Lecture Notes in Physics

By: P.A. Vermeer (Editor), S. Diebels (Editor), W. Ehlers (Editor)

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Hardcover | 1 January 2001

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A knowledge of the mechanical behaviour of both naturally occurring materials, such as soils and rocks, and artificial materials such as concrete and industrial granular matter, is of fundamental importance to their proper use in engineering and scientific applications. This volume contains selected lectures by international experts on current developments and problems in the numerical modelling of cohesive-frictional materials which provide a deeper understanding of the microscopic and macroscopic description of such materials. This book fills a gap by emphasizing the cross-fertilization of ideas between engineers and scientists engaged in this exciting field of research.

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You Can Find This Book In

Non-Fiction Engineering & Technology Mechanical Engineering & Materials Mechanical Engineering Tribology including Friction & Lubrication Materials Science Technology in General Nanotechnology Science Physics Classical Mathematics Mathematics

Applied Mathematics Materials & States of Matter Earth Sciences, Geography, Environment, Planning Earth Sciences Geology & The Lithosphere

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Published: 9th December 2010

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Computational models for failure in cohesive-frictional materials with stochastically distributed imperfections	p. 1
Introduction	p. 1
The finite element reliability method	p. 2
Introduction to the reliability method	p. 2
Discretisation of the material properties	p. 4
Response as a function of the imperfections	p. 4
Approximation of the probability of failure	p. 6
Computation of the ß-points	p. 8
Computation of the mechanical transformation	p. 9
Computation of the equilibrium path	p. 9
Computation of the gradient of the equilibrium path	p. 12
Numerical simulation	p. 13
Conclusions	p. 15
References	p. 15
Modelling of localized damage and fracture in quasibrittle materials	p. 17
Representation of localized deformation	p. 17
Kinematic description	p. 17
Constitutive models	p. 19
Numerical approximations	p. 21
Combined continuous-discontinuous description	p. 22
Elements with embedded localization zones	p. 23
Motivation	p. 23
Low-order elements	p. 25
Higher-order elements	p. 26
Enriched elements	p. 27
Concluding remarks	p. 28
References	p. 29
Microplane modelling and particle modelling of cohesive-frictional materials	p. 31
Motivation	p. 31
Continuum-based microplane models	p. 32
Microplane elasticity	p. 34
Microplane elasto-plasticity	p. 36
Example	p. 37
Discrete particle models	p. 38
Elastic particles	p. 39
Elasto-plastic particles	p. 41
Comparison	p. 43
Short-term creep of shotcrete-thermochemoplastic material modelling and nonlinear analysis of a laboratory test and of a NATM excavation by the Finite Element Method	p. 47
Introduction and motivation for the investigation of creep in shotcrete	p. 47
Thermochemoplastic material model for shotcrete	p. 48
State variables	p. 48
Field equations	p. 49
Heat conduction law	p. 49
Constitutive equations	p. 49
Algorithmic treatment of the incremental formulation for short-term creep	p. 52
Discretization of the evolution law for short-term creep	p. 52
Discretization of the incremental state equation for the stresses	p. 53
Numerical example: creep test with two instants of loading	p. 54
Re-analysis of a laboratory test	p. 55
Modelling	p. 55
Experimental determination of material properties	p. 55
Results	p. 57
Simulation of a tunnel driven according to the NATM	p. 58
Thermo-poro-mechanics of rapid fault shearing	p. 63
Introduction	p. 63
Formulation	p. 64
Mass balance	p. 64
Energy balance	p. 65
Momentum Balance	p. 66
The Mathematical Model	p. 68
Frictional shearing strain-rate softening	p. 72
A view on the variational setting of micropolar continua	p. 75
Introduction	p. 75
Geometrically linear micropolar continua	p. 76
Gradient type micropolar continuum	p. 77
Cosserat type micropolar continuum	p. 79
Mixed formulation gradient type case	p. 80
Regularized mixed formulation gradient type case	p. 81
Geometrically nonlinear micropolar continua	p. 82
Mixed formulation gradient type case	p. 83
Cosserat type micropolar continuum	p. 84
Regularized formulation gradient type case	p. 85
Conclusion	p. 87
Macromodelling of softening in non-cohesive soils	p. 89
Introduction	p. 89
Approach to friction softening	p. 90
Drucker-Prager model with local softening	p. 92
Necessity of regularization	p. 94
Nonlocal DP-model	p. 94
Internal length and numerical shear band thickness	p. 96
Empirical shear band thicknesses	p. 98
Softening scaling on h and l	p. 100
Hardening soil model	p. 102
HS-model with nonlocal softening	p. 104
Geometrical Nonlinearity	p. 106
Conclusions	p. 107
References	p. 108
An experimental investigation of the relationships between grain size distribution and shear banding in sand	p. 111
Introduction	p. 111
Experimental device and testing procedure	p. 113
Tested sands	p. 114
Experimental results	p. 117
Monodisperse sands	p. 119
Binary mixtures	p. 123
Discussion	p. 124
Conclusions	p. 126
References	p. 126
Micromechanics of the elastic behaviour of granular materials	p. 129
Introduction	p. 129
Micromechanics	p. 130
Branch and polygon vector	p. 130
Stress, strain and work	p. 132
Group averaging	p. 132
Contact constitutive relation	p. 133
Extremum principles	p. 133
Statistical minimum potential energy theory	p. 134
Discrete Element simulations	p. 134
Particle size distribution	p. 135
Assemblies	p. 135
Discrete Element simulations	p. 135
Averaging	p. 136
Results from Discrete Element simulations	p. 136
Geometry	p. 137
Moduli	p. 138
Relative displacements	p. 138
Energy distribution	p. 140
References	p. 141
On sticky-sphere assemblies	p. 143
Cohesive materials	p. 144
Conclusions and recommendations	p. 147
References	p. 147
Cohesive granular texture	p. 149
Introduction	p. 149
Simple contact laws with adhesion	p. 150
Examples of observed behaviors	p. 156
References	p. 162
Micro-mechanisms of deformation in granular materials: experiments and numerical results	p. 163
Experimental results	p. 163
Experimental procedure	p. 163
Displacements field of rods centers	p. 164
Grains rotation	p. 166
Rolling without sliding	p. 166
Local deformation and shear band	p. 167
Numerical simulations	p. 168
Numerical simulations of biaxial tests	p. 169
Local mechanisms of deformation	p. 170
Numerical simulation of pull-out test	p. 170
Conclusion	p. 172
References	p. 172
Scaling properties of granular materials	p. 173
Introduction	p. 173
The normal force Fⁿ	p. 174
Scaling properties	p. 175
Scaling large phenomena down to "lab-size" experiments	p. 177
Bouncing ball	p. 181
Consideration of the tangential force	p. 181
Conclusion	p. 183
References	p. 183
Discrete and continuum modelling of granular materials	p. 185
Introduction	p. 185
Formulation	p. 186
Continuum model	p. 186
Discrete element model	p. 189
Lagrangian particle method	p. 192
Lagrangian particles	p. 193
Numerical integration	p. 194
Element matrices and particle properties	p. 195
Particle splitting	p. 195
Element inverse mapping	p. 197
Examples	p. 198
DEM model simulating a triaxial compression test	p. 198
DEM model of granular flow	p. 199
LPM large deformation benchmark	p. 200
LPM model of discharging silo	p. 202
Concluding remarks	p. 203
References	p. 204
Difficulties and limitation of statistical homogenization in granular materials	p. 205
Definition of statistical homogenization in granular materials	p. 205
Static averaging operator	p. 206
Static localisation operator	p. 207
General formulation	p. 207
Analysis of the physical meanings of internal parameters and e_ij	p. 207
Analysis of the capacity of different localisation operators from a numerical simulation	p. 208
Kinematic averaging operator	p. 210
Kinematic localisation operator	p. 213
Conclusions	p. 214
References	p. 214
From discontinuous models towards a continuum description	p. 215
Introduction	p. 215
Model system and simulation	p. 216
The Couette shear-cell setup	p. 216
The discrete element model	p. 217
From the micro-to a macro-description	p. 218
Averaging strategy	p. 219
Averaging formalism	p. 219
Results on macroscopic scalar quantities	p. 220
Volume fraction	p. 220
Mass flux density	p. 220
Macroscopic tensorial quantities	p. 221
Fabric tensor	p. 221
Stress tensor	p. 223
Elastic deformation gradient	p. 223
Material properties	p. 223
Rotational degrees of freedom	p. 225
Summary and conclusion	p. 228
References	p. 229
From solids to granulates-Discrete element simulations of fracture and fragmentation processes in geomaterials	p. 231
Introduction	p. 231
Description of the model	p. 233
Granularity	p. 234
Elastic behaviour of the solid	p. 235
Breaking of the solid	p. 238
Stress calculation	p. 239
Simulation results	p. 239
Quasi-static loading scenarios	p. 240
Dynamic fragmentation of solids	p. 249
Conclusions	p. 256
References	p. 257
Microscopic modelling of granular materials taking into account particle rotations	p. 259
Introduction	p. 259
Kinematics	p. 261
Equations of motion	p. 262
Contact laws	p. 264
Numerical aspects	p. 268
Simulation examples and results	p. 269
Conclusions	p. 272
References	p. 273
Microstructured materials: local constitutive equation with internal lenght, theoretical and numerical studies	p. 275
Introduction	p. 275
A general theory for continua with microstructure	p. 276
Kinematic description of a continuum with microstructure	p. 276
The internal virtual work	p. 276
The external virtual work	p. 276
The balance equations and the boundary conditions	p. 277
Microstructured continuum with kinematic constraint: Second gradient models	p. 277
Equations of a second gradient model	p. 277
Local elasto-plastic second gradient models	p. 278
An application of local elasto-plastic second gradient model	p. 279
The problem to be solved	p. 279
Partial solutions	p. 280
Patch conditions and full solutions	p. 282
Discussion	p. 283
Equations with Lagrange multipliers	p. 284
Equations for the iterative procedure	p. 284
Finite Element Method	p. 286
Shape functions	p. 286
Element stiffness matrix	p. 287
Element residual terms	p. 288
Global matrices	p. 289
Applications: two dimensional elasto-plastic constitutive relation	p. 289
Conclusions	p. 291
References	p. 291
Damage in a composite material under combined mechanical and hygral load	p. 293
Introduction	p. 293
Generation of numerical concrete	p. 294
Drying process and self-desiccation	p. 295
Basic elements and equations governing the processes	p. 295
Material parameters	p. 296
An example of simulation of drying	p. 298
Endogenous and drying shrinkage	p. 299
General concept	p. 299
Table of Contents provided by Publisher. All Rights Reserved.

Lecture Notes in Physics

At a Glance

Hardcover

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How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

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