A consistent computational framework for finite micropolar hyper-elastoplasticity: formulation, linearization and application to the simulation of size effects
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Aachen
Shaker
2012
|
| Edition: | 1. Aufl. |
| Series: | Berichte aus der Mechanik
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erscheint: 9. August 2012 |
| Physical Description: | IV, 144 S. graph. Darst. 210 mm x 148 mm, 225 g |
| ISBN: | 9783844011920 |
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| 245 | 1 | 0 | |a A consistent computational framework for finite micropolar hyper-elastoplasticity |b formulation, linearization and application to the simulation of size effects |c Steffen Bauer |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PREFACE *
1. INTRODUCTION 1
1.1. MOTIVATION 1
1.2. STATE OF T H E A R T 2
1.3. AIMS A N D SCOPE 4
1.4. OUTLINE 4
1.5. NOTATIONAL CONVENTIONS 4
2. BASIC C O N C E P T S O F MICROPOLAR C O N T I N U U M M E C H A N I
C S A N D MATERIALS MODELING 7 2.1. KINEMATICS OF MICROPOLAR DEFORMATION
7
2.1.1. DEFORMATION WITHIN T H E MICROPOLAR SETTING 7
2.1.2. MICROPOLAR STRAIN A N D CURVATURE 9
2.1.3. DECOMPOSITION OF STRAIN A N D CURVATURE 10
2.1.4. RATES OF STRAIN A N D CURVATURE 10
2.2. FUNDAMENTAL BALANCE LAWS 11
2.2.1. LINEAR A N D ANGULAR M O M E N T U M BALANCE 11
2.2.2. CLAUSIUS-DUHEM INEQUALITY 12
2.3. THERMODYNARNICAL SETTING 12
2.3.1. A GENERIC SPECIFIC FREE ENERGY POTENTIAL 12
2.3.2. THERMODYNAMICALLY CONSISTENT CONSTITUTIVE EQUATIONS 13
2.4. PARTICULAR CONSTITUTIVE MODELS 14
2.4.1. GENERALIZED VON MISES PLASTICITY 14
2.4.2. A N ALTERNATIVE APPROACH: MULTI-CRITERION MICROPOLAR PLASTICITY .
. 15 2.4.3. NEO-HOOKE-TYPE MICROPOLAR HYPERELASTICTY 16
2.5. SUMMARY OF T H E BASIC CONCEPTS A N D CONSTITUTIVE RELATIONS 18
3. FORMULATION O F T H E OVERALL PROBLEM S T A T E M E N T 2 1
4. D E V E L O P M E N T O F T H E NUMERICAL SOLUTION FRAMEWORK 2 5
4.1. OUTLINE OF THE OVERALL APPROACH 26
4.2. INTEGRATION OF T H E CONSTITUTIVE EQUATIONS 28
4.2.1. T I M E DISCRETIZATION A N D T H E INCREMENTAL CONSTITUTIVE
PROBLEM . . 28 4.2.2. T H E PREDICTOR CORRECTOR ALGORITHM 31
4.3. SOLUTION OF T H E MICROPOLAR INITIAL BOUNDARY VALUE PROBLEM 38
4.3.1. WEAK FORMULATION A N D INCREMENTATION 38
I I I
HTTP://D-NB.INFO/1024139956
IMAGE 2
4.3.2. LINEARIZATION: DERIVATION OF T H E MICROPOLAR GLOBAL TANGENT . .
. . 40
4.3.3. ALGORITHMICALLY CONSISTENT TANGENT OPERATORS 45
4.4. FINITE ELEMENT DISCRETIZATION 50
4.4.1. BASIC CONCEPTS OF THE FINITE ELEMENT METHODOLOGY 50
4.4.2. T H E F - B A R APPROACH WITHIN T H E MICROPOLAR SETTING 52
4.4.3. T H E MICROPOLAR FINITE ELEMENT FORMULATION WITHIN F E A P 54
4.5. SUMMARY OF T H E COMPUTATIONAL DEVELOPMENTS 55
4.6. DISCUSSION OF POTENTIAL ALTERNATIVE METHODOLOGIES 56
5. NUMERICAL E X A M P L E S 5 9
5.1. INFINITESIMAL MICROPOLAR ELASTICITY 61
5.1.1. FIELD OF UNIFORM TENSILE STRESS WITH CIRCULAR HOLE 6 1
5.2. FINITE MICROPOLAR HYPERELASTICITY 65
5.2.1. CLAMPED BEAM: FINITE ELASTIC BENDING 65
*5.2.2. CYLINDRICAL BAR: FINITE ELASTIC TENSILE & TORSION LOADING 66
5.3. QUASI-INCOMPRESSIBLE DEFORMATIONS 72
5.3.1. BULK DEFORMATION BENCHMARK 72
5.3.2. CYLINDRICAL B A R BENCHMARK 73
5.4. FINITE MICROPOLAR HYPER-ELASTOPLASTICITY 80
5.4.1. NOTCHED SPECIMEN UNDER ELASTOPLASTIC TENSILE & TORSION LOADING .
80 5.5. PREDICTION OF EXPERIMENTAL RESULTS A N D MODEL COMPARISON 92
5.5.1. T H E SIZE EFFECT IN MICROSCOPIC C U WIRES 92
5.6. A COMPARATIVE S T U D Y ON COMPUTATIONAL EFFICIENCY 99
5.6.1. ELASTICITY 99
5.6.2. PLASTICITY 100
5.7. S U M M A R Y OF NUMERICAL RESULTS A N D T H E VALIDATION PROCESS
105
6. CONCLUSIONS 1 0 7
6.1. OVERALL S U M M A R Y 107
6.2. MAIN CONTRIBUTIONS 108
6.3. OUTLOOK 109
N O M E N C L A T U R E 1 1 1
A. LINEARIZATION O F T H E R E T U R N M A P P I N G E Q U A T I O N S
117
B. LINEARIZATION O F T H E ROTATIONAL S T A T E VARIABLES 1 2 1
C. DERIVATION O F T H E IMPLICIT DIFFERENTIATION O P E R A T O R S 1 2 5
D. DERIVATION O F T H E MICROPOLAR F-BAR T A N G E N T 1 2 9
BIBLIOGRAPHY 1 3 5
IV
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| any_adam_object | 1 |
| author | Bauer, Steffen |
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| author_facet | Bauer, Steffen |
| author_role | aut |
| author_sort | Bauer, Steffen |
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| building | Verbundindex |
| bvnumber | BV040547529 |
| ctrlnum | (OCoLC)918458064 (DE-599)DNB1024139956 |
| dewey-full | 620.11230113 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.11230113 |
| dewey-search | 620.11230113 |
| dewey-sort | 3620.11230113 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen |
| edition | 1. Aufl. |
| format | Thesis Book |
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| spelling | Bauer, Steffen Verfasser (DE-588)1026998859 aut A consistent computational framework for finite micropolar hyper-elastoplasticity formulation, linearization and application to the simulation of size effects Steffen Bauer 1. Aufl. Aachen Shaker 2012 IV, 144 S. graph. Darst. 210 mm x 148 mm, 225 g txt rdacontent n rdamedia nc rdacarrier Berichte aus der Mechanik Erscheint: 9. August 2012 Zugl.: Technische Univ. Darmstadt, Diss., 2012 Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Size-Effekt (DE-588)4181611-0 gnd rswk-swf Numerisches Modell (DE-588)4338132-7 gnd rswk-swf Elastoplastizität (DE-588)4204381-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kontinuumsmechanik (DE-588)4032296-8 s Elastoplastizität (DE-588)4204381-5 s Size-Effekt (DE-588)4181611-0 s Numerisches Modell (DE-588)4338132-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025393312&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bauer, Steffen A consistent computational framework for finite micropolar hyper-elastoplasticity formulation, linearization and application to the simulation of size effects Kontinuumsmechanik (DE-588)4032296-8 gnd Size-Effekt (DE-588)4181611-0 gnd Numerisches Modell (DE-588)4338132-7 gnd Elastoplastizität (DE-588)4204381-5 gnd |
| subject_GND | (DE-588)4032296-8 (DE-588)4181611-0 (DE-588)4338132-7 (DE-588)4204381-5 (DE-588)4113937-9 |
| title | A consistent computational framework for finite micropolar hyper-elastoplasticity formulation, linearization and application to the simulation of size effects |
| title_auth | A consistent computational framework for finite micropolar hyper-elastoplasticity formulation, linearization and application to the simulation of size effects |
| title_exact_search | A consistent computational framework for finite micropolar hyper-elastoplasticity formulation, linearization and application to the simulation of size effects |
| title_full | A consistent computational framework for finite micropolar hyper-elastoplasticity formulation, linearization and application to the simulation of size effects Steffen Bauer |
| title_fullStr | A consistent computational framework for finite micropolar hyper-elastoplasticity formulation, linearization and application to the simulation of size effects Steffen Bauer |
| title_full_unstemmed | A consistent computational framework for finite micropolar hyper-elastoplasticity formulation, linearization and application to the simulation of size effects Steffen Bauer |
| title_short | A consistent computational framework for finite micropolar hyper-elastoplasticity |
| title_sort | a consistent computational framework for finite micropolar hyper elastoplasticity formulation linearization and application to the simulation of size effects |
| title_sub | formulation, linearization and application to the simulation of size effects |
| topic | Kontinuumsmechanik (DE-588)4032296-8 gnd Size-Effekt (DE-588)4181611-0 gnd Numerisches Modell (DE-588)4338132-7 gnd Elastoplastizität (DE-588)4204381-5 gnd |
| topic_facet | Kontinuumsmechanik Size-Effekt Numerisches Modell Elastoplastizität Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025393312&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bauersteffen aconsistentcomputationalframeworkforfinitemicropolarhyperelastoplasticityformulationlinearizationandapplicationtothesimulationofsizeeffects |