Elastoplasticity theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Lecture Notes in Applied and Computational Mechanics
42 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XV, 416 S. graph. Darst. |
| ISBN: | 9783642002724 9783642002731 |
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MARC
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| 100 | 1 | |a Hashiguchi, Koichi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elastoplasticity theory |c Koichi Hashiguchi |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XV, 416 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture Notes in Applied and Computational Mechanics |v 42 | |
| 650 | 4 | |a Elastoplastizität | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Elastoplasticity | |
| 650 | 4 | |a Elastoplasticity |x Mathematical models | |
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Record in the Search Index
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| adam_text | Contents
1 Tensor
Analysis
............................................................... 1
1.1 Conventions and Symbols................................................ 1
1.1.1
Summation
Convention.......................................... 1
1.1.2 Kronecker s Delta and Permutation Symbol.................. 1
1.1.3 Matrix
and Determinant
.......................................... 2
1.2
Vector........................................................................
8
1.2.1
Definition of Vector
.............................................. 8
1.2.2
Operations for Vectors
........................................... 8
1.2.3
Component Description of Vector
.............................. 9
1.3
Tensor
...................................................................... 14
1.3.1
Definition of Tensor
.............................................. 14
1.3.2
Quotient Law
...................................................... 15
1.3.3
Notations of Tensors
............................................. 17
1.3.4
Orthogonal Tensor
................................................ 18
1.3.5
Tensor Product and Component
................................. 19
1.4
Operations of Second-Order Tensor
.................................... 20
1.4.1
Trace
............................................................... 20
1.4.2
Various Tensors
................................................... 21
1.5
Eigenvalues and Eigenvectors
........................................... 26
1.6
Calculations of Eigenvalues and Eigenvectors
........................ 31
1.6.1
Eigenvalues
........................................................ 31
1.6.2
Eigenvectors
....................................................... 32
1.7
Eigenvalue and Eigenvectors of Skew-Symmetric Tensor
.......... 33
1.8
Cayley-Hamilton s Theorem
............................................ 35
1.9
Positive Definite Tensor
................................................. 35
1.10
Polar Decomposition
....................................................... 36
1.1
1
Isotropie
Tensor-Valued Tensor Function
............................. 37
1.12
Representation of Tensor in Principal Space
.......................... 40
1.13
Two-Dimensional State
................................................... 44
1.14
Partial Differential Calculi
................................................ 47
1.15
Time Derivatives
........................................................... 50
1.16
Differentiation and Integration in Field
................................ 51
2
Motion and Strain (Rate)
.................................................... 57
2.1
Motion and Deformation
................................................. 57
2.1.1
Material, Spatial and Relative Descriptions
................... 57
2.1.2
Deformation Gradient and Deformation Tensors
............ 59
ХИ
Contents
2.2
Strain
Tensor
............................................................... 64
2.3
Strain Rate and Spin Tensors
............................................ 70
2.4
Various Simple Deformations
........................................... 81
2.4.1
Uniaxial
Loading
.................................................. 81
2.4.2
Simple Shear
...................................................... 84
2.4.3
Combination of Tension and Distortion
........................ 94
2.5
Surface Element, Volume Element and Their Rates
.................. 97
3
Conservation Laws and Stress Tensors
................................... 101
3.1
Conservation Law of Mass
.............................................. 101
3.2
Conservation Law of Momentum
....................................... 101
3.3
Conservation Law of Angular Momentum
............................ 102
3.4
Stress Tensor
............................................................... 102
3.5
Equilibrium Equation
..................................................... 105
3.6
Equilibrium Equation of Moment
....................................... 107
3.7
Virtual Work Principle
................................................... 108
4
Objectivity and Corotational Rate Tensor
...............................
Ill
4.1
Objectivity
..................................................................
Ill
4.2
Influence of Rigid-Body Rotation on Various Mechanical
Quantities
.................................................................. 112
4.3
Rate of State Variable and Corotational Rate Tensor
................ 114
4.4
Transformation of Material-Time Derivative of Scalar Function
to Its Corotational Derivative
........................................... 119
4.5
Various Objective Stress Rate Tensors
................................. 122
4.6
Work Conjugacy
.......................................................... 124
5
Elastic Constitutive Equations
.............................................. 127
5.1
Hyperelasticity
............................................................ 127
5.2
Cauchy Elasticity
......................................................... 130
5.3
Hypoelasticity
............................................................. 131
6
Basic Formulations for Elastoplastic Constitutive Equations
........ 135
6.1
Multiplicative Decomposition of Deformation Gradient and
Additive Decomposition of Strain Rate
................................ 135
6.2
Conventional Elastoplastic Constitutive Equations
.................. 142
6.3
Loading Criterion
.......................................................... 148
6.4
Associated Flow Rule
.................................................... 151
6.4.1
Positivity
of Second-Order Plastic Work Rate: Prager s
Interpretation
...................................................... 151
6.4.2
Positivity
of Work Done During Stress Cycle: Drucker s
Hypothesis
......................................................... 151
6.4.3
Positivity
of Second-Order Plastic Relaxation Work
Rate
................................................................. 152
6.4.4
Comparison of Interpretations for Associated Flow Rule...
153
Contents XIII
6.5
Anisotropy
.................................................................. 156
6.5.1
Definition of Isotropy
............................................. 156
6.5.2 Anisotropie
Plastic Constitutive Equation
..................... 157
6.6
Incorporation of Tangential-Inelastic Strain Rate
..................... 159
6.7
Hyperelastic-Plastic Constitutive Equation: Finite Strain
Theory
...................................................................... 165
7
Unconventional Elastoplasticity Model: Subloading Surface
Model
....................................................................................... 171
7.1
Mechanical Requirements
................................................ 171
7.1.1
Continuity Condition
............................................. 171
7.1.2
Smoothness Condition
........................................... 172
7.2
Subloading Surface Model
............................................... 174
7.3
Salient Features of Subloading Surface Model
........................ 181
7.4
On Bounding Surface and Bounding Surface Model
................. 184
7.5
Incorporation of Anisotropy
............................................. 186
7.6
Incorporation of Tangential Inelastic Strain Rate
..................... 187
8
Cyclic Plasticity Model: Extended Subloading Surface Model
...... 191
8.1
Classification of Cyclic Plasticity Models
............................. 191
8.2
Translation of Subyield Surface(s): Extension of
Kinematic Hardening
...................................................... 191
8.2.1
Multi-surface Model
............................................. 191
8.2.2
Two-Surface Model
.............................................. 194
8.2.3
Infinite-Surface Model
........................................... 195
8.2.4
Nonlinear Kinematic Hardening Model
........................ 195
8.3
Extended Subloading Surface Model
................................... 196
8.4
Modification of Reloading Curve
....................................... 205
8.5
Incorporation of Tangential-Inelastic Strain Rate
..................... 208
9
Viscoplastic Constitutive Equations
....................................... 211
9.1
History of Viscoplastic Constitutive Equations
....................... 211
9.2
Mechanical Response of Ordinary Overstress Model
................ 214
9.3
Modification of Overstress Model: Extension to General Rate
of Deformation
............................................................ 215
9.4
Incorporation of Subloading Surface Concept: Subloading
Overstress Model
......................................................... 217
10
Constitutive Equations of Metals
........................................... 221
10.1 Isotropie
and Kinematic Hardening
................................... 221
10.2
Cyclic Stagnation of
Isotropie
Hardening
........................... 225
10.3
On Calculation of the Normal-Yield Ratio
........................... 232
10.4
Comparisons of Test Results
.......................................... 232
10.5
Orthotropic Anisotropy
................................................. 238
XIV Contents
10.6
Representation of
Isotropie
Mises
Yield Condition
................ 244
10.6.1
Plane Stress State
............................................... 245
10.6.2
Plane Strain State
............................................... 248
11
Constitutive Equations of Soils
............................................. 249
і
1.1 Isotropie
Consolidation Characteristics
.............................. 249
1.2
Yield Conditions
......................................................... 253
1
1.3 Isotropie
Hardening Function
.......................................... 259
1
1.4
Rotational Hardening
................................................... 261
1
1.5
Extended Subloading Surface Model
................................. 265
1
1.6
Partial Derivatives of Subloading Surface Function
................ 267
11.7
Calculation of Normal-Yield Ratio
.................................... 271
11.8
Simulations of Test Results
............................................ 275
11.9
Simple Subloading Surface Model
.................................... 281
[1.10
Super-Yield Surface for Structured Soils in Natural
Deposits
................................................................. 291
11.11
Numerical Analysis of Footing Settlement Problem
.............. 301
12
Corotational Rate Tensor
..................................................... 309
12.1
Hypoelasticity
............................................................ 309
12.1.1
JaumannRate
................................................... 309
12.1.2
Green-Naghdi Rate
............................................ 311
12.2
Kinematic Hardening Material
........................................ 313
12.2.1
JaumannRate
................................................... 315
12.2.2
Green-Naghdi Rate
............................................ 316
12.3
Plastic Spin
................................................................ 317
13
Localization of Deformation
................................................ 327
13.1
Element Test
.............................................................. 327
13.2
Gradient Theory
.......................................................... 328
13.3
Shear-Band Embedded Model: Smeared Crack Model
............ 331
13.4
Necessary Condition for Shear Band Inception
..................... 333
14
Numerical Calculation
....................................................... 337
14.1
Numerical Ability of Subloading Surface Model
................... 337
14.2
Return-Mapping Algorithm Formulation for Subloading
Surface Model
........................................................... 340
15
Constitutive Equation for Friction
......................................... 349
15.1
History of Constitutive Equation for Friction
........................ 349
15.2
Decomposition of Sliding Velocity
....................................... 350
15.3
Normal Sliding-Yield and Sliding-Subloading Surfaces
........... 354
15.4
Evolution Rules of Sliding-Hardening Function and Normal
Sliding-Yield Ratio
............................................................. 355
15.4.1
Evolution Rule of Sliding-Hardening Function
........... 355
15.4.2
Evolution Rule of Normal Sliding-Yield Ratio
............ 356
Contents
XV
15.5
Relations of Contact
Traction Rate and Sliding Velocity
......... 357
15.6
Loading Criterion
................................................................... 359
15.7
Sliding-Yield Surfaces
............................................................ 360
15.8
Basic Mechanical Behavior of Subloading-Friction Model
........ 365
15.8.1
Relation of Tangential Contact Traction Rate and
Sliding Velocity
.................................................. 366
15.8.2
Numerical Experiments and Comparisons with Test
Data
............................................................................ 367
15.9
Extension to Orthotropic Anisotropy
..................................... 375
Appendixes
...................................................................... 387
Appendix
1 :
Projection of Area
................................................ 387
Appendix
2:
Proof of d(FJA I J)/dxj
- 0................................................ 388
Appendix
3:
Euler s Theorem for Homogeneous Function
............... 388
Appendix
4:
Normal Vector of Surface
....................................... 389
Appendix
5:
Convexity of Two-Dimensional Curve
....................... 390
Appendix
6:
Derivation of Eq.
(11.19)...................................... 391
Appendix
7:
Numerical Experiments for Deformation Behavior Near
Yield State
......................................................... 392
References
........................................................................ 395
Index
.............................................................................. 407
Lecture Notes
in Applied and Computational Mechanics
This series aims to report new developments in applied and computational mechanics
quickly, informally and at a high level. This includes the fields of fluid, solid and structural
mechanics, dynamics and control, and related disciplines. The applied methods can be of
analytical, numerical and computational nature.
Elastoplasticity Theory
This book was written to serve as the standard textbook for instruction of elastoplasticity
theory. It opens with an explanation of the mathematics and continuum mechanics which are
necessary as a foundation of elastoplasticity theory. Subsequently, conventional and
unconventional elastoplasticity theories are explained comprehensively for description of
general loading behavior covering
monotonie,
nonproportional,
and cyclic loading processes.
Fundamental notions such as continuity and smoothness conditions, decomposition of
deformation into elastic and plastic parts, the associated flow rule, the loading criterion and
the anisotropy are defined, and then presented with their mechanical interpretations.
Explicit constitutive equations of metals and soils, which are useful in engineering practice for
the mechanical design of machinery and structures, are also introduced. Moreover, constitutive
equations of friction with transition from static to kinetic friction and vice versa, and rotational
and orthotropic anisotropy are provided. They are indispensable for analyses of
boundary-value problems.
A distinguishing feature of this book is that it is written to be understandable without
difficulty even by beginners in the field of elastoplasticity, explaining physical backgrounds
with illustrations and descriptions of detailed derivation processes of all equations without a
jump. Furthermore, the history and the latest results related to elastoplasticity are explained
thoroughly to the extent that the fundamentals of elastoplasticity theory can be understood
and be applicable readily to analyses of engineering problems. Therein, the subloading
surface model is delineated, which possesses the high ability for the description of
elastoplastic deformation behavior. In addition it is furnished with the noticeable advantage
for the numerical calculation with the automatic controlling function to attract the stress to
the yield surface in the plastic deformation process and thus it does not require to
incorporate the convergence computer algorithm such as the return mapping in the yield state.
|
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| author | Hashiguchi, Koichi |
| author_facet | Hashiguchi, Koichi |
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| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | UF 3100 |
| ctrlnum | (OCoLC)310400724 (DE-599)BVBBV035648882 |
| dewey-full | 620.11232 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
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| discipline | Maschinenbau / Maschinenwesen Physik |
| format | Book |
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| id | DE-604.BV035648882 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:42:25Z |
| institution | BVB |
| isbn | 9783642002724 9783642002731 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017703522 |
| oclc_num | 310400724 |
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| owner | DE-703 DE-29T |
| owner_facet | DE-703 DE-29T |
| physical | XV, 416 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Lecture Notes in Applied and Computational Mechanics |
| series2 | Lecture Notes in Applied and Computational Mechanics |
| spelling | Hashiguchi, Koichi Verfasser aut Elastoplasticity theory Koichi Hashiguchi Berlin [u.a.] Springer 2009 XV, 416 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Applied and Computational Mechanics 42 Elastoplastizität Mathematisches Modell Elastoplasticity Elastoplasticity Mathematical models Elastoplastizität (DE-588)4204381-5 gnd rswk-swf Elastoplastizität (DE-588)4204381-5 s DE-604 Lecture Notes in Applied and Computational Mechanics 42 (DE-604)BV017110729 42 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017703522&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017703522&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Hashiguchi, Koichi Elastoplasticity theory Lecture Notes in Applied and Computational Mechanics Elastoplastizität Mathematisches Modell Elastoplasticity Elastoplasticity Mathematical models Elastoplastizität (DE-588)4204381-5 gnd |
| subject_GND | (DE-588)4204381-5 |
| title | Elastoplasticity theory |
| title_auth | Elastoplasticity theory |
| title_exact_search | Elastoplasticity theory |
| title_full | Elastoplasticity theory Koichi Hashiguchi |
| title_fullStr | Elastoplasticity theory Koichi Hashiguchi |
| title_full_unstemmed | Elastoplasticity theory Koichi Hashiguchi |
| title_short | Elastoplasticity theory |
| title_sort | elastoplasticity theory |
| topic | Elastoplastizität Mathematisches Modell Elastoplasticity Elastoplasticity Mathematical models Elastoplastizität (DE-588)4204381-5 gnd |
| topic_facet | Elastoplastizität Mathematisches Modell Elastoplasticity Elastoplasticity Mathematical models |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017703522&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017703522&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV017110729 |
| work_keys_str_mv | AT hashiguchikoichi elastoplasticitytheory |