Mathematical modeling in mechanics of granular materials

Cover......Page 1
Mathematical Modelingin Mechanics of Granular Materials......Page 3
Foreword......Page 5
Preface......Page 7
Contents......Page 9
10 Rotational Degrees of Freedom of Particles......Page 12
References......Page 15
2.1 Granular Material With Rigid Particles......Page 17
2.2 Elastic-Visco-Plastic Materials......Page 20
2.3 Cohesive Granular Materials......Page 25
2.4 Computer Modeling......Page 29
2.5 Fiber Composite Model......Page 39
2.6 Porous Materials......Page 45
2.7 Rheologically Complex Materials......Page 51
References......Page 57
3.1 Convex Sets and Convex Functions......Page 59
3.2 Discrete Variational Inequalities......Page 71
3.3 Subdifferential Calculus......Page 81
3.4 Kuhn--Tucker\'s Theorem......Page 92
3.5 Duality Theory......Page 101
References......Page 109
4.1 Granular Material With Elastic Properties......Page 111
4.2 Coulomb--Mohr Cone......Page 117
4.3 Von Mises--Schleicher Cone......Page 123
References......Page 131
5.1 Model of a Material With Load Dependent Strength Properties......Page 133
5.2 Static and Kinematic Theorems......Page 143
5.3 Examples of Estimates......Page 149
5.4 Computational Algorithm......Page 158
5.5 Plane Strain State......Page 167
References......Page 178
6.1 Model of an Elastic--Plastic Granular Material......Page 180
6.2 A Priori Estimates of Solutions......Page 186
6.3 Shock-Capturing Method......Page 196
6.4 Plane Signotons......Page 206
6.5 Cumulative Interaction of Signotons......Page 217
6.6 Periodic Disturbing Loads......Page 221
References......Page 228
7.1 Formulation of Contact Conditions......Page 231
7.2 Algorithm of Correction of Velocities......Page 242
7.3 Results of Computations......Page 247
7.4 Interaction of Blocks Through Viscoelastic Layers......Page 255
References......Page 265
8.1 Generalization of the Method......Page 267
8.2 Distinctive Features of Parallel Realization......Page 273
8.3 Results of Two-Dimensional Computations......Page 280
8.4 Numerical Solution of Three-Dimensional Problems......Page 283
References......Page 294
9.1 Dilatancy Effect......Page 296
9.2 Basic Properties of the Hencky Tensor......Page 304
9.3 Model of a Viscous Material with Rigid Particles......Page 311
9.4 Shear Stresses......Page 316
9.5 Couette Flow......Page 318
9.6 Motion Over an Inclined Plane......Page 321
9.7 Plane-Parallel Motion......Page 326
9.8 Radial Expansion of Spherical and Cylindrical Layers......Page 328
References......Page 336
10.1 A Model of the Cosserat Continuum......Page 339
10.2 Computational Results......Page 359
10.3 Generalization of the Model......Page 372
10.4 Finite Strains of a Medium With Rotating Particles......Page 383
10.5 Finite Strains of the Cosserat Medium......Page 388
References......Page 394