCETHEOREM........................ 21 1.10.2 STOKESCURLTHEOREM ............................. 22 1.10.3 LEIBNIZFORMULA.................................. 22 PROBLEMS.............................................. 22 2. RHEOLOGICAL PROPERTIES .................................... 27 2.1 VISCOSITY.............................................. 27 2.1.1 SHEAR-RATEDEPENDENTVISCOSITY.................... 27 2.2 NORMALSTRESSDIFFERENCES................................ 29 2.2.1 WEISSENBERGROD-CLIMBINGEFFECT................... 30 2.2.2 DIESWELL........................................ 31 2.2.3 FLOWDOWNANINCLINEDCHANNEL.................... 32 2.3 TRANSIENTRESPONSES.................................... 33 2.3.1 SMALLSTRAINOSCILLATORYFLOW...................... 33 2.3.2 STRESSOVERSHOOT................................. 34 2.3.3 STRESSRELAXATION................................. 34 2.3.4 RELAXATIONMODULUS .............................. 35 2.3.5 RECOIL........................................... 36 2.4 ELONGATIONALFLOWS ..................................... 36 2.4.1 ELONGATIONALVISCOSITY ............................ 36 2.5 VISCOELASTICINSTABILITIES................................. 38 3. KINEMATICS AND EQUATIONS OF BALANCE . . . . . . . . . . . . . . . . . . . . . 39 3.1 KINEMATICS............................................ 39 3.1.1 REFERENCECONFIGURATION........................... 39 3.1.2 VELOCITYANDACCELERATIONFIELDS.................... 40 3.1.3 MATERIALDERIVATIVE............................... 41 3.2 DEFORMATIONGRADIENTANDSTRAINTENSORS ................. 41 3.2.1 DEFORMATIONGRADIENT............................. 41 3.2.2 CAUCHYGREENSTRAINTENSOR....................... 42 3.2.3 RELATIVESTRAINTENSORS ........................... 43 3.2.4 PATHLINES ...................................... 43 3.2.5 OSCILLATORYSHEARFLOW............................ 44 3.3 RIVLINERICKSENTENSORS................................. 45 3.4 SMALLSTRAIN........................................... 48 CONTENTS XI 3.5 EQUATIONSOFBALANCE ................................... 49 3.5.1 REYNOLDSTRANSPORTTHEOREM...................... 49 3.5.2 CONSERVATIONOFMASS............................. 50 3.5.3 CONSERVATIONOFMOMENTUM........................ 51 3.5.4 CONSERVATIONOFENERGY ........................... 55 PROBLEMS.............................................. 56 4. CONSTITUTIVE EQUATION .................................... 59 4.1 SOMEWELL-KNOWNCONSTITUTIVEEQUATIONS................. 59 4.1.1 PERFECTGAS...................................... 59 4.1.2 INVISCIDFLUID.................................... 60 4.1.3 FOURIERSLAW.................................... 60 4.1.4 HOOKEANSOLID ................................... 60 4.1.5 NEWTONIANFLUID................................. 62 4.1.6 NON-NEWTONIANFLUID............................. 63 4.2 WEISSENBERGANDDEBORAHNUMBERS....................... 63 4.2.1 DEBORAHNUMBER................................. 63 4.2.2 WEISSENBERGNUMBER ............................. 64 4.3 SOMEGUIDELINESINCONSTITUTIVEMODELLING ................ 64 4.3.1 OLDROYDAPPROACH................................ 65 4.3.2 PRINCIPLEOFMATERIALOBJECTIVITY................... 66 4.3.3 OBJECTIVITYOFTHESTRESS .......................... 66 4.3.4 FRAMEINDIFFERENCE................................ 67 4.3.5 PRINCIPLEOFLOCALACTION.......................... 69 4.3.6 PRINCIPLEOFDETERMINISM.......................... 69 4.4 INTEGRITYBASES......................................... 69 4.4.1 ISOTROPICSCALAR-VALUEDFUNCTIONS .................. 69 4.4.2 ISOTROPICVECTOR-VALUEDFUNCTIONS.................. 70 4.4.3 ISOTROPICTENSOR-VALUEDFUNCTIONS.................. 71 4.5 SYMMETRYRESTRICTIONS.................................. 72 4.5.1 UNIMODULARMATRIX............................... 72 4.5.2 SYMMETRYGROUP................................. 73 4.5.3 ISOTROPICMATERIALS ............................... 73 4.6 ISOTROPICELASTICMATERIALS............................... 73 4.7 THESIMPLEMATERIAL.................................... 75 4.7.1 SIMPLEFLUID..................................... 76 4.7.2 INCOMPRESSIBLESIMPLEFLUID....................... 76 4.7.3 FADINGMEMORY.................................. 76 4.8 ORDERFLUIDS........................................... 77 4.8.1 UNSTEADYMOTION................................. 77 4.8.2 VELOCITYFIELDINASECOND-ORDERFLUID.............. 79 4.9 GREENRIVLINEXPANSION................................. 80 PROBLEMS.............................................. 80 XII CONTENTS 5. INELASTIC MODELS AND LINEAR VISCOELASTICITY ............... 85 5.1 INELASTICFLUIDS......................................... 85 5.1.1 CARREAUMODEL................................... 86 5.1.2 POWER-LAWMODEL................................. 86 5.2 LINEARVISCOELASTICITY................................... 88 5.2.1 SIMPLESHEARFLOW................................ 90 5.2.2 STEPSTRAIN...................................... 92 5.2.3 RELAXATIONSPECTRUM ............................. 93 5.3 CORRESPONDENCEPRINCIPLE................................ 94 5.3.1 QUASI-STATICAPPROXIMATION ....................... 94 5.3.2 CIRCULARCOUETTEFLOW ............................ 95 5.4 MECHANICALANALOGS..................................... 97 PROBLEMS.............................................. 97 6. STEADY VISCOMETRIC FLOWS ................................ 101 6.1 KINEMATICS............................................101 6.1.1 STEADYPARALLELFLOW..............................102 6.1.2 RECTILINEARFLOW..................................103 6.1.3 AXIALFANNEDFLOW ...............................103 6.1.4 HELICALFLOW.....................................103 6.1.5 HELICOIDALFLOW ..................................104 6.2 STRESSESINSTEADYVISCOMETRICFLOWS......................104 6.2.1 CONTROLLABLEANDPARTIALLYCONTROLLABLEFLOWS........106 PROBLEMS..............................................106 7. POLYMER SOLUTIONS ........................................ 109 7.1 CHARACTERISTICSOFAPOLYMERCHAIN.......................109 7.1.1 RANDOM-WALKMODEL .............................109 7.2 FORCESONACHAIN......................................112 7.3 FLUCTUATION-DISSIPATIONTHEOREM.........................115 7.3.1 LANGEVINEQUATION ...............................115 7.3.2 EQUI-PARTITIONOFENERGY..........................116 7.3.3 FLUCTUATION-DISSIPATIONTHEOREM...................116 7.3.4 DIFFUSIVITYSTOKESEINSTEINRELATION ................117 7.3.5 FOKKER*PLANCKEQUATION ..........................117 7.3.6 SMOOTHED-OUTBROWNIANFORCE.....................118 7.4 STRESSTENSOR ..........................................119 7.4.1 KRAMERSFORM...................................122 7.5 ELASTICDUMBBELLMODEL.................................122 7.5.1 LANGEVINEQUATIONS ..............................122 7.5.2 AVERAGEMOTION..................................123 7.5.3 STRONGANDWEAKFLOWS...........................124 7.5.4 UPPER-CONVECTEDMAXWELLMODEL...................125 7.5.5 OLDROYD-BMODEL.................................126 CONTENTS XIII 7.6 MAINFEATURESOFTHEOLDROYD-BMODEL....................126 7.6.1 SIMPLEFLOWS ....................................126 7.6.2 MULTIPLERELAXATIONTIMEUCMMODEL..............127 PROBLEMS..............................................128 8. SUSPENSIONS .............................................. 131 8.1 BULKSUSPENSIONPROPERTIES..............................132 8.2 DILUTESUSPENSIONOFSPHEROIDS...........................134 8.3 EPILOGUE ..............................................137 PROBLEMS..............................................138 REFERENCES .................................................... 141 INDEX ......................................................... 143
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spelling	Phan-Thien, Nhan 1952- Verfasser (DE-588)123614457 aut Understanding viscoelasticity basics of rheology Nhan Phan-Thien Berlin [u.a.] Springer 2002 XIII, 145 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics and astronomy online library Viscoélasticité Viscoelasticity Viskoelastizität (DE-588)4063621-5 gnd rswk-swf Viskoelastizität (DE-588)4063621-5 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009746040&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Phan-Thien, Nhan 1952- Understanding viscoelasticity basics of rheology Viscoélasticité Viscoelasticity Viskoelastizität (DE-588)4063621-5 gnd
subject_GND	(DE-588)4063621-5
title	Understanding viscoelasticity basics of rheology
title_auth	Understanding viscoelasticity basics of rheology
title_exact_search	Understanding viscoelasticity basics of rheology
title_full	Understanding viscoelasticity basics of rheology Nhan Phan-Thien
title_fullStr	Understanding viscoelasticity basics of rheology Nhan Phan-Thien
title_full_unstemmed	Understanding viscoelasticity basics of rheology Nhan Phan-Thien
title_short	Understanding viscoelasticity
title_sort	understanding viscoelasticity basics of rheology
title_sub	basics of rheology
topic	Viscoélasticité Viscoelasticity Viskoelastizität (DE-588)4063621-5 gnd
topic_facet	Viscoélasticité Viscoelasticity Viskoelastizität
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