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Constitutive Modelling of Granular Materials : Engineering Online Library - Dimitrios Kolymbas

Constitutive Modelling of Granular Materials

Engineering Online Library

Hardcover Published: 15th March 2000
ISBN: 9783540669197
Number Of Pages: 554

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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.

Authorsp. 1
Introductory considerations
The misery of constitutive modellingp. 11
Introductionp. 11
Meaning of material constantsp. 12
A review of the present situation in constitutive modellingp. 13
Validation of constitutive modelsp. 15
On the physical foundation of constitutive modelsp. 15
Requirements on constitutive modelsp. 16
How simple should a model be?p. 19
Numerical implementationsp. 20
Cooperationp. 22
The future of researchp. 23
Referencesp. 23
Does engineering need science?p. 25
Forewordp. 25
Definition of engineeringp. 25
Definition of sciencep. 25
Relations between engineering and sciencesp. 27
Some examplesp. 31
The forthcoming Middle Ages?p. 33
Referencesp. 35
The role of models in civil engineeringp. 37
Introductionp. 37
Modelsp. 38
Children's modelsp. 39
Students' modelsp. 42
Engineers' modelsp. 46
Philosophers' modelsp. 50
Conclusionp. 52
Referencesp. 55
Overview of hypoplasticity
Hypoplasticity then and nowp. 57
Introductionp. 57
A heuristic examplep. 58
Some historical remarksp. 61
Framework of hypoplasticityp. 65
Response envelope: a useful toolp. 72
Extensions: a tale of two termsp. 82
Simple boundary value problemp. 92
Miscellaneousp. 96
Concluding remarksp. 99
Referencesp. 101
A review of two different approaches to hypoplasticityp. 107
Introductionp. 107
Mathematical structurep. 109
Invertibility, consistency and limit statesp. 118
Strain localization and bifurcation analysisp. 126
Conclusionsp. 137
Referencesp. 138
Gudehus/Bauer K-hypoplastic modelp. 144
von Wolffersdorff K-hypoplastic modelp. 144
Uniqueness, second order work and bifurcation in hypoplasticityp. 147
Introductionp. 147
Existence and uniqueness of boundary value problems involving hypoplastic constitutive equationsp. 148
Rice analysis with hypoplastic constitutive equationsp. 155
Invertibility and controlability seen as boundary value problemsp. 161
Conclusionp. 163
Referencesp. 164
Stationary states in hypoplasticityp. 167
Introductionp. 167
Historical development of hypoplastic models of the Kolymbas typep. 169
Stationary states and modeling of the critical stress state surfacep. 179
Determination of the material parametersp. 183
Extension to a polar continuump. 185
Acknowledgementsp. 188
Referencesp. 189
Generalized continua and microscopic approach
Microscopic approach contributions to constitutive modellingp. 193
Introductionp. 193
Macroscopic ensemble behaviourp. 194
Induced structural anisotropyp. 194
Physics at the grain scalep. 198
Conclusionsp. 207
Acknowledgementsp. 207
Referencesp. 207
Discrete and continuum modelling of granular materialsp. 209
Introductionp. 209
Formulationp. 211
Lagrangian Particle Methodp. 217
Examplesp. 220
Concluding Remarksp. 223
Referencesp. 224
2nd Gradient constitutive modelsp. 225
The continuum assumptionp. 225
Averaging and the meaning of 2nd gradientsp. 226
A simple 2nd gradient structural modelp. 229
A Mindlin-type 2nd gradient linear elasticityp. 231
A 2nd gradient plasticity model for granular materialsp. 239
Acknowledgmentsp. 247
Referencesp. 247
Micro-mechanically based higher-order continuum models for granular materialsp. 249
Introductionp. 249
Micro-level particle interactionp. 250
From micro-level to macro-levelp. 254
Macroscopic constitutive formulationp. 256
Continuum models versus discrete lattice modelp. 259
Higher-order continuum model that includes particle rotationp. 266
Conclusionsp. 272
Referencesp. 272
Relevant local variables for the change of scale in granular materialsp. 275
Introductionp. 275
Definition of the material and considered scalesp. 275
Analysis of the change of scale when the local level is denned at thecontact between particlesp. 278
Analysis of the change of scale when the local level is denned for alocal array of particlesp. 285
Conclusionp. 287
Referencesp. 289
Physical aspects
On the physical background of soil strengthp. 291
Introductionp. 291
Steady statesp. 292
Dilatant soilsp. 294
Contractant soilsp. 298
Miscellaneousp. 299
Referencesp. 300
The influence of time derivative terms on the mechanical behaviour of loose sandsp. 303
Introductionp. 303
Experimental observationsp. 304
Mathematical Modellingp. 308
Concluding remarksp. 315
Acknowledgementsp. 317
Referencesp. 317
p. 318
An approach to plasticity based on generalised thermodynamicsp. 319
Introductionp. 319
Thermomechanical formulationp. 320
Computational Examplesp. 326
Classification of plasticity modelsp. 329
Conclusionsp. 330
Acknowledgmentp. 331
Referencesp. 331
Comparison of different approaches
Comparison of hypoplastic and elastoplastic modelling of undrained triaxial tests on loose sandp. 333
Introductionp. 333
Experimental observationsp. 333
Constitutive modelsp. 337
Comparison of experiments with calculationsp. 338
Instability surfacep. 342
Modification of the hypoplastic modelp. 344
Conclusionsp. 348
Acknowledgementp. 349
Referencesp. 349
Hypoplastic and elastoplastic modelling - a comparison with test datap. 353
Introductionp. 353
Experimental datap. 354
Hypoplastic calculationp. 355
Elastoplastic calculationsp. 360
Comparisonp. 365
Conclusionsp. 370
Acknowledgementsp. 371
Referencesp. 371
Strain response envelope: a complementary tool for evaluating hypoplastic constitutive equationsp. 375
Introductionp. 375
Experimental observationsp. 376
Hypoplastic analysisp. 380
Predictive capability of hypoplasticityp. 390
Conclusionsp. 394
Referencesp. 394
Special models
Modelling weathering effects on the mechanical behaviour of granitep. 397
Introductionp. 397
Conceptual model for weathering effects on rock behaviourp. 398
An application to the weathering of granitep. 401
Conclusionsp. 409
Referencep. 411
A plasticity-based constitutive model for natural soils: a hierarchical approachp. 413
Introductionp. 413
Some aspects of the mechanical behaviour of natural soilsp. 414
The proposed modelp. 420
Conclusionsp. 436
Referencesp. 436
Experimental bases for a new incremental non-linear constitutive relation with 5 parametersp. 439
Introductionp. 439
Non linear incremental formalismp. 439
Generalized triaxial apparatusp. 441
Sand characteristicsp. 442
Initial Experimentsp. 443
Analysis of the tangent characteristics of a curvep. 445
Classical oedometric testp. 445
Oedometric test of class C2p. 450
Oedometric test of class C3p. 453
Conclusionp. 454
Acknowledgementsp. 455
Referencesp. 456
Numerical applications
Implicit integration of hypoplastic modelsp. 457
Introductionp. 457
Introduction to hypoplasticityp. 458
A hypoplastic model for granular materials with a predefined limitstatep. 463
Finite element simulations of the direct shear box testp. 466
Concluding remarksp. 469
Referencesp. 470
Soil-water coupling analysis of progressive failure in cuts with a strain softening modelp. 471
Introductionp. 471
Elasto-plastic model with strain softeningp. 472
Finite element analysis of progressive failure in cuts of ideal model groundp. 475
Conclusionsp. 487
Referencesp. 490
Advances in modelling soil anisotropyp. 491
Introductionp. 491
Experiments on siltp. 492
Modelling anisotropic soil behaviourp. 497
Examplesp. 498
Conclusionsp. 513
Appendixp. 515
Referencesp. 519
Examples of finite element calculations with the hypoplastic lawp. 523
Settlement of earth embankment on a landfill materialp. 523
Cyclic twisting of a tube in sandp. 528
Referencesp. 538
Hypoplastic simulation of complex loading pathsp. 539
Introductionp. 539
Realization of experimentsp. 540
Hypoplastic homogeneous simulationp. 542
Numerical resultsp. 545
Hypoplastic simulation of the boundary value problemp. 548
Incremental solutionp. 550
Calculation of resultsp. 551
Referencesp. 553
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540669197
ISBN-10: 3540669191
Series: Engineering Online Library
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 554
Published: 15th March 2000
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.88  x 2.54
Weight (kg): 0.91

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