A thermodynamically consistent phase field approach to fracture:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Stuttgart
Inst. f. Mechanik (Bauwesen), Lehrstuhl I, Univ.
2014
|
| Series: | Bericht / Institut für Mechanik (Bauwesen), Lehrstuhl I
29 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 146 S. Ill., graph. Darst. |
| ISBN: | 3937859179 |
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MARC
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| 245 | 1 | 0 | |a A thermodynamically consistent phase field approach to fracture |c vorgelegt von Martina Hofacker |
| 264 | 1 | |a Stuttgart |b Inst. f. Mechanik (Bauwesen), Lehrstuhl I, Univ. |c 2014 | |
| 300 | |a IV, 146 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a Bericht / Institut für Mechanik (Bauwesen), Lehrstuhl I |v 29 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
I
CONTENTS
1. INTRODUCTION 1
1.1. MOTIVATION AND STATE OF THE ART 1
1.2. OBJECTIVES AND OVERVIEW 4
2. FUNDAMENTALS OF CONTINUUM MECHANICS 9
2.1. BASIC KINEMATICS OF SMALL DEFORMATIONS 9
2.2. INTRODUCTION OF PHENOMENOLOGICAL QUANTITIES 11
2.2.1. CONTACT TRACTION AND STRESS TENSOR 11
2.2.2. CONCEPT OF ENERGY FLUX 12
2.3. PHYSICAL BALANCE PRINCIPLES 12
2.3.1. BALANCE OF MASS 13
2.3.2. BALANCE OF LINEAR MOMENTUM 13
2.3.3. BALANCE OF ANGULAR MOMENTUM 14
2.3.4. BALANCE OF ENERGY - IST PRINCIPLE OF THERMODYNAMICS 14
2.3.5. BALANCE OF ENTROPY - 2ND PRINCIPLE OF THERMODYNAMICS 15
2.4. CONSTITUTIVE VARIATIONAL FORMULATION FOR STANDARD DISSIPATIVE
MATERIALS . . 16
2.4.1. THE INTERNAL VARIABLE FORMULATION 16
2.4.2. THE VARIATIONAL FORMULATION 18
3. FUNDAMENTALS OF CLASSICAL FRACTURE AND DAMAGE MECHANICS 21
3.1. BASIC DEFINITIONS OF FRACTURE MECHANICS 21
3.2. PHYSICAL MECHANISMS OF FRACTURE 22
3.2.1. A MICROSCOPIC VIEWPOINT OF FRACTURE 22
3.2.2. A MACROSCOPIC APPROACH TO FRACTURE 23
3.3. THE CONCEPT OF STRESS INTENSITY FACTORS - IRWIN S THEORY 24
3.4. AN ENERGETIC APPROACH TO FRACTURE MECHANICS - GRIFFITH S THEORY 25
3.4.1. ENERGY BALANCE FOR BRITTIE CRACKS 25
3.4.2. ENERGY BALANCE FOR DUCTILE CRACKS 27
3.5. FUNDAINENTALS OF DAMAGE MECHANICS 28
3.5.1. BRITTIE DAMAGE MECHANICS 29
3.5.2. DUCTILE DAMAGE MECHANICS 29
HTTP://D-NB.INFO/1055982973
II CONTENTS
4. NEW APPROACH TO REGULARIZED PHASE FIELD MODEL OF FRACTURE 31
4.1. VARIATIONAL ENERGY FORMULATIONS -
FUNDAMENTALS OF FREE DISCONTINUITY PROBLEMS 31
4.2. PHASE FIELD APPROXIMATION OF CRACK TOPOLOGY 33
4.2.1. GEOMETRIE MOTIVATION: 1-D BAR WITH A CRACK 34
4.2.2. A CONTINUOUS VARIATIONAL FORMULATION OF REGULARIZED CRACK
TOPOLOGY 36
4.2.3. SPATIAL DISCRETIZATION OF REGULARIZED CRACK TOPOLOGY 37
4.2.4. A NUMERICAL MODEL PROBLEM 38
4.3. IRREVERSIBILITY CONSTRAINT FOR CRACK EVOLUTION 39
5. A PHASE FIELD MODEL OF BRITTIE FRACTURE 41
5.1. PRIMARY FIELDS OF COUPLED PROBLEM 41
5.2. CONSTITUTIVE STORED ENERGY FUNCTIONALS 42
5.2.1. ISOTROPIE DEGRADATION OF STORED BULK ENERGY DUE TO FRACTURE ....
42
5.2.2. ANISOTROPIE DEGRADATION OF STORED BULK ENERGY DUE TO FRACTURE . .
43
5.3. KINETIC ENERGY FUNCTIONAL 44
5.4. DISSIPATION FUNCTIONALS 45
5.4.1. MODEL I: CANONICAL SETTING WITH INDICATOR FUNCTION 45
5.4.2. MODEL II: EXTENDED SETTING WITH THRESHOLD FUNCTION 47
5.5. EXTERNAL LOAD F INCTIONAL 48
5.6. VARIATIONAL PRINCIPLES AND GOVERNING EQUATIONS 48
5.6.1. MODEL I - RATE-INDEPENDENT CANONICAL SETTING 48
5.6.2. MODEL IIA - RATE-INDEPENDENT EXTENDED SETTING 49
5.6.3. MODEL IIB - VISCOUS EXTENDED SETTING 52
6. ALGORITHMIC SETTING OF BRITTIE PHASE FIELD FORMULATION 57
6.1. DISCRETE INCREMENTAL COUPLED MULTI-FIELD PROBLEM 57
6.1.1. TIME DISCRETIZATION OF COUPLED PROBLEM 57
6.1.2. SPATIAL DISCRETIZATION OF COUPLED PROBLEM 61
6.2. STAGGERED SOLUTION OF INCREMENTAL MULTI-FIELD PROBLEM 63
6.2.1. STAGGERED UPDATE SCHEME OF TIME DISCRETE FIELDS 63
6.2.2. SPATIAL DISCRETIZATION OF STAGGERED PROBLEM 66
6.3. NUMERICAL EXAMPLES OF QUASI-STATIC, BRITTIE PHASE FIELD FRACTURE 67
6.3.1. SINGLE-EDGE-NOTCHED TENSION TEST 67
CONTENTS III
6.3.2. SINGLE NOTCHED SPECIMEN UNDER PURE SHEAR LOADING 68
6.3.3. SYMMETRIE THREE POINT BENDING TEST 71
6.3.4. ASYMMETRIE NOTCHED THREE POINT BENDING TEST 75
6.3.5. THREE-DIMENSIONAL MODE-I TENSION TEST 77
6.3.6. TENSION TEST OF CUBE WITH SPHERICAL INCLUSION 79
6.4. NUMERICAL EXAMPLES OF DYNAMIC, BRITTIE PHASE FIELD FRACTURE 80
6.4.1. 2D SIMULATION OF THE KALTHOFF WINKLER LIKE TEST 80
6.4.2. 2D SINGLE EDGE NOTCHED TENSION TEST 86
6.4.3. 3D SIMULATION OF KALTHOFF WINKLER TEST 89
6.4.4. 3D KALTHOFF WINKLER TEST WITH CIRCULAR PROJECTILE 90
7. A PHASE FIELD MODEL OF BRITTIE AND DUCTILE FRACTURE 93
7.1. THE DYNAMIC FAILURE MODE TVANSITION 94
7.2. THE DUCTILE FAILURE CRITERION 96
7.3. PRIMARY FIELDS OF COUPLED PROBLEM 97
7.4. CONSTITUTIVE STORED ENERGY FUNCTIONAL 98
7.4.1. DEGRADATION OF ELASTIC ENERGY FUNCTION DUE TO FRACTURE 98
7.4.2. DEGRADATION OF PLASTIC ENERGY FUNCTION DUE TO FRACTURE 99
7.4.3. THE RATE OF THE STORED ENERGY FUNCTIONAL 100
7.5. KINETIC ENERGY FUNCTIONAL 101
7.6. DISSIPATION FUNCTIONALS 101
7.6.1. DISSIPATION FUNCTION FOR THE PLASTIC FLOW 101
7.6.2. DISSIPATION FUNCTION FOR THE EVOLUTION OF THE CRACK PHASE FIELD.
. . 102
7.6.3. THE EXTENDED DISSIPATION FUNCTIONAL 102
7.7. EXTERNAL LOAD RMCTIONAL 102
7.8. VARIATIONAL PRINCIPLES AND GOVERNING EQUATIONS 103
7.8.1. THE EXTENDED VARIATIONAL PRINCIPLE 103
7.8.2. COMPACT HISTORY-FIELD-BASED FORMULATION 104
7.8.3. VISCOUS REGULARIZATION OF THE EXTENDED VARIATIONAL PROBLEM 105
7.9. ADIABATIC EVOLUTION OF THE TEMPERATURE FIELD 107
7.9.1. THE THERMO-MECHANICAL STORED ENERGY FUNCTIONAL 107
7.9.2. THE LOCAL DISSIPATION 108
7.9.3. THE TEMPERATURE EVOLUTION EQUATION 109
IV
CONTENTS
7.9.4. A COMPACT FORMAT OF THERMO-ELASTO-PLASTIC EVOLUTION EQUATIONS .
110
7.10. GRADIENT-TYPE EXPANSION OF THE LOCAL EQUIVALENT PLASTIC STRAINS
111
8. ALGORITHMIC SETTING OF BRITTIE TO DUCTILE PHASE FIELD FRACTURE 113
8.1. STAGGERED SOLUTION OF INCREMENTAL MULTI-FIELD PROBLEM 113
8.1.1. STAGGERED UPDATE SCHEME OF TIME-DISCRETE FIELDS 113
8.1.2. SPATIAL DISCRETIZATION OF STAGGERED PROBLEM 121
8.2. REPRESENTATIVE NUMERICAL EXAMPLE 123
8.2.1. A PRE-NOTCHED STEEL PLATE IMPACTED BY A PROJECTILE 123
9. CONCLUSION SIND OUTLOOK 131
A. INVESTIGATION OF A TWO-DIMENSIONAL CRACK TIP FIELD 135
B. INTRODUCTION OF A DAMAGE-DRIVING HISTORY FIELD 137
REFERENCES
139
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| indexdate | 2024-07-10T01:10:49Z |
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| isbn | 3937859179 |
| language | English |
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| physical | IV, 146 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
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| publisher | Inst. f. Mechanik (Bauwesen), Lehrstuhl I, Univ. |
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| spelling | Hofacker, Martina 1977- Verfasser (DE-588)1050868285 aut A thermodynamically consistent phase field approach to fracture vorgelegt von Martina Hofacker Stuttgart Inst. f. Mechanik (Bauwesen), Lehrstuhl I, Univ. 2014 IV, 146 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bericht / Institut für Mechanik (Bauwesen), Lehrstuhl I 29 Zugl.: Stuttgart, Univ., Diss., 2013 (DE-588)4113937-9 Hochschulschrift gnd-content Institut für Mechanik (Bauwesen), Lehrstuhl I Bericht 29 (DE-604)BV011175295 29 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027466325&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hofacker, Martina 1977- A thermodynamically consistent phase field approach to fracture |
| subject_GND | (DE-588)4113937-9 |
| title | A thermodynamically consistent phase field approach to fracture |
| title_auth | A thermodynamically consistent phase field approach to fracture |
| title_exact_search | A thermodynamically consistent phase field approach to fracture |
| title_full | A thermodynamically consistent phase field approach to fracture vorgelegt von Martina Hofacker |
| title_fullStr | A thermodynamically consistent phase field approach to fracture vorgelegt von Martina Hofacker |
| title_full_unstemmed | A thermodynamically consistent phase field approach to fracture vorgelegt von Martina Hofacker |
| title_short | A thermodynamically consistent phase field approach to fracture |
| title_sort | a thermodynamically consistent phase field approach to fracture |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027466325&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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