MICROMECHANICS OF IDEALIZED GRANULAR SYSTEMS

The theory studies idealized granular systems--assemblies of material discs and spheres--in conditions of static equilibrium under external loads. Particles are regarded as deformable solids interacting by means of contact forces. The objective of the study is to develop means of phenomenological description suitable for efficient analysis of stress fields in granular masses. Systems are analyzed using principles of mechanics applied at the particulate level and using developed statistical and statistico-geometrical methods.;The average of the phenomenological stress tensor over an ensemble of macroscopically similar systems under inhomogeneous loads has all the field properties of the continuum mechanics stress tensor which becomes related to average forces on contacts of the same orientation and to the contact orientation distribution. Under minimal assumptions regarding the form of directional variation of forces, the latter are expressed in terms of stress tensor invariants and the influence of anisotropy in contact orientations is investigated. It is shown that the displacement gradient considered in continuum mechanics can be introduced through conditions of particle micro-compatibility in contacts.;Distributions of contact forces for assemblies of bonded particles are developed using principles of the information theory. Constitutive relationships for assemblies of bonded particles with linear contact interactions are derived by minimization of complementary work of internal deformations. For isotropic assemblies of spheres, the tensor of elasticity is isotropic; Poisson's ratio is given as a function of the ratio of tangential to normal stiffnesses and is automatically within thermodynamic limits. Poisson's result ((nu) = 1/4) corresponds to zero tangential contact stiffness. Fluctuations of the phenomenological stress tensor in finite volumes are assessed. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of school.) UMI;The phenomonological stress tensor is introduced as a fluctuating function of volume through volume-additive combinations of a system's micro-parameters, contact forces and orientations of contact normals. It is shown that the introduced tensor has properties of the continuum mechanics stress tensor in the limit of an infinite homogeneous assembly under homogeneous loads on infinity.