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Tables of Contents for Material Instabilities in Solids
Chapter/Section Title
Page #
Page Count
Preface
xiii
2
List of Contributors
xv
1 Introduction to Material Instabilities in Solids
1
14
E. vander Giessen
R. de Borst
1.1 General introduction
1
5
1.2 Classical Bifurcation Theory
6
1
1.3 Experiments and Physical Mechanisms
7
1
1.4 Localization Without Internal Length Scales
8
2
1.5 Localization With Internal Length Scales
10
3
References
13
2
2 Stability of Layered Geological Structures: An Asymptotic Solution
15
12
Y.M. Leroy
N. Triantafyllidis
2.1 Introduction
15
1
2.2 Model Problems and Variational Formulation
16
3
2.3 Asymptotic Solution
19
6
References
25
2
3 Analysis of Shear Failure in Concrete Materials
27
14
K. William
H. Kang
B. Shing
E. Spacone
3.1 Introduction
27
1
3.2 Triaxial Concrete Model
28
3
3.3 Failure Modes of Concrete Model
31
2
3.4 Failure of Triaxial Concrete Model
33
5
3.5 Concluding Remarks
38
1
Acknowledgements
39
1
References
39
2
4 On the Effects of Intertial Coupling on the Wave-Speeds of Elastic-Plastic Fluid-Saturated Porous Media
41
14
B. Loret
E. Rizzi
4.1 Introduction
41
1
4.2 Equations of Motion
42
2
4.3 Consecutive Equations
44
3
4.4 Wave-Speeds
47
4
Acknowledgements
51
1
References
51
1
Appendix A
52
3
5 Microstructured Solids: Non-Linear Model and Analysis of Magneto-Elastic Wave Processes
55
10
V. Erofeyeu
S. Kovalev
5.1 Introduction
55
1
5.2 Non-Linear Magnetic-Elastic Equations
55
1
5.3 Plain Longitudinal Waves
56
5
5.4 Plain Shear Waves
61
3
Acknowledgement
64
1
References
64
1
6 Thermodynamics of Crystal Viscoplasticity and Instability Phenomena
65
26
P. Perzyna
6.1 Introduction
66
1
6.2 Experimental and Physical Motivations
67
1
6.3 Thermodynamic Constitutive Structures of Inelastic Single Crystals
68
5
6.4 Rate Independent Response of Single Crystals
73
1
6.5 Adiabatic Process
74
4
6.6 Macroscopic Adiabatic Shear Band Formation
78
4
6.7 Discussion of the Synergetic Effects and Comparison with Experimental
82
4
6.8 Observations
86
1
Final Comments
87
1
Acknowledgement
87
4
References
7 Instability Issues in Single Crystal Plasticity
91
16
P. Steinmann
7.1 Introduction
91
1
7.2 Multisurface Plasticity Framework
92
2
7.3 Multisurface Localization Analysis
94
3
7.4 Non Schmic Single Crystal Plasticity
97
3
7.5 Planar Localization Analysis
100
2
7.6 Model Adaptive Strategy
102
2
7.7 Summary and Conclusion
104
1
References
105
2
8 On the Use of Strain-Softening Models for the Simulation of Strong Discontinuities in Solids
107
18
J. Oliver
M. Cervera
O. Manzoli
8.1 Strain Softening, Strain Localization and Displacement Discontinuities
107
3
8.2 The Strong Discontinuity Approach
110
3
8.3 Generalization to 2D Problems
113
8
8.4 Representative Numerical Simulation
121
1
8.5 Concluding Remarks
121
2
References
123
2
9 Thermomechanics Based Theory and Analysis of Cracking Localization in Concrete Dam under Earthquake Excitation
125
12
H. Horii
J. Inoue
M. Brocca
9.1 Introduction
126
1
9.2 Localization in Simple Spring-Crack Element Models
127
3
9.3 General Theory
130
2
9.4 FEM Analysis of Cracking Localization
132
4
9.5 Concluding Remarks
136
1
References
136
1
10 Localisation Patterns in Ductile and Brittle Geomaterials
137
22
J. Desrues
Introduction
137
2
10.1 Shear Bands in Field Cases and Laboratory Tests
139
1
10.2 Localisation in Granular Bodies
140
8
10.3 Localisation in Cohesive Geomaterials
148
5
Conclusion
153
3
References
156
3
11 In-Plane Crushing of a Polymeric Honeycomb
159
26
S.D. Papka
S. Kyriakides
11.1 Introduction
159
1
11.2 Uniaxial Crushing Experiments
160
5
11.3 Analysis of Uniaxial Crushing
165
6
11.4 Biaxial Crushing of Honeycomb
171
11
Acknowledgements
182
1
References
182
3
12 Experimental and Numerical Investigation of Size Scale Effects in Concrete Fracture
185
22
M.R.A. van Vliet
J.G.M. van Mier
12.1 Introduction
185
4
12.2 New Size Effect Tests
189
6
12.3 Preliminary Experimental Results
195
1
12.4 Numerical Littice Model
196
8
12.5 Results and Conclusion
204
1
Acknowledgements
205
1
References
205
2
13 Post-Peak Behaviour of Rocks and Natural Building Stones in Unixial Compression
207
20
I. Vardoulakis
S. Kourkoulis
A. Skjaerstein
13.1 Introduction
207
2
13.2 The Compression Test in the Post-Peak Regime
209
4
13.3 Post-Peak Stress Diffusion Theory
213
7
13.4 Experimental Results and Discussion
220
6
13.5 Conclusions
226
1
Acknowledgements
226
1
References
226
1
14 Inelastic Deformation of F.C.C. Single Crystals by Slip and Twinning
227
16
A. Staroselsky
L. Anand
14.1 Introduction
228
1
14.2 Constitutive Equations
228
4
14.3 Plane-Strain Deformation of F.C.C. Co-8 percentage Fe Single Crystals
230
5
14.4 Concluding Remarks
237
1
Acknowledgements
238
1
References
238
2
Appendix
240
3
15 Effects of Strain Paths on Sheet Metal Limit Strains
243
12
P.D. Wu
K.W. Neale
E. van der Giessen
15.1 Introduction
243
1
15.2 Constitutive Equations
244
1
15.3 Problem Formulation and Method of Solution
245
3
15.4 Results
248
4
15.5 Conclusions
252
1
Acknowledgements
253
1
References
253
2
16 Three-Dimensional Analysis of Localized Necking
255
14
A. Benallal
16.1 Introduction
255
2
16.2 Constitutive Equations
257
1
16.3 Field Equations and Boundary Conditions
258
1
16.4 Bifurcation Versus Perturbation Approach
259
1
16.5 Local 3D Analysis of the Deformation of the Sheet
260
5
16.6 Plane Stress Analysis
265
2
16.7 Concluding Remarks
267
1
Acknowledgements
267
1
References
267
2
17 Effects of Heterogeneties and Localization on Polymer Deformation and Recovery
269
18
M.C. Boyce
C. Chui
17.1 Introduction
269
3
17.2 Model Description
272
6
17.3 Simulation Results
278
6
17.4 Concluding Remarks
284
1
Acknowledgements
284
1
References
284
3
18 Strain Localization and Void Growth in Polymers
287
16
A.C. Steenbrink
E. vander Giessen
18.1 Introduction
287
1
18.2 Material Model
288
2
18.3 Localization and Shear Band Propagation
290
2
18.4 Numerical Model
292
1
18.5 Results
292
8
18.6 Discussion
300
1
References
301
2
19 Nonaffine Network Model for Glassy Polymer and Prediction of Instability Propagation
303
20
Y. Tomita
T. Adachi
19.1 Introduction
303
1
19.2 Constitutive Equation
304
4
19.3 Identification of Deformation of Materials Parameters and Uniform
308
2
19.4 Deformation
310
8
19.5 Computational Prediction of Instability Propagation
318
2
Conclusion
320
1
Acknowledgements
320
3
References
320
3
20 Damage Localisation in Short Fibre Cementitious Composites
323
16
B.L. Karihaloo
J. Wang
20.1 Introduction
323
2
20.2 Problem Formulation and Mathematical Solution
325
3
20.3 Perturbation in Crack Lengths
328
6
20.4 Perturbation in Bridging Stiffnesses
334
1
20.5 Conclusion
335
2
Acknowledgements
337
1
References
337
2
21 Fracture Instabilities in Heterogeneous Materials: Brittleness, Size Effects and Fractality
339
16
A. Carpinteri
21.1 Introduction
340
1
21.2 Size Effects in Structural Brittleness
340
8
21.3 Size Effects on Materials Strength and Toughness
348
4
21.4 Acknowledgements
352
1
References
353
2
22 Compression Fracture-Mechanics of Damage Localization and Size Effect
355
14
Z.P. Bazant
22.1 Introduction
355
1
22.2 Mechanism of Size Effect
356
4
22.3 Lack of Size in Axial Splitting
360
1
22.4 Size Effect for the Case of Many Independent Loads
361
1
22.5 Asymptotic Scaling for Tensile or Compressive Cracks with Residual Cohesive
362
1
22.6 Stress
363
1
The Questions of Size Effect on Kint Band Failure of Composities
363
1
Acknowledgements
364
5
References
23 Nonlinear Modelling of Geomaterials and Self-Organization Phenomena
369
18
V.N. Nikolaevskiy
23.1 Abstract
369
1
23.2 Soils and Fragmented Rocks with Internal Oscillators
369
2
23.3 Interpenetrating Continua for Saturated Geomaterials
371
3
23.4 Dynamics of Geomaterials with Microstructure
374
5
23.5 Sine-Gordon Equation for Rotation Waves in Fragmented Rocks
379
6
References
385
2
24 Quasi-Static and Dynamic Characteristics of Strain Gradient Dependent Non-Local Constitutive Models
387
18
F. Oka
H.B. Muhlhaus
A. Yashima
K. Sawada
24.1 Introduction
387
1
24.2 Gradient Dependent Elastic Model
388
5
24.3 Gradient Dependent Viscoplastic Model
393
10
24.4 Conclusions
403
1
References
403
2
25 Higher-Order Damage Models for the Analysis of Fracture in Quasi-Brittle Materials
405
20
M.G.D. Geers
R.H.J. Peerlings
R.de Borst
W.A.M. Brekelmans
25.1 Introduction
405
2
25.2 Numerical Models
407
2
25.3 Applications
409
12
25.4 Conclusions
421
1
References
422
3
26 On Gradient Regulatization for Numerical Analyses in the Presence of Damage
425
16
C. Comi
L. Driemeier
26.1 Introduction
425
1
26.2 Gradient-Dependent Damage Models
426
1
26.3 One Dimensional Wave Propagation
427
3
26.4 Finite-Step Boundary Value Problems
430
3
26.5 Generalized Variables Finite-Element Formulation
433
2
26.6 Numerical Tests
435
4
26.7 Conclusions
439
1
Acknowledgements
439
1
References
440
1
27 Localisation of Damage in Quasi-Brittle Materials and Influence of Chemically Activated Damage
441
16
G. Pijaudier-Cabot B. Gerard
B. Gerard
N. Burlion
L. Molez
27.1 Introduction
441
1
27.2 Model Description
442
5
27.3 One-Dimensional Analysis of Strain Localisation
447
2
27.4 Numerical Simulations
449
2
27.5 Gradient Damage Model
451
4
27.6 Closure
455
1
Acknowledgement
455
1
References
455
2
28 Nonlocal Damage Effects on Plastic Flow Localization under Dynamic Loading
457
16
V. Tvergaard
A. Needleman
28.1 Introduction
457
2
28.2 Material Model
461
2
28.3 Numerical Model for the Nothced Bar
463
5
28.4 Results
463
1
28.5 Concluding Remarks
468
1
Acknowledgements
469
1
References
469
4
29 Instabilities and Size Effects in Plasticity: Continuum and Dislocation Approaches
473
16
H.M. Zbib
29.1 Introduction
473
2
29.2 Basic Relationship for Elastic-Plastic Deformation
475
1
29.3 Strain Gradient Plasticity
476
6
29.4 Three-Dimensional Dislocation Model
482
4
29.5 Concluding Remarks
486
1
Acknowledgements
486
1
References
486
3
30 Macroscopic Modelling of Stationary and Propagative Instabilities
489
18
L.J. Sluys
W.M. Wang
30.1 Introduction
489
1
30.2 A Classification of Macroscopic Instabilities
490
1
30.3 Constitutive Modelling
491
3
30.4 Algorithmic Aspects
494
5
30.5 Numerical Examples
499
6
References
505
2
31 A Discussion of Strain Gradient Plasticity Theories and Applications to Shear Bands
507
14
N.A. Fleck
J.W. Hutchinson
31.1 Introduction
507
1
31.2 Review of Fleck-Hutchinson Strain Gradient Theory
508
4
31.3 Study of Shear Localisation using Fleck-Hutchinson Non-Linear Deformation Theory
512
3
31.4 The Role of Imperfections in Shear Localisation according to the Fleck-Hutchinson Deformation Theory
515
4
Acknowledgements
519
1
References
519
2
32 A Beam Theory for Gradient Continua
521
12
H.B. Muhlhaus
P. Hornby
32.1 Introduction
521
3
32.2 Field Equations
524
2
32.3 Constitutive Relations
526
1
32.4 Example
527
4
32.5 Conclusion
531
1
References
532
1
33 Recent Progress on Gradient Theory and Applications
533
16
E.C. Aifantis
33.1 Introduction
533
3
33.2 Gradient-Dependent Flow Stress Macroscopic Shear Bands
536
1
33.3 Gradient-Dependent Dislocation Dynamics and MD Patterning
537
1
33.4 Gradient Interpretation of Size Effects
538
3
33.5 Gradient Elasticity Solutions for Cracks and Dislocations
541
2
33.6 Size-Dependent Hardness
543
1
33.7 Forming Limit Diagrams (FLADs)
544
1
Acknowledgements
545
1
References
545
4
Index
549