Rearrangements and Dilatancy for Sheared Dense Materials

Constitutive equations are proposed for dense materials, based on the identification of two types of free-volume activated rearrangements associated to shear and compaction. Two situations are studied: the case of an amorphous solid in a stress-strain test, and the case of a lubricant in tribology test. Varying parameters, strain softening, shear thinning, and stick-slip motion can be observed.Comment: 4 pages, 3 figure

The Origin of a Repose Angle: Kinetics of Rearrangements for Granular Materials

A microstructural theory of dense granular materials is presented, based on two main ideas. Firstly, that macroscopic shear results form activated local rearrangements at a mesoscopic scale. Secondly, that the update frequency of microscopic processes is determined by granular temperature. In a shear cell, the resulting constitutive equations account for Bagnold's scaling and for the existence of a Coulomb criterion of yield. In the case of a granular flow down an inclined plane, they account for the rheology observed in recent experiments and for the temperature and velocity profiles measured numerically.Comment: submitted to PR

Stiffness pathologies in discrete granular systems: bifurcation, neutral equilibrium, and instability in the presence of kinematic constraints

The paper develops the stiffness relationship between the movements and forces among a system of discrete interacting grains. The approach is similar to that used in structural analysis, but the stiffness matrix of granular material is inherently non-symmetric because of the geometrics of particle interactions and of the frictional behavior of the contacts. Internal geometric constraints are imposed by the particles' shapes, in particular, by the surface curvatures of the particles at their points of contact. Moreover, the stiffness relationship is incrementally non-linear, and even small assemblies require the analysis of multiple stiffness branches, with each branch region being a pointed convex cone in displacement-space. These aspects of the particle-level stiffness relationship gives rise to three types of micro-scale failure: neutral equilibrium, bifurcation and path instability, and instability of equilibrium. These three pathologies are defined in the context of four types of displacement constraints, which can be readily analyzed with certain generalized inverses. That is, instability and non-uniqueness are investigated in the presence of kinematic constraints. Bifurcation paths can be either stable or unstable, as determined with the Hill-Bazant-Petryk criterion. Examples of simple granular systems of three, sixteen, and sixty four disks are analyzed. With each system, multiple contacts were assumed to be at the friction limit. Even with these small systems, micro-scale failure is expressed in many different forms, with some systems having hundreds of micro-scale failure modes. The examples suggest that micro-scale failure is pervasive within granular materials, with particle arrangements being in a nearly continual state of instability

Stress-corrosion behavior of aluminum-lithium alloys in aqueous environments

The stress corrosion susceptibility of two powder metallurgy (P/M) alloys, Al-Li-Cu and Al-Li-Cu-Mg two mechanically attrited (M/A) alloys, Al-Li-Cu and Al-Li-Mg; and two wrought, ingot alloys, X-2020 and AA7475, are compared. Time-dependent fracture in an aqueous sodium chloride environment under alternate immersion condition was found to vary significantly between alloys. The stress corrosion behavior of the two powder metallurgy processed alloys was studied in detail under conditions of crack initiation, static crack growth, and fatigue crack growth. A variety of stress corrosion tests were performed including smooth surface, time-to-failure tests; potentiostatic tests on smooth surfaces exposed to constant applied strain rates; and fracture mechanics-type tests under static and cyclic loads. Both alloys show surface pitting and subsequent intergranular corrosion. Pitting is more severe in the magnesium-bearing alloy and is associated with stringer particles strung along the extrusion direction as a result of P/M processing

Amorphous Systems in Athermal, Quasistatic Shear

We present results on a series of 2D atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit. The athermal quasistatic trajectories are shown to separate into smooth, reversible elastic branches which are intermittently broken by discrete catastrophic plastic events. The onset of a typical plastic event is studied with precision, and it is shown that the mode of the system which is responsible for the loss of stability has structure in real space which is consistent with a quadrupolar source acting on an elastic matrix. The plastic events themselves are shown to be composed of localized shear transformations which organize into lines of slip which span the length of the simulation cell, and a mechanism for the organization is discussed. Although within a single event there are strong spatial correlations in the deformation, we find little correlation from one event to the next, and these transient lines of slip are not to be confounded with the persistent regions of localized shear -- so-called "shear bands" -- found in related studies. The slip lines gives rise to particular scalings with system length of various measures of event size. Strikingly, data obtained using three differing interaction potentials can be brought into quantitative agreement after a simple rescaling, emphasizing the insensitivity of the emergent plastic behavior in these disordered systems to the precise details of the underlying interactions. The results should be relevant to understanding plastic deformation in systems such as metallic glasses well below their glass temperature, soft glassy systems (such as dense emulsions), or compressed granular materials.Comment: 21 pages, 18 figure

Interactive Terrain Simulation and Force Distribution Models in Sand Piles

This paper presents an application of Cellular Automata in the field of dry Granular Systems modelling. While the study of granular systems is not a recent field, no efficient models exist, from a computational point of view, in classical methodologies. Some previous works showed that the use of Cellular Automata is suitable for the development of models that can be used in real time applications. This paper extends the existing Cellular Automata models in order to make them interactive. A model for the reaction to external forces and a pressure distribution model are presented and analyzed, with numerical examples and simulations

Boundary lubrication with a glassy interface

Recently introduced constitutive equations for the rheology of dense, disordered materials are investigated in the context of stick-slip experiments in boundary lubrication. The model is based on a generalization of the shear transformation zone (STZ) theory, in which plastic deformation is represented by a population of mesoscopic regions which may undergo non affine deformations in response to stress. The generalization we study phenomenologically incorporates the effects of aging and glassy relaxation. Under experimental conditions associated with typical transitions from stick-slip to steady sliding and stop start tests, these effects can be dominant, although the full STZ description is necessary to account for more complex, chaotic transitions