Continuous and discontinuous modelling of cohesive frictional materials:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2001
|
| Series: | Lecture notes in physics
568 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 307 S. graph. Darst. |
| ISBN: | 3540415254 |
Staff View
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| 245 | 1 | 0 | |a Continuous and discontinuous modelling of cohesive frictional materials |c P. A. Vermeer ... (ed.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2001 | |
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| 650 | 4 | |a Friction |x Mathematical models | |
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Record in the Search Index
| _version_ | 1804128312922996736 |
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| adam_text | CONTENTS COMPUTATIONAL MODELS FOR FAILURE IN COHESIVE-FRICTIONAL
MATERIALS WITH STOCHASTICALLY DISTRIBUTED IMPERFECTIONS M.A. GUTI´
ERREZ, R. DE BORST ......................................... 1 1
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 1 2 THE FINITE ELEMENT
RELIABILITY METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 2 2.1 INTRODUCTION TO THE RELIABILITY METHOD . . . . . . . . . . .
. . . . . . . . . . . . . . 2 2.2 DISCRETISATION OF THE MATERIAL
PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 RESPONSE
AS A FUNCTION OF THE IMPERFECTIONS . . . . . . . . . . . . . . . . . . .
. 4 2.4 APPROXIMATION OF THE PROBABILITY OF FAILURE . . . . . . . . . .
. . . . . . . . . . 6 2.5 COMPUTATION OF THE * -POINTS . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 8 3 COMPUTATION OF THE
MECHANICAL TRANSFORMATION . . . . . . . . . . . . . . . . . . . . . 9
3.1 COMPUTATION OF THE EQUILIBRIUM PATH . . . . . . . . . . . . . . . .
. . . . . . . . . 9 3.2 COMPUTATION OF THE GRADIENT OF THE EQUILIBRIUM
PATH . . . . . . . . . . . . 12 4 NUMERICAL SIMULATION . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 15 REFERENCES . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 15 MODELLING OF LOCALIZED DAMAGE AND
FRACTURE IN QUASIBRITTLE MATERIALS M. JIR´ ASEK
........................................................ 17 1
REPRESENTATION OF LOCALIZED DEFORMATION . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 17 1.1 KINEMATIC DESCRIPTION . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2
CONSTITUTIVE MODELS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 19 1.3 NUMERICAL APPROXIMATIONS . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4 COMBINED
CONTINUOUS-DISCONTINUOUS DESCRIPTION . . . . . . . . . . . . . . . . 22
2 ELEMENTS WITH EMBEDDED LOCALIZATION ZONES . . . . . . . . . . . . . .
. . . . . . . . . . 23 2.1 MOTIVATION . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2
LOW-ORDER ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 25 2.3 HIGHER-ORDER ELEMENTS . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4
ENRICHED ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 27 3 CONCLUDING REMARKS . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 29 VIII CONTENTS
MICROPLANE MODELLING AND PARTICLE MODELLING OF COHESIVE-FRICTIONAL
MATERIALS E. KUHL, G.A. D*ADDETTA, M. LEUKART, E. RAMM
....................... 31 1 MOTIVATION . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 31 2 CONTINUUM-BASED MICROPLANE MODELS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 32 2.1 MICROPLANE ELASTICITY . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2
MICROPLANE ELASTO-PLASTICITY . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 36 2.3 EXAMPLE . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3
DISCRETE PARTICLE MODELS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 38 3.1 ELASTIC PARTICLES . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 39 3.2 ELASTO-PLASTIC PARTICLES . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 41 4 COMPARISON . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 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 M. LECHNER, CH. HELLMICH,
H.A. MANG .............................. 47 1 INTRODUCTION AND
MOTIVATION FOR THE INVESTIGATION OF CREEP IN SHOTCRETE . 47 2
THERMOCHEMOPLASTIC MATERIAL MODEL FOR SHOTCRETE . . . . . . . . . . . .
. . . . . . 48 2.1 STATE VARIABLES . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2 FIELD
EQUATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 49 2.3 HEAT CONDUCTION LAW . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.4
CONSTITUTIVE EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 49 3 ALGORITHMIC TREATMENT OF THE INCREMENTAL
FORMULATION FOR SHORT-TERM CREEP . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 52 3.1 DISCRETIZATION
OF THE EVOLUTION LAW FOR SHORT-TERM CREEP . . . . . . . . . . 52 3.2
DISCRETIZATION OF THE INCREMENTAL STATE EQUATION FOR THE STRESSES . . 53
3.3 NUMERICAL EXAMPLE: CREEP TEST WITH TWO INSTANTS OF LOADING . . . . .
. 54 4 RE-ANALYSIS OF A LABORATORY TEST . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 55 4.1 MODELLING . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 55 4.2 EXPERIMENTAL DETERMINATION OF MATERIAL PROPERTIES . . . .
. . . . . . . . . . 55 4.3 RESULTS. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5
SIMULATION OF A TUNNEL DRIVEN ACCORDING TO THE NATM . . . . . . . . . .
. . . . 58 THERMO-PORO-MECHANICS OF RAPID FAULT SHEARING I. VARDOULAKIS
..................................................... 63 1 INTRODUCTION.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 63 2 FORMULATION . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 64 2.1 MASS BALANCE . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 64 2.2 ENERGY BALANCE . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 65 2.3 MOMENTUM BALANCE . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 66 3 THE MATHEMATICAL MODEL
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 68 4 FRICTIONAL SHEARING STRAIN-RATE SOFTENING . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 72 CONTENTS IX A VIEW ON THE
VARIATIONAL SETTING OF MICROPOLAR CONTINUA P. STEINMANN
..................................................... 75 1 INTRODUCTION.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 75 2 GEOMETRICALLY LINEAR MICROPOLAR
CONTINUA . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.1
GRADIENT TYPE MICROPOLAR CONTINUUM . . . . . . . . . . . . . . . . . . .
. . . . . . . 77 2.2 COSSERAT TYPE MICROPOLAR CONTINUUM . . . . . . . .
. . . . . . . . . . . . . . . . . . 79 2.3 MIXED FORMULATION GRADIENT
TYPE CASE . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.4
REGULARIZED MIXED FORMULATION GRADIENT TYPE CASE . . . . . . . . . . . .
. . 81 3 GEOMETRICALLY NONLINEAR MICROPOLAR CONTINUA . . . . . . . . . .
. . . . . . . . . . . . . 82 3.1 MIXED FORMULATION GRADIENT TYPE CASE .
. . . . . . . . . . . . . . . . . . . . . . . . 83 3.2 COSSERAT TYPE
MICROPOLAR CONTINUUM . . . . . . . . . . . . . . . . . . . . . . . . . .
84 3.3 REGULARIZED FORMULATION GRADIENT TYPE CASE . . . . . . . . . . .
. . . . . . . . . 85 4 CONCLUSION . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
MACROMODELLING OF SOFTENING IN NON-COHESIVE SOILS T. MARCHER, P.A.
VERMEER .......................................... 89 1 INTRODUCTION. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 89 2 APPROACH TO FRICTION SOFTENING . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3
DRUCKER-PRAGER MODEL WITH LOCAL SOFTENING . . . . . . . . . . . . . . .
. . . . . . . . . . 92 4 NECESSITY OF REGULARIZATION . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5 NONLOCAL
DP-MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 94 6 INTERNAL LENGTH AND NUMERICAL SHEAR BAND
THICKNESS . . . . . . . . . . . . . . . . . 96 7 EMPIRICAL SHEAR BAND
THICKNESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 98 8 SOFTENING SCALING ON H AND L . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 100 9 HARDENING SOIL MODEL . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 102 10 HS-MODEL WITH NONLOCAL SOFTENING . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 104 11 GEOMETRICAL
NONLINEARITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 106 12 CONCLUSIONS . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 108 AN EXPERIMENTAL
INVESTIGATION OF THE RELATIONSHIPS BETWEEN GRAIN SIZE DISTRIBUTION AND
SHEAR BANDING IN SAND G. VIGGIANI, M. K¨ UNTZ, J. DESRUES
................................... 111 1 INTRODUCTION. . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 111 2 EXPERIMENTAL DEVICE AND TESTING PROCEDURE . . . . .
. . . . . . . . . . . . . . . . . . . . 113 3 TESTED SANDS . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 114 4 EXPERIMENTAL RESULTS . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.1
MONODISPERSE SANDS . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 119 4.2 BINARY MIXTURES . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5
DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 124 6 CONCLUSIONS . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 126 REFERENCES . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 126 X CONTENTS MICROMECHANICS OF THE ELASTIC BEHAVIOUR OF GRANULAR
MATERIALS N.P. KRUYT, L. ROTHENBURG
.......................................... 129 1 INTRODUCTION. . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 129 2 MICROMECHANICS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
2.1 BRANCH AND POLYGON VECTOR . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 130 2.2 STRESS, STRAIN AND WORK . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 2.3
GROUP AVERAGING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 132 2.4 CONTACT CONSTITUTIVE RELATION . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 3
EXTREMUM PRINCIPLES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 133 3.1 STATISTICAL MINIMUM
POTENTIAL ENERGY THEORY . . . . . . . . . . . . . . . . . . . 134 4
DISCRETE ELEMENT SIMULATIONS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 134 4.1 PARTICLE SIZE DISTRIBUTION . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.2
ASSEMBLIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 135 4.3 DISCRETE ELEMENT SIMULATIONS .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.4
AVERAGING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 136 5 RESULTS FROM DISCRETE ELEMENT
SIMULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.1
GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 137 5.2 MODULI . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 138 5.3 RELATIVE DISPLACEMENTS . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 138 5.4 ENERGY DISTRIBUTION .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 140 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 ON
STICKY-SPHERE ASSEMBLIES J. D. GODDARD
..................................................... 143 1 COHESIVE
MATERIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 144 2 CONCLUSIONS AND RECOMMENDATIONS . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 147 COHESIVE GRANULAR
TEXTURE F. RADJA¨ *, I. PREECHAWUTTIPONG, R. PEYROUX
............................ 149 1 INTRODUCTION. . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 149 2 SIMPLE CONTACT LAWS WITH ADHESION . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 150 3 EXAMPLES OF OBSERVED
BEHAVIORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 156 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
MICRO-MECHANISMS OF DEFORMATION IN GRANULAR MATERIALS: EXPERIMENTS AND
NUMERICAL RESULTS J. LANIER
......................................................... 163 1
EXPERIMENTAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 163 1.1 EXPERIMENTAL PROCEDURE . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
1.2 DISPLACEMENTS FIELD OF RODS CENTERS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 164 1.3 GRAINS ROTATION . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 1.4
ROLLING WITHOUT SLIDING . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 166 1.5 LOCAL DEFORMATION AND SHEAR BAND . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 167 2 NUMERICAL
SIMULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 168 2.1 NUMERICAL SIMULATIONS OF BIAXIAL TESTS .
. . . . . . . . . . . . . . . . . . . . . . . . 169 CONTENTS XI 2.2
LOCAL MECHANISMS OF DEFORMATION . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 170 2.3 NUMERICAL SIMULATION OF PULL-OUT TEST . . . .
. . . . . . . . . . . . . . . . . . . . . 170 3 CONCLUSION . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 172 REFERENCES . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 172 SCALING PROPERTIES OF GRANULAR MATERIALS T. P¨ OSCHEL, C. SALUE*
NA, T. SCHWAGER ................................. 173 1 INTRODUCTION. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 173 2 THE NORMAL FORCE F N . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
174 3 SCALING PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 175 4 SCALING LARGE
PHENOMENA DOWN TO *LAB-SIZE* EXPERIMENTS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 177 5 BOUNCING BALL . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 181 6 CONSIDERATION OF THE TANGENTIAL FORCE . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 181 7 CONCLUSION . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 183 REFERENCES . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 183 DISCRETE AND CONTINUUM MODELLING OF GRANULAR MATERIALS H.-B.
M¨ UHLHAUS, H. SAKAGUCHI, L. MORESI, M. FAHEY ................... 185 1
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 185 2 FORMULATION . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 186 2.1 CONTINUUM MODEL . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 2.2
DISCRETE ELEMENT MODEL . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 189 3 LAGRANGIAN PARTICLE METHOD . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 3.1
LAGRANGIAN PARTICLES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 193 3.2 NUMERICAL INTEGRATION . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 3.3
ELEMENT MATRICES AND PARTICLE PROPERTIES . . . . . . . . . . . . . . . .
. . . . . . . 195 3.4 PARTICLE SPLITTING . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 195 3.5 ELEMENT
INVERSE MAPPING . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 197 4 EXAMPLES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
4.1 DEM MODEL SIMULATING A TRIAXIAL COMPRESSION TEST . . . . . . . . . .
. . . . 198 4.2 DEM MODEL OF GRANULAR FLOW . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 199 4.3 LPM LARGE DEFORMATION
BENCHMARK . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 4.4
LPM MODEL OF DISCHARGING SILO . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 202 5 CONCLUDING REMARKS . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 204 DIFFICULTIES AND
LIMITATION OF STATISTICAL HOMOGENIZATION IN GRANULAR MATERIALS B.
CAMBOU, PH. DUBUJET ............................................ 205 1
DEFINITION OF STATISTICAL HOMOGENIZATION IN GRANULAR MATERIALS . . . . .
. . . . 205 2 STATIC AVERAGING OPERATOR . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 206 3 STATIC
LOCALISATION OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 207 3.1 GENERAL FORMULATION . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 3.2
ANALYSIS OF THE PHYSICAL MEANINGS OF INTERNAL PARAMETERS µ AND E IJ . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 XII CONTENTS
3.3 ANALYSIS OF THE CAPACITY OF DIFFERENT LOCALISATION OPERATORS FROM A
NUMERICAL SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 208 4 KINEMATIC AVERAGING OPERATOR . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 210 5 KINEMATIC
LOCALISATION OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 213 6 CONCLUSIONS . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
214 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 214 FROM
DISCONTINUOUS MODELS TOWARDS A CONTINUUM DESCRIPTION M. L¨ ATZEL, S.
LUDING, H.J. HERRMANN ................................. 215 1
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 215 2 MODEL SYSTEM AND
SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 216 2.1 THE COUETTE SHEAR-CELL SETUP . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 216 2.2 THE DISCRETE ELEMENT
MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
217 3 FROM THE MICRO- TO A MACRO-DESCRIPTION . . . . . . . . . . . . . .
. . . . . . . . . . . . . 218 3.1 AVERAGING STRATEGY . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 3.2
AVERAGING FORMALISM . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 219 4 RESULTS ON MACROSCOPIC SCALAR
QUANTITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 4.1
VOLUME FRACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 220 4.2 MASS FLUX DENSITY . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
220 5 MACROSCOPIC TENSORIAL QUANTITIES . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 221 5.1 FABRIC TENSOR . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 221 5.2 STRESS TENSOR . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 223 5.3 ELASTIC
DEFORMATION GRADIENT . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 223 5.4 MATERIAL PROPERTIES . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 223 6 ROTATIONAL
DEGREES OF FREEDOM . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 225 7 SUMMARY AND CONCLUSION. . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 REFERENCES .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 229 FROM SOLIDS TO GRANULATES *
DISCRETE ELEMENT SIMULATIONS OF FRACTURE AND FRAGMENTATION PROCESSES IN
GEOMATERIALS G.A. D*ADDETTA , F. KUN, E. RAMM, H.J. HERRMANN
................... 231 1 INTRODUCTION. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
231 2 DESCRIPTION OF THE MODEL . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 233 2.1 GRANULARITY . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 234 2.2 ELASTIC BEHAVIOUR OF THE SOLID . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 235 2.3 BREAKING OF THE SOLID
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 238 2.4 STRESS CALCULATION . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 239 3 SIMULATION RESULTS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 239 3.1 QUASI*STATIC LOADING SCENARIOS . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 240 3.2 DYNAMIC
FRAGMENTATION OF SOLIDS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 249 4 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 257 CONTENTS XIII
MICROSCOPIC MODELLING OF GRANULAR MATERIALS TAKING INTO ACCOUNT PARTICLE
ROTATIONS W. EHLERS, S. DIEBELS, T. MICHELITSCH
................................. 259 1 INTRODUCTION . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 259 2 KINEMATICS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 3
EQUATIONS OF MOTION . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 262 4 CONTACT LAWS . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 264 5 NUMERICAL ASPECTS . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 268 6 SIMULATION
EXAMPLES AND RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 269 7 CONCLUSIONS . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 273 MICROSTRUCTURED
MATERIALS: LOCAL CONSTITUTIVE EQUATION WITH INTERNAL LENGHT, THEORETICAL
AND NUMERICAL STUDIES R. CHAMBON, T. MATSUCHIMA, D. CAILLERIE
............................ 275 1 INTRODUCTION. . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 275 2 A GENERAL THEORY FOR CONTINUA WITH MICROSTRUCTURE . . . . .
. . . . . . . . . . . . . 276 2.1 KINEMATIC DESCRIPTION OF A CONTINUUM
WITH MICROSTRUCTURE . . . . . . . 276 2.2 THE INTERNAL VIRTUAL WORK . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
2.3 THE EXTERNAL VIRTUAL WORK . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 276 2.4 THE BALANCE EQUATIONS AND THE
BOUNDARY CONDITIONS . . . . . . . . . . . . 277 3 MICROSTRUCTURED
CONTINUUM WITH KINEMATIC CONSTRAINT: SECOND GRADIENT MODELS . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 277 3.1 EQUATIONS OF A SECOND GRADIENT MODEL
. . . . . . . . . . . . . . . . . . . . . . . . 277 3.2 LOCAL
ELASTO-PLASTIC SECOND GRADIENT MODELS . . . . . . . . . . . . . . . . .
. . 278 4 AN APPLICATION OF LOCAL ELASTO-PLASTIC SECOND GRADIENT MODEL .
. . . . . . . . . . . . . . . . . . . . . . . 279 4.1 THE PROBLEM TO BE
SOLVED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 279 4.2 PARTIAL SOLUTIONS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 280 4.3 PATCH CONDITIONS AND
FULL SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
4.4 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 283 5 EQUATIONS WITH LAGRANGE
MULTIPLIERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
284 6 EQUATIONS FOR THE ITERATIVE PROCEDURE . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 284 7 FINITE ELEMENT METHOD . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
286 7.1 SHAPE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 286 7.2 ELEMENT STIFFNESS MATRIX
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 287 7.3 ELEMENT RESIDUAL TERMS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 288 7.4 GLOBAL MATRICES . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 289 8 APPLICATIONS: TWO DIMENSIONAL ELASTO-PLASTIC CONSTITUTIVE
RELATION . . . . . . 289 9 CONCLUSIONS . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 291 DAMAGE IN A
COMPOSITE MATERIAL UNDER COMBINED MECHANICAL AND HYGRAL LOAD H. SADOUKI,
F. H. WITTMANN ........................................ 293 1
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 293 XIV CONTENTS 2
GENERATION OF NUMERICAL CONCRETE . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 294 3 DRYING PROCESS AND SELF-DESICCATION . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 3.1
BASIC ELEMENTS AND EQUATIONS GOVERNING THE PROCESSES . . . . . . . . . .
. 295 3.2 MATERIAL PARAMETERS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 296 3.3 AN EXAMPLE OF SIMULATION
OF DRYING . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 4
ENDOGENOUS AND DRYING SHRINKAGE . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 299 4.1 GENERAL CONCEPT . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
4.2 SHRINKAGE IN NORMAL AND HIGH PERFORMANCE CONCRETE . . . . . . . . .
. . . . 300 5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
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| callnumber-raw | TA404.2 |
| callnumber-search | TA404.2 |
| callnumber-sort | TA 3404.2 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | UD 8220 UQ 8050 |
| ctrlnum | (OCoLC)45621689 (DE-599)BVBBV013520542 |
| dewey-full | 620.1/1292 |
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| genre | (DE-588)1071861417 Konferenzschrift 2000 Stuttgart gnd-content |
| genre_facet | Konferenzschrift 2000 Stuttgart |
| id | DE-604.BV013520542 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:47:15Z |
| institution | BVB |
| isbn | 3540415254 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009228814 |
| oclc_num | 45621689 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-11 |
| physical | XIV, 307 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics Physics and astronomy online library |
| spelling | Continuous and discontinuous modelling of cohesive frictional materials P. A. Vermeer ... (ed.) Berlin [u.a.] Springer 2001 XIV, 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 568 Physics and astronomy online library Mathematisches Modell Cohesion Mathematical models Friction Mathematical models Materials Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Werkstoff (DE-588)4065579-9 gnd rswk-swf Kohäsion (DE-588)4164485-2 gnd rswk-swf Modell (DE-588)4039798-1 gnd rswk-swf Innere Reibung (DE-588)4161806-3 gnd rswk-swf Granulärer Stoff (DE-588)4256351-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2000 Stuttgart gnd-content Werkstoff (DE-588)4065579-9 s Kohäsion (DE-588)4164485-2 s Innere Reibung (DE-588)4161806-3 s Modell (DE-588)4039798-1 s DE-604 Granulärer Stoff (DE-588)4256351-3 s Mathematisches Modell (DE-588)4114528-8 s Vermeer, Pieter A. Sonstige oth Lecture notes in physics 568 (DE-604)BV000003166 568 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009228814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Continuous and discontinuous modelling of cohesive frictional materials Lecture notes in physics Mathematisches Modell Cohesion Mathematical models Friction Mathematical models Materials Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Werkstoff (DE-588)4065579-9 gnd Kohäsion (DE-588)4164485-2 gnd Modell (DE-588)4039798-1 gnd Innere Reibung (DE-588)4161806-3 gnd Granulärer Stoff (DE-588)4256351-3 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4065579-9 (DE-588)4164485-2 (DE-588)4039798-1 (DE-588)4161806-3 (DE-588)4256351-3 (DE-588)1071861417 |
| title | Continuous and discontinuous modelling of cohesive frictional materials |
| title_auth | Continuous and discontinuous modelling of cohesive frictional materials |
| title_exact_search | Continuous and discontinuous modelling of cohesive frictional materials |
| title_full | Continuous and discontinuous modelling of cohesive frictional materials P. A. Vermeer ... (ed.) |
| title_fullStr | Continuous and discontinuous modelling of cohesive frictional materials P. A. Vermeer ... (ed.) |
| title_full_unstemmed | Continuous and discontinuous modelling of cohesive frictional materials P. A. Vermeer ... (ed.) |
| title_short | Continuous and discontinuous modelling of cohesive frictional materials |
| title_sort | continuous and discontinuous modelling of cohesive frictional materials |
| topic | Mathematisches Modell Cohesion Mathematical models Friction Mathematical models Materials Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Werkstoff (DE-588)4065579-9 gnd Kohäsion (DE-588)4164485-2 gnd Modell (DE-588)4039798-1 gnd Innere Reibung (DE-588)4161806-3 gnd Granulärer Stoff (DE-588)4256351-3 gnd |
| topic_facet | Mathematisches Modell Cohesion Mathematical models Friction Mathematical models Materials Mathematical models Werkstoff Kohäsion Modell Innere Reibung Granulärer Stoff Konferenzschrift 2000 Stuttgart |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009228814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT vermeerpietera continuousanddiscontinuousmodellingofcohesivefrictionalmaterials |