Understanding viscoelasticity: basics of rheology
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Physics and astronomy online library
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 145 S. Ill., graph. Darst. |
| ISBN: | 3540433953 |
Internformat
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Datensatz im Suchindex
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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
CAYLEY*HAMILTONTHEOREM ........................ 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
CAUCHY*GREENSTRAINTENSOR....................... 42 3.2.3
RELATIVESTRAINTENSORS ........................... 43 3.2.4 PATHLINES
...................................... 43 3.2.5
OSCILLATORYSHEARFLOW............................ 44 3.3
RIVLIN*ERICKSENTENSORS................................. 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
FOURIER*SLAW.................................... 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
GREEN*RIVLINEXPANSION................................. 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
DIFFUSIVITYSTOKES*EINSTEINRELATION ................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
|
| any_adam_object | 1 |
| author | Phan-Thien, Nhan 1952- |
| author_GND | (DE-588)123614457 |
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| classification_tum | PHY 216f |
| ctrlnum | (OCoLC)49326906 (DE-599)BVBBV014214288 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.0533 |
| dewey-search | 532/.0533 |
| dewey-sort | 3532 3533 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:59:45Z |
| institution | BVB |
| isbn | 3540433953 |
| language | English |
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| physical | XIII, 145 S. Ill., graph. Darst. |
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| series2 | Physics and astronomy online library |
| 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 |
| url | 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 |
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