Finite elasticity theory:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford, United Kingdom
Oxford Univ Press
2017
|
| Ausgabe: | First edition |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029850317&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xii, 184 Seiten Diagramme |
| ISBN: | 9780198567783 |
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Datensatz im Suchindex
| _version_ | 1819294522353385472 |
|---|---|
| adam_text | Titel: Finite elasticity theory
Autor: Steigmann, David
Jahr: 2017
CONTENTS
1 Concept of an elastic material 1
2 Observers andinvariance ................................ 7
3 Mechanical power and hyperelasticity 15
3.1 Elasticity and energy 15
3.2 Work inequality 19
4 Material symmetry 23
4.1 Stress response 23
4.2 Strain energy 27
4.3 Isotropy 28
5 Fiber symmetry 35
6 Stress response in the presence of local constraints
on the deformation 42
6.1 Local constraints 43
6.2 Constraint manifolds and the Lagrange multiplier rule 43
6.3 Material symmetry in the presence of constraints 47
7 Some boundary-value problems for uniform isotropic
incompressible materials 51
7.1 Problems exhibiting radial symmetry with respect to a fixed axis 51
7.1.1 Pressurized cylinder 51
7.1.2 Azimuthal shear 59
7.1.3 Torsion of a solid circular cylinder 63
7.1.4 Combined extension and torsion 66
7.2 Problems exhibiting radial symmetry with respect to a fixed point 67
7.2.1 Integration of the equation 70
7.2.2 Pressurized shells, cavitation 71
8 Some examples involving uniform, compressible isotropic
materials 75
8.1 Spherical symmetry, revisited 75
8.2 Plane strain 78
8.3 Radial expansion/compaction 80
9 Material stability, strong ellipticity and smoothness of
equilibria
9.1 Small motions superposed on finitely deformed equilibrium states 85
9.2 Smoothness of equilibria 89
9.3 Incompressibility 93
xii | CONTENTS
10 Membrane theory
10.1 General theory 95
10.2 Pressurized membranes 99
10.3 Uniqueness of the director
10.4 Isotropic materials ^
10.5 Axially symmetric deformations of a cylindrical membrane 104
10.6 Bulging of a cylinder ^
11 Stability and the energy criterion 113
11.1 The energy norm - H3
11.2 Instability
11.3 Quasiconvexity 121
11.4 Ordinary convexity 123
11.4.1 Objections to ordinary convexity 123
11.5 Polyconvexity 126
11.6 Rank-one convexity 128
11.7 Equilibria with discontinuous deformation gradients 131
11.8 The Maxwell-Eshelby relation 132
11.8.1 Example: alternating simple shear 133
12 Linearized theory, the second variation and bifurcation of
equilibria 137
13 Elements of plasticity theory 142
13.1 Elastic and plastic deformations 143
13.2 Constitutive response 146
13.3 Energy and dissipation 148
13.4 Invariance 152
13.5 Yielding, the work inequality and plastic flow 153
13.6 Isotropy 156
13.7 Rigid-plastic materials 160
13.8 Plane strain of rigid-perfectly plastic materials: slip-line theory 161
13.8.1 State of stress, equilibrium 161
13.8.2 Velocity field 163
Supplemental notes
1 Thecofactor 167
2 Gradients of scalar-valued functions of tensors 168
3 Chain rule 169
4 Gradients of the principal invariants of a symmetric tensor 169
5 Relations among gradients 171
6 Extensions 172
7 Korn s inequality 174
8 Poincar6 s inequality 174
Index yjy
|
| any_adam_object | 1 |
| author | Steigmann, David J. |
| author_facet | Steigmann, David J. |
| author_role | aut |
| author_sort | Steigmann, David J. |
| author_variant | d j s dj djs |
| building | Verbundindex |
| bvnumber | BV044449356 |
| classification_rvk | UF 3000 |
| ctrlnum | (OCoLC)1004636025 (DE-599)BVBBV044449356 |
| discipline | Physik |
| edition | First edition |
| format | Book |
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| id | DE-604.BV044449356 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T18:03:25Z |
| institution | BVB |
| isbn | 9780198567783 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029850317 |
| oclc_num | 1004636025 |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | xii, 184 Seiten Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Oxford Univ Press |
| record_format | marc |
| spellingShingle | Steigmann, David J. Finite elasticity theory Elastizitätstheorie (DE-588)4123124-7 gnd |
| subject_GND | (DE-588)4123124-7 |
| title | Finite elasticity theory |
| title_auth | Finite elasticity theory |
| title_exact_search | Finite elasticity theory |
| title_full | Finite elasticity theory David J. Steigmann |
| title_fullStr | Finite elasticity theory David J. Steigmann |
| title_full_unstemmed | Finite elasticity theory David J. Steigmann |
| title_short | Finite elasticity theory |
| title_sort | finite elasticity theory |
| topic | Elastizitätstheorie (DE-588)4123124-7 gnd |
| topic_facet | Elastizitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029850317&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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