ISBN: 3540669191
TITLE: Constitutive Modelling of Granular Materials
AUTHOR: Kolymbas, Dimitrios (Ed.)
TOC:

AUTHORS 1
Introductory considerations
The misery of constitutive modelling 11
D. KOLYMBAS
1 Introduction 11
2 Meaning of material constants 12
3 A review of the present situation in constitutive modelling 13
4 Validation of constitutive models 15
5 On the physical foundation of constitutive models 15
6 Requirements on constitutive models 16
7 How simple should a model be? 19
8 Numerical implementations 20
9 Cooperation 22
10 The future of research 23
References 23
Does engineering need science? 25
C. VIGGIANI
1 Foreword 25
2 Definition of engineering 25
3 Definition of science 25
4 Relations between engineering and sciences 27
5 Some examples 31
6 The forthcoming Middle Ages? 33
References 35
The role of models in civil engineering 37
D. MUIR WOOD
1 Introduction 37
2 Models 38
3 Children's models 39
4 Students' models 42
5 Engineers' models 46
6 Philosophers' models 50
7 Conclusion 52


References 55
Overview of hypoplasticity
Hypoplasticity then and now 57
W. WU, D. KOLYMBAS
1 Introduction 57
2 A heuristic example 58
3 Some historical remarks 61
4 Framework of hypoplasticity 65
5 Response envelope: a useful tool 72
6 Extensions: a tale of two terms 82
7 Simple boundary value problem 92
8 Miscellaneous 96
9 Concluding remarks 99
References 101
A review of two different approaches to hypoplasticity 107
C. TAMAGNINI, G. VIGGIANI, R. CHAMBON
1 Introduction 107
2 Mathematical structure 109
3 Invertibility, consistency and limit states 118
4 Strain localization and bifurcation analysis 126
5 Conclusions 137
References 138
A Gudehus/Bauer K-hypoplastic model 144
B von Wolffersdorff K-hypoplastic model 144
Uniqueness, second order work and bifurcation in hypoplasticity 147
R. CHAMBON
1 Introduction 147
2 Existence and uniqueness of boundary value problems involving hypoplastic constitutive equations 148
3 Rice analysis with hypoplastic constitutive equations 155
4 Invertibility and controlability seen as boundary value problems 161
5 Conclusion 163
References 164
Stationary states in hypoplasticity 167
E. BAUER, I. HERLE
1 Introduction 167
2 Historical development of hypoplastic models of the Kolymbas type 169
3 Stationary states and modeling of the critical stress state surface 179
4 Determination of the material parameters 183
5 Extension to a polar continuum 185
Acknowledgements 188
References 189
Generalized continua and microscopic approach
Microscopic approach contributions to constitutive modelling 193
C. THORNTON
1 Introduction 193
2 Macroscopic ensemble behaviour 194
3 Induced structural anisotropy 194
4 Physics at the grain scale 198
5 Conclusions 207
6 Acknowledgements 207
References 207
Discrete and continuum modelling of granular materials 209
H.-B. MHLHAUS, L. MORESI, H. SAKAGUCHI
1 Introduction 209
2 Formulation 211

3 Lagrangian Particle Method 217
4 Examples 220
5 Concluding Remarks 223
References 224
2nd Gradient constitutive models 225
I. VARDOULAKIS
1 The continuum assumption 225
2 Averaging and the meaning of 2nd gradients 226
3 A simple 2nd gradient structural model 229
4 A Mindlin-type 2nd gradient linear elasticity 231
5 A 2nd gradient plasticity model for granular materials 239
6 Acknowledgments 247
References 247
Micro-mechanically based higher-order continuum models for granular materials 249
A.S. J. SUIKER, R. de BORST, C.S. CHANG
1 Introduction 249
2 Micro-level particle interaction 250
3 From micro-level to macro-level 254
4 Macroscopic constitutive formulation 256
5 Continuum models versus discrete lattice model 259
6 Higher-order continuum model that includes particle rotation 266
7 Conclusions 272
References 272
Relevant local variables for the change of scale in granular materials 275
B. CAMBOU, F. DEDECKER, M. CHAZE
1 Introduction 275
2 Definition of the material and considered scales 275
3 Analysis of the change of scale when the local level is defined at the contact between particles 278
4 Analysis of the change of scale when the local level is defined for a local array of particles 285
5 Conclusion 287
References 289
Physical aspects
On the physical background of soil strength 291
G. GUDEHUS
1 Introduction 291
2 Steady states 292
3 Dilatant soils 294
4 Contractant soils 298
5 Miscellaneous 299
References 300
The influence of time derivative terms on the mechanical behaviour of loose sands 303
C. di PRISCO, S. IMPOSIMATO
1 Introduction 303
2 Experimental observations 304
3 Mathematical Modelling 308
4 Concluding remarks 315
5 Acknowledgements 317
References 317
Appendix A 318
An approach to plasticity based on generalised thermodynamics 319
G.T. HOULSBY, A.M. PUZRIN
1 Introduction 319
2 Thermomechanical formulation 320
3 Computational Examples 326
4 Classification of plasticity models 329
5 Conclusions 330
6 Acknowledgment 331
References 331
Comparison of different approaches
Comparison of hypoplastic and elastoplastic modelling of undrained triaxial tests on loose sand 333
I. HERLE, T. DOANH, W. WU
1 Introduction 333
2 Experimental observations 333
3 Constitutive models 337
4 Comparison of experiments with calculations 338
5 Instability surface 342
6 Modification of the hypoplastic model 344
7 Conclusions 348
Acknowledgement 349
References 349
Hypoplastic and elastoplastic modelling - a comparison with test data 353
Th. MARCHER, P.A VERMEER, P.-A. von WOLFFERSDORFF
1 Introduction 353
2 Experimental data 354
3 Hypoplastic calculation 355
4 Elastoplastic calculations 360
5 Comparison 365
6 Conclusions 370
7 Acknowledgements 371
References 371
Strain response envelope: a complementary tool for evaluating hypoplastic constitutive equations 375
T. DOANH
1 Introduction 375
2 Experimental observations 376
3 Hypoplastic analysis 380
4 Predictive capability of hypoplasticity 390
5 Conclusions 394
References 394
Special models
Modelling weathering effects on the mechanical behaviour of granite 397
R. NOVA
1 Introduction 397
2 Conceptual model for weathering effects on rock behaviour 398
3 An application to the weathering of granite 401
4 Conclusions 409
Reference 411
A plasticity-based constitutive model for natural soils: a hierarchical approach 413
A. AMOROSI, M. J KAVVADAS
1 Introduction 413
2 Some aspects of the mechanical behaviour of natural soils 414
3 The proposed model 420
4 Conclusions 436
References 436
Experimental bases for a new incremental non-linear constitutive relation with 5 parameters 439
F. DARVE, X. ROGUIEZ
1 Introduction 439
2 Non linear incremental formalism 439
3 Generalized triaxial apparatus 441
4 Sand characteristics 442
5 Initial Experiments 443
6 Analysis of the tangent characteristics of a curve 445
7 Classical oedometric test 445
8 Oedometric test of class C_2 450
9 Oedometric test of class C_3 453
10 Conclusion 454
11 Acknowledgements 455
References 456
Numerical applications
Implicit integration of hypoplastic models 457
0. M. HEERES, R. de BORST
1 Introduction 457
2 Introduction to hypoplasticity 458
3 A hypoplastic model for granular materials with a predefined limit state 463
4 Finite element simulations of the direct shear box test 466
5 Concluding remarks 469
References 470
Soil-water coupling analysis of progressive failure in cuts with a strain softening model 471
T. ADACHI, F. OKA, H. OSAKI, F. ZHANG
1 Introduction 471
2 Elasto-plastic model with strain softening 472
3 Finite element analysis of progressive failure in cuts of ideal model ground 475
4 Conclusions 487
References 490
Advances in modelling soil anisotropy 491
L. ZDRAVKOVIC, D.M. POTTS
1 Introduction 491
2 Experiments on silt 492
3 Modelling anisotropic soil behaviour 497
4 Examples 498
5 Conclusions 513
Appendix 515
References 519
Examples of finite element calculations with the hypoplastic law 523
K. NOBEL, R. CUDMANI
1 Settlement of earth embankment on a landfill material 523
2 Cyclic twisting of a tube in sand 528
References 538
Hypoplastic simulation of complex loading, paths 539
S. V. LAVRIKOV, A. Ph. REVUZHENKO
1 Introduction 539
2 Realization of experiments 540
3 Hypoplastic homogeneous simulation 542
4 Numerical results 545
5 Hypoplastic simulation of the boundary value problem 548
6 Incremental solution 550
7 Calculation of results 551
References 553
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