Variational methods for crystalline microstructure: theory and computation
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
2002
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Leipzig, Univ., Habil.-Schr., 2002. - Zsfassung in dt. Sprache |
| Physical Description: | II, 175 S. Ill., graph. Darst. |
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| 245 | 1 | 0 | |a Variational methods for crystalline microstructure |b theory and computation |c vorgelegt von Georg Dolzmann |
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| 500 | |a Leipzig, Univ., Habil.-Schr., 2002. - Zsfassung in dt. Sprache | ||
| 650 | 4 | |a Kristall - Mikrostruktur - Phasenumwandlung - Nichtkonvexes Variationsproblem | |
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Record in the Search Index
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CONTENTS
CHAPTER 1. INTRODUCTION 1
1.1. MICROSTRUCTURE AND QUASICONVEX HULLS 1
1.2. ANALYTICAL RESULTS 7
1.3. NUMERICAL ANALYSIS AND COMPUTATION 10
CHAPTER 2. PRELIMINARIES 15
2.1. NOTATION 15
2.2. NOTIONS OF CONVEXITY 16
2.3. EXISTENCE OF RANK-ONE CONNECTIONS 21
2.4. USEFUL FORMULAE 23
CHAPTER 3. SEMICONVEX HULLS OF MATRICES 27
3.1. SEMICONVEX HULLS IN TWO DIMENSIONS 28
3.1.1. SEMICONVEX HULLS FOR
DACOROGNA'S
EIGHT POINT EXAMPLE 28
3.1.2. SETS INVARIANT UNDER SO(2) 35
3.1.2.1. THE ONE-WELL PROBLEM 35
3.1.2.2. THE TWO-WELL PROBLEM 35
3.1.2.3. THE
N-WELL PROBLEM WITH EQUAL DETERMINANT 37
3.1.2.4. THE GENERAL THEOREM 42
3.1.2.5. AN SO(2) INVARIANT SET WITH
KRC ^ KPC 44
3.1.3. SETS INVARIANT UNDER 0(2) 47
3.1.4. WELLS DEFINED BY SINGULAR VALUES 48
3.1.5. AN OPTIMAL
TAYLOR
BOUND 49
3.2. SEMICONVEX HULLS IN THREE DIMENSIONS 51
3.2.1. THE TWO-WELL PROBLEM IN THREE DIMENSIONS 51
3.2.2. PROBLEMS THAT CAN BE REDUCED TO THE TWO-DIMENSIONAL CASE 54
3.2.3. WELLS DEFINED BY SINGULAR VALUES 54
CHAPTER 4. A THREE-DIMENSIONAL MODEL FOR NEMATIC ELASTOMERS 59
4.1. CONVEXITY OF FUNCTIONS DEFINED BY SINGULAR VALUES 60
4.2. AN UPPER BOUND FOR THE RELAXATION 61
4.3. THE POLYCONVEX AND THE RANK-ONE CONVEX ENVELOPE OF THE ENERGY 65
4.4. THE QUASICONVEX ENVELOPE OF THE ENERGY 70
CHAPTER 5. UNIQUENESS OF MICROSTRUCTURE 73
5.1. A SUFFICIENT CRITERION FOR UNIQUENESS 73
5.2. NECESSARY AND SUFFICIENT CONDITIONS FOR UNIQUENESS IN TWO
DIMENSIONS 77
5.2.1. NECESSARY AND SUFFICIENT CONDITIONS FOR SO(2) INVARIANT WELLS 77
5.2.2. NECESSARY AND SUFFICIENT CONDITIONS FOR 0(2) INVARIANT WELLS 78
5.2.3. NECESSARY AND SUFFICIENT CONDITIONS FOR THE THIN FILM CASE 81
5.3. APPLICATION TO AUSTENITE-MARTENSITE TRANSFORMATIONS IN THREE
DIMENSIONS 82
5.3.1. THE CUBIC TO TETRAGONAL TRANSFORMATION 82
I
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/965047857
CONTENTS
II
SFI
5.3.2. THE CUBIC TO TRIGONAL TRANSFORMATION
5.3.3. THE CUBIC TO ORTHORHOMBIC TRANSFORMATION 86
5.3.4. THE TETRAGONAL TO MONOCLINIC TRANSFORMATIONS 92
CHAPTER 6. MICROSTRUCTURE AND FINITE ELEMENT MINIMIZERS 99
6.1. PROBABILISTIC ANALYSIS OF MICROSTRUCTURE - AN OVERVIEW 101
6.2. DEFINITION OF STABILITY 104
6.3. STABILITY FOR SIMPLE LAMINATES IN THREE DIMENSIONS 105
6.4. STABILITY FOR SECOND LAMINATES IN THREE DIMENSIONS 112
6.5. STABILITY FOR 0(2) INVARIANT WELLS H4
6.6. STABILITY FOR THIN FILMS H8
CHAPTER 7. COMPUTATION OF RANK-ONE CONVEX HULLS AND LAMINATES 125
7.1. THE ALGORITHM FOR THE COMPUTATION OF ENVELOPES OF FUNCTIONS 126
7.2. NUMERICAL EXPERIMENTS FOR THE COMPUTATION OF ENVELOPES OF FUNCTIONS
129
7.2.1.
THE KOHN-STRANG EXAMPLE
129
7.2.2.
DACOROGNA'S
EIGHT POINT EXAMPLE 151
7.3. THE ALGORITHM FOR THE COMPUTATION OF LAMINATES 132
7.4. NUMERICAL EXPERIMENTS FOR THE COMPUTATION OF LAMINATES 138
7.4.1. AN INFINITE LAMINATE 138
7.4.2.
DACOROGNA'S
EIGHT POINT EXAMPLE 139
APPENDIX A. PHASE TRANSFORMATIONS 143
A.L. CRYSTALLOGRAPHY AND AUSTENITE-MARTENSITE TRANSFORMATIONS 143
A. 1.1. CUBIC TO TETRAGONAL TRANSFORMATION 146
A. 1.2. CUBIC TO TRIGONAL TRANSFORMATION 147
A. 1.3. CUBIC TO ORTHORHOMBIC TRANSFORMATION 147
A.1.4. TETRAGONAL TO MONOCLINIC TRANSFORMATION 148
A.L.5. CUBIC TO MONOCLINIC TRANSFORMATION 149
A.2. NEMATIC ELASTOMERS AND ISOTROPIC-NEMATIC TRANSFORMATIONS 150
DEUTSCHSPRACHIGE KURZFASSUNG 152
1. MIKROSTRUKTUREN UND QUASIKONVEXE HIILLEN 154
2. ANALYTISCHE RESULTATE 159
3. NUMERISCHE RESULTATE 163
INDEX 169
BIBLIOGRAPHY 171 |
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| indexdate | 2024-10-09T18:03:52Z |
| institution | BVB |
| language | English |
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| physical | II, 175 S. Ill., graph. Darst. |
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| spelling | Dolzmann, Georg Verfasser aut Variational methods for crystalline microstructure theory and computation vorgelegt von Georg Dolzmann 2002 II, 175 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Leipzig, Univ., Habil.-Schr., 2002. - Zsfassung in dt. Sprache Kristall - Mikrostruktur - Phasenumwandlung - Nichtkonvexes Variationsproblem Nichtkonvexes Variationsproblem (DE-588)4707126-6 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Mikrostruktur (DE-588)4131028-7 gnd rswk-swf Kristall (DE-588)4033209-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kristall (DE-588)4033209-3 s Mikrostruktur (DE-588)4131028-7 s Phasenumwandlung (DE-588)4132140-6 s Nichtkonvexes Variationsproblem (DE-588)4707126-6 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009984172&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dolzmann, Georg Variational methods for crystalline microstructure theory and computation Kristall - Mikrostruktur - Phasenumwandlung - Nichtkonvexes Variationsproblem Nichtkonvexes Variationsproblem (DE-588)4707126-6 gnd Phasenumwandlung (DE-588)4132140-6 gnd Mikrostruktur (DE-588)4131028-7 gnd Kristall (DE-588)4033209-3 gnd |
| subject_GND | (DE-588)4707126-6 (DE-588)4132140-6 (DE-588)4131028-7 (DE-588)4033209-3 (DE-588)4113937-9 |
| title | Variational methods for crystalline microstructure theory and computation |
| title_auth | Variational methods for crystalline microstructure theory and computation |
| title_exact_search | Variational methods for crystalline microstructure theory and computation |
| title_full | Variational methods for crystalline microstructure theory and computation vorgelegt von Georg Dolzmann |
| title_fullStr | Variational methods for crystalline microstructure theory and computation vorgelegt von Georg Dolzmann |
| title_full_unstemmed | Variational methods for crystalline microstructure theory and computation vorgelegt von Georg Dolzmann |
| title_short | Variational methods for crystalline microstructure |
| title_sort | variational methods for crystalline microstructure theory and computation |
| title_sub | theory and computation |
| topic | Kristall - Mikrostruktur - Phasenumwandlung - Nichtkonvexes Variationsproblem Nichtkonvexes Variationsproblem (DE-588)4707126-6 gnd Phasenumwandlung (DE-588)4132140-6 gnd Mikrostruktur (DE-588)4131028-7 gnd Kristall (DE-588)4033209-3 gnd |
| topic_facet | Kristall - Mikrostruktur - Phasenumwandlung - Nichtkonvexes Variationsproblem Nichtkonvexes Variationsproblem Phasenumwandlung Mikrostruktur Kristall Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009984172&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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