Engineering Online Library

By: Dimitrios Kolymbas

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Hardcover | 15 March 2000

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572 Pages

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23.5 x 15.88 x 2.54

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In view of its extreme complexity the mathematical description of the mechanical behaviour of granular materials is an extremely difficult task. Today many different models compete with each other. However, the complexity of the models hinders their comparison, and the potential users are confused and, often, disencouraged. This book is expected to serve as a milestone in the present situation, to evaluate the present methodes, to clear up the situation, to focus and encourage for further research activities.

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Authors	p. 1
Introductory considerations
The misery of constitutive modelling	p. 11
Introduction	p. 11
Meaning of material constants	p. 12
A review of the present situation in constitutive modelling	p. 13
Validation of constitutive models	p. 15
On the physical foundation of constitutive models	p. 15
Requirements on constitutive models	p. 16
How simple should a model be?	p. 19
Numerical implementations	p. 20
Cooperation	p. 22
The future of research	p. 23
References	p. 23
Does engineering need science?	p. 25
Foreword	p. 25
Definition of engineering	p. 25
Definition of science	p. 25
Relations between engineering and sciences	p. 27
Some examples	p. 31
The forthcoming Middle Ages?	p. 33
References	p. 35
The role of models in civil engineering	p. 37
Introduction	p. 37
Models	p. 38
Children's models	p. 39
Students' models	p. 42
Engineers' models	p. 46
Philosophers' models	p. 50
Conclusion	p. 52
References	p. 55
Overview of hypoplasticity
Hypoplasticity then and now	p. 57
Introduction	p. 57
A heuristic example	p. 58
Some historical remarks	p. 61
Framework of hypoplasticity	p. 65
Response envelope: a useful tool	p. 72
Extensions: a tale of two terms	p. 82
Simple boundary value problem	p. 92
Miscellaneous	p. 96
Concluding remarks	p. 99
References	p. 101
A review of two different approaches to hypoplasticity	p. 107
Introduction	p. 107
Mathematical structure	p. 109
Invertibility, consistency and limit states	p. 118
Strain localization and bifurcation analysis	p. 126
Conclusions	p. 137
References	p. 138
Gudehus/Bauer K-hypoplastic model	p. 144
von Wolffersdorff K-hypoplastic model	p. 144
Uniqueness, second order work and bifurcation in hypoplasticity	p. 147
Introduction	p. 147
Existence and uniqueness of boundary value problems involving hypoplastic constitutive equations	p. 148
Rice analysis with hypoplastic constitutive equations	p. 155
Invertibility and controlability seen as boundary value problems	p. 161
Conclusion	p. 163
References	p. 164
Stationary states in hypoplasticity	p. 167
Introduction	p. 167
Historical development of hypoplastic models of the Kolymbas type	p. 169
Stationary states and modeling of the critical stress state surface	p. 179
Determination of the material parameters	p. 183
Extension to a polar continuum	p. 185
Acknowledgements	p. 188
References	p. 189
Generalized continua and microscopic approach
Microscopic approach contributions to constitutive modelling	p. 193
Introduction	p. 193
Macroscopic ensemble behaviour	p. 194
Induced structural anisotropy	p. 194
Physics at the grain scale	p. 198
Conclusions	p. 207
Acknowledgements	p. 207
References	p. 207
Discrete and continuum modelling of granular materials	p. 209
Introduction	p. 209
Formulation	p. 211
Lagrangian Particle Method	p. 217
Examples	p. 220
Concluding Remarks	p. 223
References	p. 224
2^nd Gradient constitutive models	p. 225
The continuum assumption	p. 225
Averaging and the meaning of 2^nd gradients	p. 226
A simple 2^nd gradient structural model	p. 229
A Mindlin-type 2^nd gradient linear elasticity	p. 231
A 2^nd gradient plasticity model for granular materials	p. 239
Acknowledgments	p. 247
References	p. 247
Micro-mechanically based higher-order continuum models for granular materials	p. 249
Introduction	p. 249
Micro-level particle interaction	p. 250
From micro-level to macro-level	p. 254
Macroscopic constitutive formulation	p. 256
Continuum models versus discrete lattice model	p. 259
Higher-order continuum model that includes particle rotation	p. 266
Conclusions	p. 272
References	p. 272
Relevant local variables for the change of scale in granular materials	p. 275
Introduction	p. 275
Definition of the material and considered scales	p. 275
Analysis of the change of scale when the local level is denned at thecontact between particles	p. 278
Analysis of the change of scale when the local level is denned for alocal array of particles	p. 285
Conclusion	p. 287
References	p. 289
Physical aspects
On the physical background of soil strength	p. 291
Introduction	p. 291
Steady states	p. 292
Dilatant soils	p. 294
Contractant soils	p. 298
Miscellaneous	p. 299
References	p. 300
The influence of time derivative terms on the mechanical behaviour of loose sands	p. 303
Introduction	p. 303
Experimental observations	p. 304
Mathematical Modelling	p. 308
Concluding remarks	p. 315
Acknowledgements	p. 317
References	p. 317
	p. 318
An approach to plasticity based on generalised thermodynamics	p. 319
Introduction	p. 319
Thermomechanical formulation	p. 320
Computational Examples	p. 326
Classification of plasticity models	p. 329
Conclusions	p. 330
Acknowledgment	p. 331
References	p. 331
Comparison of different approaches
Comparison of hypoplastic and elastoplastic modelling of undrained triaxial tests on loose sand	p. 333
Introduction	p. 333
Experimental observations	p. 333
Constitutive models	p. 337
Comparison of experiments with calculations	p. 338
Instability surface	p. 342
Modification of the hypoplastic model	p. 344
Conclusions	p. 348
Acknowledgement	p. 349
References	p. 349
Hypoplastic and elastoplastic modelling - a comparison with test data	p. 353
Introduction	p. 353
Experimental data	p. 354
Hypoplastic calculation	p. 355
Elastoplastic calculations	p. 360
Comparison	p. 365
Conclusions	p. 370
Acknowledgements	p. 371
References	p. 371
Strain response envelope: a complementary tool for evaluating hypoplastic constitutive equations	p. 375
Introduction	p. 375
Experimental observations	p. 376
Hypoplastic analysis	p. 380
Predictive capability of hypoplasticity	p. 390
Conclusions	p. 394
References	p. 394
Special models
Modelling weathering effects on the mechanical behaviour of granite	p. 397
Introduction	p. 397
Conceptual model for weathering effects on rock behaviour	p. 398
An application to the weathering of granite	p. 401
Conclusions	p. 409
Reference	p. 411
A plasticity-based constitutive model for natural soils: a hierarchical approach	p. 413
Introduction	p. 413
Some aspects of the mechanical behaviour of natural soils	p. 414
The proposed model	p. 420
Conclusions	p. 436
References	p. 436
Experimental bases for a new incremental non-linear constitutive relation with 5 parameters	p. 439
Introduction	p. 439
Non linear incremental formalism	p. 439
Generalized triaxial apparatus	p. 441
Sand characteristics	p. 442
Initial Experiments	p. 443
Analysis of the tangent characteristics of a curve	p. 445
Classical oedometric test	p. 445
Oedometric test of class C₂	p. 450
Oedometric test of class C3	p. 453
Conclusion	p. 454
Acknowledgements	p. 455
References	p. 456
Numerical applications
Implicit integration of hypoplastic models	p. 457
Introduction	p. 457
Introduction to hypoplasticity	p. 458
A hypoplastic model for granular materials with a predefined limitstate	p. 463
Finite element simulations of the direct shear box test	p. 466
Concluding remarks	p. 469
References	p. 470
Soil-water coupling analysis of progressive failure in cuts with a strain softening model	p. 471
Introduction	p. 471
Elasto-plastic model with strain softening	p. 472
Finite element analysis of progressive failure in cuts of ideal model ground	p. 475
Conclusions	p. 487
References	p. 490
Advances in modelling soil anisotropy	p. 491
Introduction	p. 491
Experiments on silt	p. 492
Modelling anisotropic soil behaviour	p. 497
Examples	p. 498
Conclusions	p. 513
Appendix	p. 515
References	p. 519
Examples of finite element calculations with the hypoplastic law	p. 523
Settlement of earth embankment on a landfill material	p. 523
Cyclic twisting of a tube in sand	p. 528
References	p. 538
Hypoplastic simulation of complex loading paths	p. 539
Introduction	p. 539
Realization of experiments	p. 540
Hypoplastic homogeneous simulation	p. 542
Numerical results	p. 545
Hypoplastic simulation of the boundary value problem	p. 548
Incremental solution	p. 550
Calculation of results	p. 551
References	p. 553
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