Eigendamage: an eigendeformation model for the variational approximation of cohesive fracture
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Logos
[2019]
|
| Series: | Augsburger Schriften zur Mathematik, Physik und Informatik
Band 36 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | vi, 142 Seiten Illustrationen 21 cm |
| ISBN: | 9783832549695 3832549692 |
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MARC
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| 245 | 1 | 0 | |a Eigendamage |b an eigendeformation model for the variational approximation of cohesive fracture |c Veronika Antonie Auer-Volkmann |
| 264 | 1 | |a Berlin |b Logos |c [2019] | |
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| 653 | |a cohesive fracture | ||
| 653 | |a eigendeformation | ||
| 653 | |a Gamma-convergence | ||
| 653 | |a non-local approximation | ||
| 653 | |a two-field approximation | ||
| 653 | |a 29 | ||
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Record in the Search Index
| _version_ | 1804180720493527040 |
|---|---|
| adam_text | CONTENTS
1
INTRODUCTION
1
2
NOTATION
AND
PRELIMINARY
RESULTS
15
2.1
BASIC
NOTATION
2.2
MEASURE
THEORY
15
2.3
FUNCTIONS
OF
BOUNDED
VARIATION
20
2.4
F-CONVERGENCE
.........................................................
24
2.5
SLICING
...............................................................
26
3
SOME
PREPARATORY
WORK
29
3.1
AN
OPTIMIZATION
PROBLEM
29
3.2
A
RELAXATION
RESULT
IN
THE
SPACE
BV(FI)
32
4
EIGENDAMAGE:
AN
EIGENDEFORMATION
MODEL
FOR
THE
VARIATIONAL
APPROXIMATION
OF
COHESIVE
FRACTURE:
THE
ONE-DIMENSIONAL
CASE
45
4.1
SETTING
OF
THE
PROBLEM
AND
MAIN
RESULTS
45
4.2
COMPACTNESS
49
4.3
ESTIMATE
FROM
BELOW
OF
THE
JUMP
PART
53
4.4
ESTIMATE
FROM
BELOW
OF
THE
VOLUME
AND
CANTOR
TERMS
56
4.5
ESTIMATE
FROM
BELOW
OF
THE
F-LOWER
LIMIT
65
4.6
ESTIMATE
FROM
ABOVE
OF
THE
F-UPPER
LIMIT
67
4.7
F-CONVERGENCE
FOR
THE
MINIMAL
ENERGIES
WITH
RESPECT
TO
7
73
5
EIGENDAMAGE:
AN
EIGENDEFORMATION
MODEL
FOR
THE
VARIATIONAL
APPROXIMATION
OF
COHESIVE
FRACTURE:
THE
D-DIMENSIONAL
CASE
WITH
PURE
ANTIPLANE
SHEAR
DEFORMATIONS
75
5.1
SETTING
OF
THE
PROBLEM
AND
MAIN
RESULTS
76
5.2
COMPACTNESS
78
5.3
ESTIMATE
FROM
BELOW
OF
THE
SURFACE
TERM
84
5.4
ESTIMATE
FROM
BELOW
OF
THE
VOLUME
TERM
103
5.5
ESTIMATE
FROM
BELOW
OF
THE
CANTOR
TERM
106
5.6
ESTIMATE
FROM
BELOW
OF
THE
F-LOWER
LIMIT
ILL
V
5.7
ESTIMATE
FROM
ABOVE
OF
THE
F-UPPER
LIMIT
.....................................................
112
5.8
F-CONVERGENCE
FOR
THE
MINIMAL
ENERGIES
WITH
RESPECT
TO
7
.............................
121
APPENDIX
A
NEGATIVE
SOBOLEV
SPACES,
EMBEDDING
THEOREMS
AND
THE
FLAT
TOPOLOGY
125
A.L
NEGATIVE
SOBOLEV
SPACES
AND
EMBEDDING
THEOREMS
......................................
125
A.
2
FLAT
TOPOLOGY
....................................................................................................
126
APPENDIX
B
CONVOLUTION
129
APPENDIX
C
CONVEX
SETS
AND
CONCAVE
FUNCTIONS
131
LIST
OF
SYMBOLS
133
BIBLIOGRAPHY
135
INDEX
140
VI
|
| any_adam_object | 1 |
| author | Auer-Volkmann, Veronika Antonie ca. 20./21. Jh |
| author_GND | (DE-588)1201511119 |
| author_facet | Auer-Volkmann, Veronika Antonie ca. 20./21. Jh |
| author_role | aut |
| author_sort | Auer-Volkmann, Veronika Antonie ca. 20./21. Jh |
| author_variant | v a a v vaa vaav |
| building | Verbundindex |
| bvnumber | BV046274541 |
| ctrlnum | (OCoLC)1130268635 (DE-599)DNB1195547773 |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-10T08:40:15Z |
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| isbn | 9783832549695 3832549692 |
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| physical | vi, 142 Seiten Illustrationen 21 cm |
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| series | Augsburger Schriften zur Mathematik, Physik und Informatik |
| series2 | Augsburger Schriften zur Mathematik, Physik und Informatik |
| spelling | Auer-Volkmann, Veronika Antonie ca. 20./21. Jh. Verfasser (DE-588)1201511119 aut Eigendamage an eigendeformation model for the variational approximation of cohesive fracture Veronika Antonie Auer-Volkmann Berlin Logos [2019] © 2019 vi, 142 Seiten Illustrationen 21 cm txt rdacontent n rdamedia nc rdacarrier Augsburger Schriften zur Mathematik, Physik und Informatik Band 36 Dissertation Universität Augsburg 2019 Bruchverhalten (DE-588)4121051-7 gnd rswk-swf Gamma-Konvergenz (DE-588)4311219-5 gnd rswk-swf Variationsproblem (DE-588)4187419-5 gnd rswk-swf cohesive fracture eigendeformation Gamma-convergence non-local approximation two-field approximation 29 (DE-588)4113937-9 Hochschulschrift gnd-content Bruchverhalten (DE-588)4121051-7 s Variationsproblem (DE-588)4187419-5 s Gamma-Konvergenz (DE-588)4311219-5 s DE-604 Logos Verlag Berlin (DE-588)1065538812 pbl Augsburger Schriften zur Mathematik, Physik und Informatik Band 36 (DE-604)BV017601953 36 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=c6d6b1d05b68447eb4edb6064548d68b&prov=M&dok_var=1&dok_ext=htm Inhaltstext B:DE-101 application/pdf https://d-nb.info/1195547773/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031652289&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Auer-Volkmann, Veronika Antonie ca. 20./21. Jh Eigendamage an eigendeformation model for the variational approximation of cohesive fracture Augsburger Schriften zur Mathematik, Physik und Informatik Bruchverhalten (DE-588)4121051-7 gnd Gamma-Konvergenz (DE-588)4311219-5 gnd Variationsproblem (DE-588)4187419-5 gnd |
| subject_GND | (DE-588)4121051-7 (DE-588)4311219-5 (DE-588)4187419-5 (DE-588)4113937-9 |
| title | Eigendamage an eigendeformation model for the variational approximation of cohesive fracture |
| title_auth | Eigendamage an eigendeformation model for the variational approximation of cohesive fracture |
| title_exact_search | Eigendamage an eigendeformation model for the variational approximation of cohesive fracture |
| title_full | Eigendamage an eigendeformation model for the variational approximation of cohesive fracture Veronika Antonie Auer-Volkmann |
| title_fullStr | Eigendamage an eigendeformation model for the variational approximation of cohesive fracture Veronika Antonie Auer-Volkmann |
| title_full_unstemmed | Eigendamage an eigendeformation model for the variational approximation of cohesive fracture Veronika Antonie Auer-Volkmann |
| title_short | Eigendamage |
| title_sort | eigendamage an eigendeformation model for the variational approximation of cohesive fracture |
| title_sub | an eigendeformation model for the variational approximation of cohesive fracture |
| topic | Bruchverhalten (DE-588)4121051-7 gnd Gamma-Konvergenz (DE-588)4311219-5 gnd Variationsproblem (DE-588)4187419-5 gnd |
| topic_facet | Bruchverhalten Gamma-Konvergenz Variationsproblem Hochschulschrift |
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| volume_link | (DE-604)BV017601953 |
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