Continuum mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Physics and astronomy online library
Advanced texts in physics |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 297 S. graph. Darst. |
| ISBN: | 3540430199 |
Staff View
MARC
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| 245 | 1 | 0 | |a Continuum mechanics |c I-Shih Liu |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XII, 297 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Physics and astronomy online library | |
| 490 | 0 | |a Advanced texts in physics | |
| 650 | 4 | |a Continuum mechanics | |
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Record in the Search Index
| _version_ | 1804129130536501248 |
|---|---|
| adam_text | Contents
1.
Kinematics
............................................... 1
1.1
Configuration and Deformation
........................... 1
1.1.1
Change of Reference Configuration
................. 4
1.2
Strain and Rotation
.................................... 4
1.3
Linear Strain Tensors
................................... 8
1.4
Motion
................................................ 13
1.4.1
Material and Spatial Descriptions
.................. 14
1.5
Relative Deformation
................................... 17
1.6
Rate of Deformation
.................................... 20
1.7
Change of Frame and Objective Tensors
................... 22
1.7.1
Transformation Property of Motion
................. 25
1.7.2
Property of Some Kinematic Quantities
............. 26
2.
Balance Laws
............................................. 31
2.1
General Balance Equation
............................... 31
2.1.1
Field Equation and Jump Condition
................ 35
2.1.2
Balance Equations in Material Coordinates
.......... 36
2.2
Conservation of Mass
................................... 38
2.3
Laws of Dynamics
...................................... 41
2.3.1
Forces and Moments
.............................. 42
2.3.2
Stress Tensor
.................................... 43
2.3.3
Conservation of Linear and Angular Momenta
....... 50
2.4
Conservation of Energy
................................. 51
2.5
Summary of Basic Equations
............................. 54
2.5.1
Basic Equations in Material Coordinates
............ 56
2.5.2
Boundary Conditions of a Material Body
............ 57
2.6
Field Equations in Arbitrary Frames
...................... 58
3.
Basic Principles of Constitutive Theories
................. 63
3.1
Constitutive Relation
................................... 63
3.2
Principle of Material Objectivity
......................... 65
3.2.1
In Referential Description
......................... 68
3.2.2
An Example: a Particular Class of Materials
......... 70
3.3
Simple Material Bodies
.................................. 72
X
Contents
3.4
Reduced Constitutive Relations
.......................... 75
3.5
Material Symmetry
..................................... 77
3.5.1
Constitutive Equation for a Simple Solid Body
....... 81
3.5.2
Constitutive Equation for a Simple Fluid
............ 82
3.5.3
Fluid Crystal with an Intrinsic Direction
............ 84
3.6 Isotropie
Materials
...................................... 86
3.6.1
Constitutive Equation of an
Isotropie
Material
....... 88
3.7
Fading Memory
........................................ 89
3.7.1
Linear Viscoelasticity
............................. 90
3.7.2
Boltzmann-Volterra Theory of Viscoelasticity
........ 92
3.7.3
Linear Viscoelasticity of Rate Type
................. 93
3.7.4
Remark on Objectivity of Linear Elasticity
.......... 94
4.
Representation of Constitutive Functions
................. 97
4.1
Materials of Grade
η
.................................... 97
4.2 Isotropie
Functions
..................................... 98
4.2.1 Isotropie
Elastic Materials and Linear Elasticity
......107
4.2.2
Reiner-Rivlin Fluids and Navier-Stokes Fluids
.......109
4.2.3
Elastic Fluids
....................................
Ill
4.3
Representation of
Isotropie
Functions
.....................112
4.3.1 Isotropie Thermoelastic
Solids
and Viscous Heat-Conducting Fluids
................118
4.4
Hemitropic Invariants
...................................119
4.5 Anisotropie
Invariants
...................................122
4.5.1
Transverse Isotropy and Orthotropy
................124
4.5.2
On Irreducibility of Invariant Sets
..................126
5.
Entropy Principle
.........................................129
5.1
Entropy Inequality
.....................................129
5.2
Entropy Principle
......................................131
5.3
Thermodynamics of Elastic Materials
.....................132
5-3.1
Linear Thermoelasticity
...........................135
5.4
Elastic Materials with Internal Constraints
................139
5.5
Stability of Equilibrium
.................................144
5.5.1
Thermodynamic Stability Criteria
..................148
5.6
Phase Equilibrium
......................................149
6.
Isotropie
Elastic Solids
...................................153
6.1
Constitutive Equations
..................................153
6.2
Boundary Value Problems in Elasticity
....................155
6.3
Homogeneous Stretch
...................................157
6.3.1
Uniaxial
Stretch
..................................158
6.3.2
Biaxial Stretch
...................................159
6.4
Symmetric Loading of a Square Sheet
.....................160
6.4.1
Stability of a Square Sheet
........................162
Contents
XI
6.5 Simple
Shear...........................................
166
6.6
Pure Shear of a Square Block
............................169
6.7
Finite Deformation of Spherical Shells
.....................173
6.7.1
Eversion
of a Spherical Shell
.......................175
6.7.2
Inflation of a Spherical Shell
.......................176
6.8
Stability of Spherical Shells
..............................179
6.8.1
Stability under Constant Pressures
.................180
6.8.2
Stability for an Enclosed Spherical Shell
.............181
7.
Thermodynamics with
Lagrange
Multipliers
..............183
7.1
Supply-Free Bodies
.....................................183
7.2
Viscous Heat-Conducting Fluid
..........................184
7.2.1
General Results
..................................186
7.2.2
Navier-Stokes-Fourier Fluids
......................188
7.3
Method of
Lagrange
Multipliers
..........................189
7.3.1
An Algebraic Problem
............................190
7.3.2
Local Solvability
.................................191
7.4
Relation Between Entropy Flux and Heat Flux
.............194
7.4.1
Theorem of Parallel
Isotropie
Vector Functions
.......194
8.
Rational Extended Thermodynamics
.....................199
8.1
Introduction
...........................................199
8.2
Formal Structure of System of Balance Equations
..........200
8.2.1
Symmetric Hyperbolic System
.....................201
8.2.2
Galilean
Invariance
...............................204
8.3
System of Moment Equations
............................207
8.4
Closure Problem
.......................................213
8.4.1
Entropy Principle
................................214
8.4.2
Formal Procedures
...............................216
8.5
Thirteen-Moment Theory
of Viscous Heat-Conducting Fluid
........................217
8.5.1
Field Equations
..................................223
8.5.2
Entropy and Entropy Flux
........................225
8.6
Monatomic Ideal Gases
..................................226
8.6.1
Thirteen-Moment Theory
.........................227
8.6.2
Constitutive Equations
............................228
8.7
Stationary Heat Conduction in Ideal Gases
................228
8.7.1
Fourier s Law and Heat Conduction
................229
8.7.2
Heat Conduction in Thirteen-Moment Theory
........229
8.7.3
Remark on Boundary Value Problems
...............232
XII Contents
A. Elementary Tensor Analysis
..............................233
A.I Linear Algebra
.........................................233
A.I.I Inner Product
....................................234
A.1.2 Dual Bases
......................................235
A.1.3 Tensor Product
..................................238
A.
1.4
Ή
-ansformation
Rules for Components
..............243
A.
1.5
Determinant and Trace
...........................245
A.
1.6
Exterior Product and Vector Product
...............251
A.I.
7
Second-Order Tensors
.............................254
A.
1.8
Some Theorems of Linear Algebra
..................256
A.2 Tensor Calculus
........................................262
A.
2.1
Euclidean Point Space
............................262
A.2.2 Differentiation
...................................263
A.2.3 Coordinate System
...............................272
A.
2.4
Covariant Derivatives
.............................275
A.2.5 Other Differential Operators
.......................277
A.
2.6
Physical Components
.............................281
A.2.7 Orthogonal Coordinate Systems
....................282
References
....................................................289
Index
.........................................................293
|
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| author | Liu, I-Shih 1943- |
| author_GND | (DE-588)123509912 |
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| author_role | aut |
| author_sort | Liu, I-Shih 1943- |
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| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV014242923 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:00:15Z |
| institution | BVB |
| isbn | 3540430199 |
| language | English |
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| physical | XII, 297 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Physics and astronomy online library Advanced texts in physics |
| spelling | Liu, I-Shih 1943- Verfasser (DE-588)123509912 aut Continuum mechanics I-Shih Liu Berlin [u.a.] Springer 2002 XII, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics and astronomy online library Advanced texts in physics Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009765703&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, I-Shih 1943- Continuum mechanics Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4032296-8 |
| title | Continuum mechanics |
| title_auth | Continuum mechanics |
| title_exact_search | Continuum mechanics |
| title_full | Continuum mechanics I-Shih Liu |
| title_fullStr | Continuum mechanics I-Shih Liu |
| title_full_unstemmed | Continuum mechanics I-Shih Liu |
| title_short | Continuum mechanics |
| title_sort | continuum mechanics |
| topic | Continuum mechanics Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Continuum mechanics Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009765703&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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