Understanding viscoelasticity: an introduction to Rheology
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Heidelberg [u.a.]
Springer
2013
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIII, 202 S. Ill., graph. Darst. |
| ISBN: | 9783642329579 3642329578 9783642329586 |
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Datensatz im Suchindex
| _version_ | 1807955394945875968 |
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IMAGE 1
CONTENTS
1 TENSOR NOTATION 1
1.1 CARTESIAN FRAME OF REFERENCE 1
1.1.1 POSITION VECTOR 3
1.2 FRAME ROTATION 3
1.2.1 ORTHOGONAL MATRIX 3
1.2.2 ROTATION MATRIX 4
1.3 TENSORS 4
1.3.1 ZERO-ORDER TENSORS 4
1.3.2 FIRST-ORDER TENSOR 4
1.3.3 OUTER PRODUCTS 5
1.3.4 SECOND-ORDER TENSORS 5
1.3.5 THIRD-ORDER TENSORS 6
1.3.6 TRANSPOSE OPERATION 6
1.3.7 DECOMPOSITION 7
1.3.8 SOME COMMON VECTORS 7
1.3.9 GRADIENT O F A SCALAR 7
1.3.10 SOME COMMON TENSORS 8
1.4 TENSOR AND LINEAR VECTOR FUNCTION 9
1.4.1 CLAIM 9
1.4.2 DYADIC NOTATION 10
1.5 TENSOR OPERATIONS 10
1.5.1 SUBSTITUTION 10
1.5.2 CONTRACTION 11
1.5.3 TRANSPOSE 11
1.5.4 PRODUCTS OF TWO SECOND-ORDER TENSORS 11
1.6 INVARIANTS 12
1.6.1 INVARIANT O F A VECTOR 12
1.6.2 INVARIANTS O F A TENSOR 12
1.7 DECOMPOSITIONS 13
1.7.1 EIGENVALUE AND EIGENVECTOR 13
I X
HTTP://D-NB.INFO/1024629198
IMAGE 2
X C O N T E N T S
1.7.2 SQUARE ROOT THEOREM 14
1.7.3 POLAR DECOMPOSITION THEOREM 14
1.7.4 CAYLEY-HAMILTON THEOREM 14
1.8 DERIVATIVE OPERATIONS 15
1.8.1 DERIVATIVE OF DET (A) 16
1.8.2 DERIVATIVE O F TR (A) 16
1.8.3 DERIVATIVE O F TR (A 2 ) 16
1.9 GRADIENT OF A FIELD 17
1.9.1 FIELD 17
1.9.2 CARTESIAN FRAME 17
1.9.3 NON-CARTESIAN FRAMES 19
1.9.4 SPHERICAL COORDINATES 21
1.10 INTEGRAL THEOREMS 22
1.10.1 GAUSS DIVERGENCE THEOREM 22
1.10.2 STOKES CURL THEOREM 23
1.10.3 LEIBNIZ FORMULA 23
1.11 PROBLEMS 24
2 RHEOLOGICAL PROPERTIES 29
2.1 VISCOSITY 29
2.1.1 SHEAR-RATE DEPENDENT VISCOSITY 29
2.2 NORMAL STRESS DIFFERENCES 31
2.2.1 WEISSENBERG ROD-CLIMBING EFFECT 32
2.2.2 DIE SWELL 32
2.2.3 FLOW DOWN AN INCLINED CHANNEL 33
2.3 TRANSIENT RESPONSES 34
2.3.1 SMALL STRAIN OSCILLATORY FLOW 34
2.3.2 STRESS OVERSHOOT 35
2.3.3 STRESS RELAXATION 36
2.3.4 RELAXATION MODULUS 36
2.3.5 RECOIL 36
2.4 ELONGATIONAL FLOWS 37
2.4.1 ELONGATIONAL VISCOSITY 37
2.5 VISCOELASTIC INSTABILITIES 38
3 KINEMATICS AND EQUATIONS O F BALANCE 41
3.1 KINEMATICS 41
3.1.1 REFERENCE CONFIGURATION 41
3.1.2 VELOCITY AND ACCELERATION FIELDS 42
3.1.3 MATERIAL DERIVATIVE 43
3.2 DEFORMATION GRADIENT AND STRAIN TENSORS 43
3.2.1 DEFORMATION GRADIENT 43
3.2.2 CAUCHY-GREEN STRAIN TENSOR 44
3.2.3 RELATIVE STRAIN TENSORS 45
3.2.4 PATH LINES 46
3.2.5 OSCILLATORY SHEAR FLOW 47
IMAGE 3
C O N T E N T S XI
3.3 RIVLIN-ERICKSEN TENSORS 48
3.4 SMALL STRAIN 50
3.5 EQUATIONS OF BALANCE 51
3.5.1 REYNOLDS TRANSPORT THEOREM 51
3.5.2 CONSERVATION OF MASS 53
3.5.3 CONSERVATION OF MOMENTUM 54
3.5.4 CONSERVATION OF ENERGY 58
3.6 PROBLEMS 59
4 CONSTITUTIVE EQUATION: GENERAL PRINCIPLES 61
4.1 SOME WELL-KNOWN CONSTITUTIVE EQUATIONS 61
4.1.1 PERFECT GAS 61
4.1.2 INVISCID FLUID 61
4.1.3 FOURIER'S LAW 62
4.1.4 HOOKEAN SOLID 63
4.1.5 NEWTONIAN FLUID 64
4.1.6 NON-NEWTONIAN FLUID 65
4.2 WEISSENBERG AND DEBORAH NUMBERS 65
4.2.1 DEBORAH NUMBER 66
4.2.2 WEISSENBERG NUMBER 66
4.3 SOME GUIDELINES IN CONSTITUTIVE MODELING 67
4.3.1 OLDROYD APPROACH 67
4.3.2 PRINCIPLE OF MATERIAL OBJECTIVITY 68
4.3.3 OBJECTIVITY OF THE STRESS 68
4.3.4 FRAME INDIFFERENCE 69
4.3.5 PRINCIPLE OF LOCAL ACTION 71
4.3.6 PRINCIPLE OF DETERMINISM 71
4.4 INTEGRITY BASES 72
4.4.1 ISOTROPIC SCALAR-VALUED FUNCTIONS 72
4.4.2 ISOTROPIC VECTOR-VALUED FUNCTIONS 73
4.4.3 ISOTROPIC TENSOR-VALUED FUNCTIONS 73
4.5 SYMMETRY RESTRICTIONS 74
4.5.1 UNIMODULAR MATRIX 74
4.5.2 SYMMETRY GROUP 75
4.5.3 ISOTROPIC MATERIALS 75
4.6 ISOTROPIC ELASTIC MATERIALS 76
4.7 THE SIMPLE MATERIAL 77
4.7.1 SIMPLE FLUID 78
4.7.2 INCOMPRESSIBLE SIMPLE FLUID 78
4.7.3 FADING MEMORY 79
4.8 ORDER FLUIDS 79
4.8.1 UNSTEADY MOTION 79
4.8.2 VELOCITY FIELD IN A SECOND-ORDER FLUID 81
4.9 GREEN-RIVLIN EXPANSION 82
4.10 PROBLEMS 83
IMAGE 4
X J J C O N T E N T S
5 INELASTIC MODELS AND LINEAR VISCOELASTICITY 89
5.1 INELASTIC FLUIDS 89
5.1.1 CARREAU MODEL 9 0
5.1.2 POWER-LAW MODEL 9 0
5.2 LINEAR VISCOELASTICITY 92
5.2.1 SIMPLE SHEAR FLOW 9 4
5.2.2 STEP STRAIN 96
5.2.3 RELAXATION SPECTRUM 97
5.3 CORRESPONDENCE PRINCIPLE 98
5.3.1 QUASI-STATIC APPROXIMATION 98
5.3.2 CIRCULAR COUETTE FLOW 99
5.4 MECHANICAL ANALOGS 100
5.5 PROBLEMS 102
6 STEADY VISCOMETRIC FLOWS 105
6.1 KINEMATICS 105
6.1.1 STEADY PARALLEL FLOW 106
6.1.2 RECTILINEAR FLOW 107
6.1.3 AXIAL FANNED FLOW 107
6.1.4 HELICAL FLOW 108
6.1.5 HELICOIDAL FLOW 108
6.2 STRESSES IN STEADY VISCOMETRIC FLOWS 109
6.2.1 CONTROLLABLE AND PARTIALLY CONTROLLABLE FLOWS 110
6.3 PROBLEMS 110
7 POLYMER SOLUTIONS 113
7.1 CHARACTERISTICS OF A POLYMER CHAIN 113
7.1.1 RANDOM-WALK MODEL 113
7.2 FORCES ON A CHAIN 116
7.3 FLUCTUATION-DISSIPATION THEOREM 119
7.3.1 LANGEVIN EQUATION 119
7.3.2 EQUI-PARTITION OF ENERGY 120
7.3.3 FLUCTUATION-DISSIPATION THEOREM 121
7.3.4 DIFFUSIVITY STOKES-EINSTEIN RELATION 122
7.3.5 FOKKER-PLANCK EQUATION 122
7.3.6 SMOOTHED-OUT BROWNIAN FORCE 123
7.4 STRESS TENSOR 123
7.4.1 KRAMERS FORM 126
7.5 ELASTIC DUMBBELL MODEL 127
7.5.1 LANGEVIN EQUATIONS 127
7.5.2 AVERAGE MOTION 128
7.5.3 STRONG AND WEAK FLOWS 129
7.5.4 UPPER-CONVECTED MAXWELL MODEL 130
7.5.5 OLDROYD-B MODEL 131
7.6 MAIN FEATURES OF THE OLDROYD-B MODEL 132
7.6.1 SIMPLE FLOWS 132
IMAGE 5
C O N T E N T S XIII
7.6.2 MULTIPLE RELAXATION TIME UCM MODEL 134
7.7 PROBLEMS 135
8 SUSPENSIONS 137
8.1 BULK SUSPENSION PROPERTIES 138
8.2 DILUTE SUSPENSION OF SPHEROIDS 140
8.3 PROBLEMS 143
9 DISSIPATIVE PARTICLE DYNAMICS (DPD) 147
9.1 I D MODEL 148
9.2 DPD FLUID 151
9.2.1 LANGEVIN EQUATIONS 151
9.2.2 PHASE-SPACE DESCRIPTION: FOKKER-PLANCK EQUATION 156 9.2.3
DISTRIBUTION FUNCTIONS 157
9.2.4 EQUATION OF CHANGE 158
9.2.5 CONSERVATION OF MASS 158
9.2.6 CONSERVATION OF LINEAR MOMENTUM 159
9.2.7 ENERGY EQUATION 164
9.3 SOME APPROXIMATE RESULTS 166
9.3.1 HIGH DAMPING LIMIT 166
9.3.2 STANDARD DPD PARAMETERS 168
9.3.3 EFFECTIVE SIZE O F A DPD PARTICLE 168
9.4 MODIFICATION OF THE WEIGHTING FUNCTION 169
9.5 NUMERICAL IMPLEMENTATION 171
9.5.1 VELOCITY VERLET SCHEME 171
9.5.2 EXPONENTIAL TIME DIFFERENCING SCHEME 172
9.5.3 IMPLEMENTATION O F NO-SLIP BOUNDARY CONDITIONS 175
9.5.4 COMPUTATION O F INTERPARTICLE FORCES 177
9.5.5 CALCULATION OF STRESS TENSOR 177
9.5.6 COMPLEX-STRUCTURE FLUID 177
9.6 FLOW VERIFICATIONS AND SOME TYPICAL PROBLEMS 179
9.7 EPILOGUE 190
9.8 PROBLEMS 191
REFERENCES 195
INDEX 199 |
| any_adam_object | 1 |
| author | Phan-Thien, Nhan 1952- |
| author_GND | (DE-588)123614457 |
| author_facet | Phan-Thien, Nhan 1952- |
| author_role | aut |
| author_sort | Phan-Thien, Nhan 1952- |
| author_variant | n p t npt |
| building | Verbundindex |
| bvnumber | BV040880033 |
| classification_rvk | UF 3000 UF 3500 |
| ctrlnum | (OCoLC)827774366 (DE-599)DNB1024629198 |
| dewey-full | 532.0533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.0533 |
| dewey-search | 532.0533 |
| dewey-sort | 3532.0533 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 2. ed. |
| format | Book |
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| physical | XIII, 202 S. Ill., graph. Darst. |
| publishDate | 2013 |
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| spelling | Phan-Thien, Nhan 1952- Verfasser (DE-588)123614457 aut Understanding viscoelasticity an introduction to Rheology Nhan Phan-Thien 2. ed. Heidelberg [u.a.] Springer 2013 XIII, 202 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Literaturangaben Viskoelastizität (DE-588)4063621-5 gnd rswk-swf Viskoelastizität (DE-588)4063621-5 s DE-604 Erscheint auch als Online-Ausgabe Understanding Viscoelasticity X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4093473&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025859813&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Phan-Thien, Nhan 1952- Understanding viscoelasticity an introduction to Rheology Viskoelastizität (DE-588)4063621-5 gnd |
| subject_GND | (DE-588)4063621-5 |
| title | Understanding viscoelasticity an introduction to Rheology |
| title_auth | Understanding viscoelasticity an introduction to Rheology |
| title_exact_search | Understanding viscoelasticity an introduction to Rheology |
| title_full | Understanding viscoelasticity an introduction to Rheology Nhan Phan-Thien |
| title_fullStr | Understanding viscoelasticity an introduction to Rheology Nhan Phan-Thien |
| title_full_unstemmed | Understanding viscoelasticity an introduction to Rheology Nhan Phan-Thien |
| title_short | Understanding viscoelasticity |
| title_sort | understanding viscoelasticity an introduction to rheology |
| title_sub | an introduction to Rheology |
| topic | Viskoelastizität (DE-588)4063621-5 gnd |
| topic_facet | Viskoelastizität |
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