Nonlinear solid mechanics: a continuum approach for engineering
Providing a modern and comprehensive coverage of continuum mechanics, this volume includes information on "variational principles" - significant, as this is the only method by which such material is actually utilized in engineering practice.
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2008
|
| Edition: | Reprinted |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Providing a modern and comprehensive coverage of continuum mechanics, this volume includes information on "variational principles" - significant, as this is the only method by which such material is actually utilized in engineering practice. |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIV, 455 S. graph. Darst. |
| ISBN: | 9780471823193 0471823198 |
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MARC
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| 245 | 1 | 0 | |a Nonlinear solid mechanics |b a continuum approach for engineering |c Gerhard A. Holzapfel |
| 250 | |a Reprinted | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2008 | |
| 300 | |a XIV, 455 S. |b graph. Darst. | ||
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| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
Acknowledgements
xiii
1
Introduction to Vectors and Tensors
1
1.1
Algebra of Vectors
........................... 1
1.2
Algebra of Tensors
........................... 9
1.3
Higher-order Tensors
.......................... 20
1.4
Eigenvalues, Eigenvectors of Tensors
................. 24
1.5
Transformation Laws for Basis Vectors and Components
....... 28
1.6
General Bases
............................. 32
1.7
Scalar, Vector, Tensor Functions
.................... 40
1.8
Gradients and Related Operators
.................... 44
1.9
Integral Theorems
........................... 52
2
Kinematics
55
2.1
Configurations, and Motions of Continuum Bodies
.......... 56
2.2
Displacement, Velocity, Acceleration Fields
.............. 61
2.3
Material, Spatial Derivatives
...................... 64
2.4
Deformation Gradient
......................... 70
2.5
Strain Tensors
............................. 76
2.6
Rotation, Stretch Tensors
........................ 85
2.7
Rates of Deformation Tensors
..................... 95
2.8
Lie Time Derivatives
.......................... 106
v
v¡
Contents
3
The Concept
of
Stress
109
3.1
Traction Vectors,
and Stress
Tensors
.................. 109
3.2
Extremal Stress Values
.........................
H9
3.3
Examples of States of Stress
......................
I23
3.4
Alternative Stress Tensors
....................... 127
4
Balance Principles
131
4.1
Conservation of Mass
......................... 131
4.2
Reynolds Transport Theorem
..................... 138
4.3
Momentum Balance Principles
..................... 141
4.4
Balance of Mechanical Energy
..................... 152
4.5
Balance of Energy in Continuum Thermodynamics
.......... 161
4.6
Entropy Inequality Principle
...................... 166
4.7
Master Balance Principle
........................ 174
5
Some Aspects of Objectivity
179
5.1
Change of Observer, and Objective Tensor Fields
........... 179
5.2
Superimposed Rigid-body Motions
.................. 187
5.3
Objective Rates
............................. 192
5.4
Invariance
of Elastic Material Response
................ 196
6
Hyperelastic Materials
205
6.1
General Remarks on Constitutive Equations
.............. 206
6.2 Isotropie
Hyperelastic Materials
.................... 212
6.3
Incompressible Hyperelastic Materials
................. 222
6.4
Compressible Hyperelastic Materials
................. 227
6.5
Some Forms of Strain-energy Functions
................ 235
6.6
Elasticity Tensors
............................ 252
6.7
Transversely
Isotropie
Materials
.................... 265
Contents
vii
6.8
Composite
Materials
with Two
Families
of Fibers
........... 272
6.9
Constitutive Models with Internal Variables
.............. 278
6.10
Viscoelastic Materials at Large Strains
................. 282
6.11
Hyperelastic Materials with
Isotropie
Damage
............ 295
7
Thermodynamics of Materials
305
7.1
Physical Preliminaries
......................... 306
7.2
Thermoelasticity of Macroscopic Networks
.............. 311
7.3
Thermodynamic Potentials
....................... 321
7.4
Calorimetry
............................... 325
7.5
Isothermal, Isentropic Elasticity Tensors
................ 328
7.6 Entropie
Elastic Materials
....................... 333
7.7
Thermodynamic Extension of Ogden s Material Model
........ 337
7.8
Simple Tension of
Entropie
Elastic Materials
............. 343
7.9
Thermodynamics with Internal Variables
............... 357
8
Variational Principles
371
8.1
Virtual Displacements, Variations
................... 372
8.2
Principle of Virtual Work
........................ 377
8.3
Principle of Stationary Potential Energy
................ 386
8.4
Linearization of the Principle of Virtual Work
............. 392
8.5
Two-field Variational Principles
.................... 402
8.6
Three-field Variational Principles
................... 409
References
415
Index
435
|
| any_adam_object | 1 |
| author | Holzapfel, Gerhard A. 1961- |
| author_GND | (DE-588)136155820 |
| author_facet | Holzapfel, Gerhard A. 1961- |
| author_role | aut |
| author_sort | Holzapfel, Gerhard A. 1961- |
| author_variant | g a h ga gah |
| building | Verbundindex |
| bvnumber | BV035315075 |
| classification_rvk | UF 2000 |
| classification_tum | PHY 210f |
| ctrlnum | (OCoLC)254772940 (DE-599)BVBBV035315075 |
| discipline | Physik |
| edition | Reprinted |
| format | Book |
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| id | DE-604.BV035315075 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:06Z |
| institution | BVB |
| isbn | 9780471823193 0471823198 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017119755 |
| oclc_num | 254772940 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XIV, 455 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Wiley |
| record_format | marc |
| spelling | Holzapfel, Gerhard A. 1961- Verfasser (DE-588)136155820 aut Nonlinear solid mechanics a continuum approach for engineering Gerhard A. Holzapfel Reprinted Chichester [u.a.] Wiley 2008 XIV, 455 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Providing a modern and comprehensive coverage of continuum mechanics, this volume includes information on "variational principles" - significant, as this is the only method by which such material is actually utilized in engineering practice. Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Nichtlineare Mechanik (DE-588)4042095-4 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s Nichtlineare Mechanik (DE-588)4042095-4 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=017119755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holzapfel, Gerhard A. 1961- Nonlinear solid mechanics a continuum approach for engineering Kontinuumsmechanik (DE-588)4032296-8 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd |
| subject_GND | (DE-588)4032296-8 (DE-588)4042095-4 |
| title | Nonlinear solid mechanics a continuum approach for engineering |
| title_auth | Nonlinear solid mechanics a continuum approach for engineering |
| title_exact_search | Nonlinear solid mechanics a continuum approach for engineering |
| title_full | Nonlinear solid mechanics a continuum approach for engineering Gerhard A. Holzapfel |
| title_fullStr | Nonlinear solid mechanics a continuum approach for engineering Gerhard A. Holzapfel |
| title_full_unstemmed | Nonlinear solid mechanics a continuum approach for engineering Gerhard A. Holzapfel |
| title_short | Nonlinear solid mechanics |
| title_sort | nonlinear solid mechanics a continuum approach for engineering |
| title_sub | a continuum approach for engineering |
| topic | Kontinuumsmechanik (DE-588)4032296-8 gnd Nichtlineare Mechanik (DE-588)4042095-4 gnd |
| topic_facet | Kontinuumsmechanik Nichtlineare Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017119755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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