Fundamentals of continuum mechanics: with applications to mechanical, thermomechanical, and smart materials
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam [u.a.]
Academic Press
2015
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027218418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 330 S. Ill., graph. Darst. |
| ISBN: | 012394600X 9780123946003 |
Internformat
MARC
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| 020 | |a 012394600X |9 0-12-394600-X | ||
| 020 | |a 9780123946003 |9 978-0-12-394600-3 | ||
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| 100 | 1 | |a Bechtel, Stephen E. |e Verfasser |0 (DE-588)1078935211 |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of continuum mechanics |b with applications to mechanical, thermomechanical, and smart materials |c Stephen E. Bechtel ; Robert L. Lowe |
| 264 | 1 | |a Amsterdam [u.a.] |b Academic Press |c 2015 | |
| 300 | |a XV, 330 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Kontinuumsmechanik |0 (DE-588)4032296-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Lowe, Robert L. |e Verfasser |0 (DE-588)1078935955 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027218418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027218418 | |
Datensatz im Suchindex
| _version_ | 1819308023116464128 |
|---|---|
| adam_text | Contents
Pl
Preface
................................................................................xiii
PARTI THE BEGINNING
_______________________________
CHAPTER
1
What Is a Continuum?
...........................................
з
CHAPTER
2
Our Mathematical Playground
................................5
2.1
Real numbers and Euclidean space
..................................5
2.1.1
Properties of real numbers
.................................5
2.1.2
Properties of Euclidean space
..............................7
2.2
Tensor algebra
.......................................................12
2.2.1
Second-order tensors, zero tensor, identity tensor
.......12
2.2.2
Product, transpose, symmetry
.............................16
2.2.3
Dyadic product
............................................22
2.2.4
Cartesian components,
indiciai
notation, summation
convention
.................................................24
2.2.5
Trace, scalar product, determinant
........................35
2.2.6
Inverse, orthogonality, positive definiteness
..............39
2.2.7
Vector product, scalar triple product
......................42
2.3
Eigenvalues, eigenvectors, polar decomposition, invariants
......44
2.4
Tensors of order three and four
.....................................47
2.5
Tensor calculus
......................................................48
2.5.1
Partial derivatives
..........................................48
2.5.2
Chain rule, gradient, divergence, curl.
divergence theorem
........................................52
2.5.3
Tensor calculus in Cartesian component form
...........56
2.6
Curvilinear coordinates
.............................................59
2.6.1
Covariant and
contravariant
basis vectors
................60
2.6.2
Physical components
......................................63
2.6.3
Spatial derivatives: Covariant differentiation
.............65
PART II KINEMATICS, KINETICS, AND THE
FUNDAMENTAL LAWS OF MECHANICS AND
________
THERMODYNAMICS
___________________________
CHAPTER
3
Kinematics: Motion and Deformation
......................75
3.1
Body, configuration, motion, displacement
........................75
3.2
Material derivative, velocity, acceleration
.........................80
VII
νϋί
Contents
3.3 Deformation
and strain
..............................................85
3.3.1
Deformation gradient
......................................85
3.3.2
Stretch, rotation, Green s deformation tensor,
Cauchy deformation tensor
...............................88
3.3.3
Polar decomposition, stretch tensors, rotation tensor
— 91
3.3.4
Principal stretches and principal directions
..............94
3.3.5
Other measures of deformation and strain
...............96
3.4
Velocity gradient, rate of deformation tensor, vorticity tensor
..104
3.5
Material point, material line, material surface,
material volume
................................................... 109
3.6
Volume elements and surface elements in volume
and surface integrations
........................................... 110
CHAPTER
4
The Fundamental Laws of Thermomechanics
.........115
4.1
Mass
............................................................... 115
4.2
Forces and moments, linear and angular momentum
............ 116
4.3
Equations of motion (mechanical conservation laws)
........... 117
4.4
The first law of thermodynamics (conservation of energy)
..... 118
4.5
The transport and localization theorems
......................... 120
4.5.1
The transport theorem
................................... 120
4.5.2
The localization theorem
................................ 122
4.6
Cauchy stress tensor, heat flux vector
............................ 124
4.7
The energy theorem and stress power
............................ 130
4.8
Local forms of the conservation laws
............................ 131
4.9
Lagrangian forms of the integral conservation laws
............. 137
4.9.1
Mass, forces, moments, linear and angular
momentum
............................................... 139
4.9.2
Conservation of mass, linear momentum, and
angular momentum
...................................... 140
4.9.3
First law of thermodynamics
............................ 141
4.9.4
Summary
................................................. 141
4.10
Piola-
Kirchhoff
stress tensors, referential heat flux vector
...... 142
4.10.1
Relations between spatial and referential quantities
... 142
4.11
The Lagrangian form of the energy theorem
..................... 143
4.12
Local conservation laws in Lagrangian form
.................... 144
4.13
The second law of thermodynamics
.............................. 148
PARTIU
CONSTITUTIVE MODELING
______________________
CHAPTER
5
Constitutive Modeling in Mechanics and
Thermomechanics
............................................157
Part I: Mechanics
.................................................................... 157
5.1
Fundamental laws, constitutive equations, a well-posed
initial-value boundary-value problem
............................ 157
Contents
5.2
Restrictions on the constitutive equations
........................ 159
5.2.1
Invariance
under superposed rigid body motions
...... 160
5.2.2
Material symmetry
...................................... 171
Part II: Thermomechanics
........................................................... 174
5.3
Fundamental laws, constitutive equations, thermomechanical
processes
........................................................... 175
5.4
Restrictions on the constitutive equations
........................ 178
5.4.1
Invariance
under superposed rigid body motions
...... 178
CHAPTER
6
Nonlinear Elasticity
..........................................
I8i
6.1
Mechanical theory
................................................. 181
6.2
Thermomechanical theory
........................................ 183
6.2.1
Restrictions imposed by the second law
of thermodynamics
...................................... 183
6.2.2
Restrictions imposed by
invariance
under
superposed rigid body motions and conservation
of angular momentum
................................... 187
6.2.3
Restrictions imposed by material symmetry:
Isotropy
.................................................. 191
6.3
Strain energy models
.............................................. 194
CHAPTER? Fluid Mechanics
...............................................197
7.1
Mechanical theory
................................................. 197
7.1.1
Viscous fluids
............................................ 197
7.1.2
Inviscid fluids
............................................ 205
7.2
Thermomechanical theory
........................................ 206
7.2.1
Viscous fluids
............................................ 206
7.2.2
Inviscid fluids
............................................212
CHAPTER
8
Incompressibility and Thermal Expansion
.............215
8.1
Introduction
........................................................215
8.1.1
Motion-temperature constraints
......................... 216
8.1.2
Motion-entropy constraints
.............................217
8.2
Newtonian fluids
..................................................218
8.2.1
The compressible theory: A brief review
............... 218
8.2.2
Incompressibility
........................................ 220
8.2.3
Incompressibility as a constitutive limit: An
alternative perspective
................................... 227
8.2.4
Thermal expansion
......................................229
8.2.5
Thermal expansion as a constitutive limit: An
alternative perspective
...................................234
Contents
8.3
Nonlinear elastic solids
........................................... 236
8.3.1
The compressible theory: A brief review
...............236
8.3.2
Incompressibility
........................................237
8.3.3
Incompressible strain energy models
................... 241
PART IV BEYOND MECHANICS AND
THERMOMECHANICS
CHAPTER
9
Modeling of
Thermo-Electro-Magneţo-
Mechanical Behavior, with Application to Smart
Materials
........................................................249
9.1
The fundamental laws of continuum electrodynamics:
Integral forms
...................................................... 250
9.1.1
Notation and nomenclature
............................. 250
9.1.2
Conservation of mass
....................................251
9.1.3
Balance of linear momentum
...........................252
9.1.4
Balance of angular momentum
.........................256
9.1.5
First law of thermodynamics
............................257
9.1.6
Second law of thermodynamics
.........................259
9.1.7
Conservation of electric charge
......................... 260
.8
Faraday s law
............................................ 262
.9
Gauss s law for magnetism
..............................262
9.
9.
9.
9.
9.
. 10
Gauss s law for electricity
............................... 263
. 11
Ampère-Maxwell
law
................................... 264
.12
Transformations between spatial and referential
TEMM quantities
........................................ 265
9.2
The fundamental laws of continuum electrodynamics:
Pointwise forms
................................................... 269
9.2.1
Eulerian fundamental laws
.............................. 269
9.2.2
Lagrangian fundamental laws
........................... 275
9.3
Modeling of the effective electromagnetic fields
................ 277
9.3.1
Minkowski model
....................................... 278
9.3.2
Lorentz
model
........................................... 278
9.3.3
Statistical model
.........................................278
9.3.4
Chu
model
...............................................279
9.3.5
A comparison of the four models
.......................279
9.4
Modeling of the electromagnetically induced coupling
terms
............................................................... 280
9.4.1
An alternative approach
................................. 281
9.5
Thermo-electro-magneto-mechanical process
...................283
Contents
9.6
Constitutive model development for
thermo-electro-magneto-elastic materials:
Large-deformation theory
......................................... 284
9.6.1
The reduced Clausius-Duhem inequality, work
conjugates
................................................284
9.6.2
The all-extensive formulation
........................... 285
9.6.3
Other formulations
...................................... 288
9.6.4
Restrictions imposed by
invariance
under
superposed rigid body motions and conservation
of angular momentum
................................... 293
9.7
Constitutive model development for
thermo-electro-magneto-elastic materials:
Small-deformation theory
......................................... 294
9.7.1
Small-deformation kinematics, kinetics,
electromagnetic fields, and fundamental laws
..........294
9.7.2
Linear constitutive equations
........................... 296
9.7.3
Material symmetry
...................................... 298
9.8
Linear, reversible, thermo-electro-magneto-mechanical
processes
........................................................... 299
9.9
Specialization of the small-deformation
thermo-electro-magneto-elastic framework to piezoelectric
materials
........................................................... 302
APPENDIX A Different Notions of
Invariance
..........................
зоѕ
APPENDIX
В
The Physical Basis of Constitutive Assumptions
.307
APPENDIXC
Isotropie
Tensors
.............................................309
APPENDIX
D
A Family of Thermomechanical Processes
...........
зі і
APPENDIX
E
Energy Formulations and Stability Conditions for
Newtonian Fluids
.............................................
зіз
E.
1
Governing equations
............................................. 313
E.
1.1
Density-entropy formulation
............................. 314
E.
1.2
Density-temperature formulation
........................ 315
E.
1.3
Pressure-entropy formulation
............................ 315
E.
1.4
Pressure-temperature formulation
........................ 316
E.2 Stability conditions
.............................................. 317
APPENDIX
F
Additional Energy Formulations for
Thermo-Electro-Magneto-Mechanical Materials
. 319
F.1 Deformation-temperature-electric displacement-magnetic
induction formulation
............................................ 319
Bibliography
......................................................................... 321
Index
................................................................................. 325
|
| any_adam_object | 1 |
| author | Bechtel, Stephen E. Lowe, Robert L. |
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| id | DE-604.BV041772453 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:54:43Z |
| institution | BVB |
| isbn | 012394600X 9780123946003 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027218418 |
| oclc_num | 903082977 |
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| physical | XV, 330 S. Ill., graph. Darst. |
| publishDate | 2015 |
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| publisher | Academic Press |
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| spellingShingle | Bechtel, Stephen E. Lowe, Robert L. Fundamentals of continuum mechanics with applications to mechanical, thermomechanical, and smart materials Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4032296-8 |
| title | Fundamentals of continuum mechanics with applications to mechanical, thermomechanical, and smart materials |
| title_auth | Fundamentals of continuum mechanics with applications to mechanical, thermomechanical, and smart materials |
| title_exact_search | Fundamentals of continuum mechanics with applications to mechanical, thermomechanical, and smart materials |
| title_full | Fundamentals of continuum mechanics with applications to mechanical, thermomechanical, and smart materials Stephen E. Bechtel ; Robert L. Lowe |
| title_fullStr | Fundamentals of continuum mechanics with applications to mechanical, thermomechanical, and smart materials Stephen E. Bechtel ; Robert L. Lowe |
| title_full_unstemmed | Fundamentals of continuum mechanics with applications to mechanical, thermomechanical, and smart materials Stephen E. Bechtel ; Robert L. Lowe |
| title_short | Fundamentals of continuum mechanics |
| title_sort | fundamentals of continuum mechanics with applications to mechanical thermomechanical and smart materials |
| title_sub | with applications to mechanical, thermomechanical, and smart materials |
| topic | Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027218418&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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