Continuum thermodynamics: 1 Foundations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2008
|
| Schriftenreihe: | Series on advances in mathematics for applied sciences
77 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 403 S. Ill., graph. Darst. |
| ISBN: | 9789812835567 9812835563 |
Internformat
MARC
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| 100 | 1 | |a Wilmański, Krzysztof |d 1940-2012 |e Verfasser |0 (DE-588)118171607 |4 aut | |
| 245 | 1 | 0 | |a Continuum thermodynamics |n 1 |p Foundations |c Krzysztof Wilmanski |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2008 | |
| 300 | |a X, 403 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on advances in mathematics for applied sciences |v 77 | |
| 490 | 0 | |a Series on advances in mathematics for applied sciences |v ... | |
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| 650 | 0 | 7 | |a Kontinuumsmechanik |0 (DE-588)4032296-8 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017137861 | ||
Datensatz im Suchindex
| _version_ | 1804138646614310912 |
|---|---|
| adam_text | Contents
Preface
v
1.
Introduction
1
2.
Geometry
9
2.1 Deformation
gradient,
material vectors
.......... 9
2.2
Measures of deformation
.................. 13
2.3
Extension, dilatation, shear
................ 20
2.4
Displacement
........................ 24
2.5
Geometrical compatibility conditions
........... 25
2.6
Geometrical compatibility condition for singular
surfaces
........................... 27
3.
Kinematics
31
3.1
Basic notions
........................ 31
3.2
Objective time derivatives
................. 34
3.3
Boundaries, kinematical compatibility condition for
singular surfaces
...................... 37
3.3.1
Introduction
.................... 37
3.3.2
Modicum of surface geometry
.......... 38
3.3.3
Time dependence of surfaces
........... 42
3.3.4
Kinematical compatibility conditions
...... 44
viii Contents
4. Balance
equations
49
4.1 Balance
laws in Lagrangian description..........
49
4.2 Balance
laws in Eulerian description
........... 58
4.3
Extension on membranes and interfaces
.......... 64
5.
Second law of thermodynamics
69
5.1
Entropy inequality, thermodynamical admissibility
... 69
5.1.1
Motivation
..................... 69
5.1.2
Entropy inequality
................ 73
5.1.2.1
Entropy principle
............ 73
5.1.2.2
Thermoelasticity
............ 76
5.1.3
I-Shih Liu Theorem
................ 81
5.2
Isotropy, material objectivity
................ 86
5.2.1
Example
-
rigid heat conductor
......... 86
5.2.2
Isotropy
...................... 90
5.2.3
Material objectivity, example: Monney-Rivlin
materials
...................... 96
5.3
Materials with constraints
................. 102
5.4
Constitutive relations for various thermoelastic
materials
........................... 108
5.4.1
Neo-Hookean material
.............. 108
5.4.2
Mooney-Rivlin material
.............. 109
5.4.3
Biological tissue
.................. 109
5.4.4
Ogden s materials
................. 110
5.4.5
Gent s material
.................. 110
5.4.6
Generalized Blatz-Ko material
.......... 110
5.4.7
Signiorini s material
................
Ill
5.4.8
St.Venant-Kirchoff material
........... 112
5.5
Proportionality Theorem
.................. 112
6.
Equilibrium Gibbs thermodynamics
119
6.1
Thermostatics of gases
................... 119
6.2
Thermostatic theory of homogeneous mixtures
...... 132
7.
Kinetic theories
137
7.1
Liouville equation
...................... 137
7.2
BBGKY-hierarchy
..................... 142
7.3
Boltzmann equation
..................... 147
Contents ix
8.
Extended thermodynamics
161
8.1
General structure
...................... 161
8.2
Nonrelativistic ideal gases
................. 168
8.3
A few remarks on boundary conditions
.......... 179
9.
Thermodynamical model of viscoelastic materials
185
9.1
Foundations
......................... 185
9.2
Thermodynamical admissibility
.............. 187
9.3
Viscous fluids, linear viscoelastic solids
.......... 193
9.4
Maxwell fluid, Rivlin-Ericksen fluids
........... 197
9.4.1
Preliminary remarks
............... 197
9.4.2
Extended thermodynamics of
non-Newtonian non-conducting fluids
...... 199
9.4.3
Thermodynamics of a heat
conducting Maxwellian fluid
........... 212
9.4.3.1
Evaluation of the entropy inequality
. 212
9.4.3.2
Transitions to second order fluids
. . . 219
10.
Elasto-viscoplastic materials
221
10.1
Preliminaries
......................... 221
10.2
Local configurations
..................... 222
10.3
Crystal plasticity of monocrystals
............. 224
10.4
Polycrystals and orientation distribution function
.... 230
10.5
Thermodynamical admissibility
.............. 234
10.6
Two particular classes of models
.............. 236
11.
Thermodynamics of
miscible
mixtures
239
11.1
General structure and field equations
........... 239
11.2
Thermodynamical admissibility
.............. 247
12.
Thermodynamics of immiscible mixtures: Introduction
and models without the field of porosity
257
13.
Thermodynamics of poroelastic materials with the
balance equation of porosity
271
13.1
General structure
...................... 271
13.2
Two-component poroelastic materials
........... 284
13.3
Linear models of saturated poroelastic materials
..... 303
χ
Contents
13.4
Waves in poroelastic materials
............... 319
13.5
On adsorption in porous materials
............. 334
13.5.1
Adsorption for large channel diameter
...... 334
13.5.2
Adsorption for small channel diameter;
capillarity
..................... 340
14.
Final remarks
345
Appendix A Vectors and tensors on Euclidean spaces
353
A.I Reminder of tensor calculus
................ 353
A.
2
Coordinates
......................... 360
A.3 Euclidean shifters, differentiation
............. 363
A.4 Physical components
.................... 367
A.
5
Transformations of Green and Kelvin
........... 370
Appendix
В
Basic physical units
371
Bibliography
373
Index
397
|
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| author | Wilmański, Krzysztof 1940-2012 |
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| bvnumber | BV035333452 |
| classification_rvk | UG 1000 UG 1200 |
| ctrlnum | (OCoLC)635219458 (DE-599)BVBBV035333452 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV035333452 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:30Z |
| institution | BVB |
| isbn | 9789812835567 9812835563 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017137861 |
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| physical | X, 403 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | World Scientific |
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| series | Series on advances in mathematics for applied sciences |
| series2 | Series on advances in mathematics for applied sciences |
| spelling | Wilmański, Krzysztof 1940-2012 Verfasser (DE-588)118171607 aut Continuum thermodynamics 1 Foundations Krzysztof Wilmanski New Jersey [u.a.] World Scientific 2008 X, 403 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 77 Series on advances in mathematics for applied sciences ... Thermodynamische Eigenschaft (DE-588)4126056-9 gnd rswk-swf Thermodynamik (DE-588)4059827-5 gnd rswk-swf Kontinuumsphysik (DE-588)4165166-2 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Thermodynamik (DE-588)4059827-5 s Kontinuumsphysik (DE-588)4165166-2 s DE-604 Kontinuumsmechanik (DE-588)4032296-8 s Thermodynamische Eigenschaft (DE-588)4126056-9 s (DE-604)BV035333450 1 Series on advances in mathematics for applied sciences 77 (DE-604)BV004569239 77 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017137861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wilmański, Krzysztof 1940-2012 Continuum thermodynamics Series on advances in mathematics for applied sciences Thermodynamische Eigenschaft (DE-588)4126056-9 gnd Thermodynamik (DE-588)4059827-5 gnd Kontinuumsphysik (DE-588)4165166-2 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4126056-9 (DE-588)4059827-5 (DE-588)4165166-2 (DE-588)4032296-8 |
| title | Continuum thermodynamics |
| title_auth | Continuum thermodynamics |
| title_exact_search | Continuum thermodynamics |
| title_full | Continuum thermodynamics 1 Foundations Krzysztof Wilmanski |
| title_fullStr | Continuum thermodynamics 1 Foundations Krzysztof Wilmanski |
| title_full_unstemmed | Continuum thermodynamics 1 Foundations Krzysztof Wilmanski |
| title_short | Continuum thermodynamics |
| title_sort | continuum thermodynamics foundations |
| topic | Thermodynamische Eigenschaft (DE-588)4126056-9 gnd Thermodynamik (DE-588)4059827-5 gnd Kontinuumsphysik (DE-588)4165166-2 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Thermodynamische Eigenschaft Thermodynamik Kontinuumsphysik Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017137861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035333450 (DE-604)BV004569239 |
| work_keys_str_mv | AT wilmanskikrzysztof continuumthermodynamics1 |