Читать книгу The Physics of the Deformation of Densely Packed Granular Materials - M A C Koenders - Страница 7
Contents
Оглавление1.1Introduction
1.2The isostatic state and jamming
1.3The statically indeterminate case and computer simulations
1.6Contact laws in terms of material parameters
1.7Interaction for small particles in a fluid environment
Chapter 2Continuum Mechanics and Cartesian Tensor Calculus
2.1Initial considerations
2.11Objectivity and pre-stressed materials, the Jaumann derivative
Chapter 3The Bounds of Static Equilibrium
3.1Criteria for rupture
3.2The context of second order, partial differential equations
3.3Wave speeds and strong ellipticity
4.4Transverse anisotropic material
5.4Strain in a granular medium
5.5Stress in a granular medium
5.6Calculating averages in a contacting granular material
Chapter 6Stress-Strain Relations of Granular Assemblies: A Frictionless Assembly
6.1General considerations
6.4Perturbations to the mean-field theory
6.6Connectivity in a granular medium
6.7Estimates of the correction to the moduli due to heterogeneity
Chapter 7Stress-Strain Relations of Granular Assemblies: Normal and Tangential Interactions
7.1Particle spin
7.2The interaction and the quasi-static equilibrium equations
7.3Mean-field stiffness estimate
7.4Heterogeneity with tangential interactions
7.5Solution of the strain fluctuations for a two-dimensional isotropic medium
7.6Considerations for an isotropic contact distribution in two special cases
7.8A few remarks on the theory
Chapter 8Frictional Granular Materials
8.1The frictional interaction
8.3Mean-field estimate with randomly distributed slip angles
8.4Mean-field estimate with concentrated slip angles
8.6Fabric heterogeneity and other refinements
8.7The evolution of an assembly in a biaxial cell test
Appendix AMathematical Appendix
A.1Isotropic tensors
A.2Integrals of strings of unit vectors
A.4Fourier transforms and harmonic density
Appendix BList of Symbols and Notations
B.1List of symbols
