Material Instabilities in Solids

, by de Borst, René; van der Giessen, Erik

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ISBN: 9780471974604 | 0471974609
Cover: Hardcover
Copyright: 10/15/1998

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Modern, powerful computational methods, combined with major improvements in experimental techniques, have resulted in significant advances in the study of material instabilities. This book presents the latest research in the field of material instabilities in solid materials (soils, concrete, rocks, ceramics, metals, polymers and composites) and associated phenomena, such as strain localisation, fracture and failure in general. Collected within this volume are the cutting edge contributions from the prestigious IUTAM Symposium of 1997. A broad spectrum of materials is covered, with the emphasis on common aspects of failure, and a full range of experimental, analytical and numerical methods are addressed. In addition, the state-of-the-art, and recent advances covered in the book are summarised in the introductory chapter. No other treatise is available which is so up to date and compiled by such a broad spectrum of leading researchers. This book will find a wide appeal amongst practising engineers, researchers and students in civil, mechanical and aerospace engineering, and researchers and students in materials science.

Preface

xiii

(2)

List of Contributors

1 Introduction to Material Instabilities in Solids

(14)

E. vander Giessen

R. de Borst

1.1 General introduction

(5)

1.2 Classical Bifurcation Theory

(1)

1.3 Experiments and Physical Mechanisms

(1)

1.4 Localization Without Internal Length Scales

(2)

1.5 Localization With Internal Length Scales

(3)

References

(2)

2 Stability of Layered Geological Structures: An Asymptotic Solution

(12)

Y.M. Leroy

N. Triantafyllidis

2.1 Introduction

(1)

2.2 Model Problems and Variational Formulation

(3)

2.3 Asymptotic Solution

(6)

References

(2)

3 Analysis of Shear Failure in Concrete Materials

(14)

K. William

H. Kang

B. Shing

E. Spacone

3.1 Introduction

(1)

3.2 Triaxial Concrete Model

(3)

3.3 Failure Modes of Concrete Model

(2)

3.4 Failure of Triaxial Concrete Model

(5)

3.5 Concluding Remarks

(1)

Acknowledgements

(1)

References

(2)

4 On the Effects of Intertial Coupling on the Wave-Speeds of Elastic-Plastic Fluid-Saturated Porous Media

(14)

B. Loret

E. Rizzi

4.1 Introduction

(1)

4.2 Equations of Motion

(2)

4.3 Consecutive Equations

(3)

4.4 Wave-Speeds

(4)

Acknowledgements

(1)

References

(1)

Appendix A

(3)

5 Microstructured Solids: Non-Linear Model and Analysis of Magneto-Elastic Wave Processes

(10)

V. Erofeyeu

S. Kovalev

5.1 Introduction

(1)

5.2 Non-Linear Magnetic-Elastic Equations

(1)

5.3 Plain Longitudinal Waves

(5)

5.4 Plain Shear Waves

(3)

Acknowledgement

(1)

References

(1)

6 Thermodynamics of Crystal Viscoplasticity and Instability Phenomena

(26)

P. Perzyna

6.1 Introduction

(1)

6.2 Experimental and Physical Motivations

(1)

6.3 Thermodynamic Constitutive Structures of Inelastic Single Crystals

(5)

6.4 Rate Independent Response of Single Crystals

(1)

6.5 Adiabatic Process

(4)

6.6 Macroscopic Adiabatic Shear Band Formation

(4)

6.7 Discussion of the Synergetic Effects and Comparison with Experimental

(4)

6.8 Observations

(1)

Final Comments

(1)

Acknowledgement

(4)

References

7 Instability Issues in Single Crystal Plasticity

(16)

P. Steinmann

7.1 Introduction

(1)

7.2 Multisurface Plasticity Framework

(2)

7.3 Multisurface Localization Analysis

(3)

7.4 Non Schmic Single Crystal Plasticity

(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

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Material Instabilities in Solids

Summary

Author Biography

Table of Contents

Supplemental Materials