From Elasticity to Hypoplasticity: Dynamics of Granular Solids

"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well with models from soil mechanics

Measurement of Indeterminacy in Packings of Perfectly Rigid Disks

Static packings of perfectly rigid particles are investigated theoretically and numerically. The problem of finding the contact forces in such packings is formulated mathematically. Letting the values of the contact forces define a vector in a high-dimensional space enable us to show that the set of all possible contact forces is convex, facilitating its numerical exploration. It is also found that the boundary of the set is connected with the presence of sliding contacts, suggesting that a stable packing should not have more than 2M-3N sliding contacts in two dimensions, where M is the number of contacts and N is the number of particles. These results were used to analyze packings generated in different ways by either molecular dynamics or contact dynamics simulations. The dimension of the set of possible forces and the number of sliding contacts agrees with the theoretical expectations. The indeterminacy of each component of the contact forces are found, as well as the an estimate for the diameter of the set of possible contact forces. We also show that contacts with high indeterminacy are located on force chains. The question of whether the simulation methods can represent a packing's memory of its formation is addressed.Comment: 12 pages, 13 figures, submitted to Phys Rev

Ratcheting of granular materials

We investigate the quasi-static mechanical response of soils under cyclic loading using a discrete model of randomly generated convex polygons. This response exhibits a sequence of regimes, each one characterized by a linear accumulation of plastic deformation with the number of cycles. At the grain level, a quasi-periodic ratchet-like behavior is observed at the contacts, which excludes the existence of an elastic regime. The study of this slow dynamics allows to explore the role of friction in the permanent deformation of unbound granular materials supporting railroads and streets.Comment: Changed content Submitted to Physical Review Letter

Indeterminacy, Memory, and Motion in a Simple Granular Packing

We apply two theoretical and two numerical methods to the problem of a disk placed in a groove and subjected to gravity and a torque. Methods assuming rigid particles are indeterminate -- certain combinations of forces cannot be calculated, but only constrained by inequalities. In methods assuming deformable particles, these combinations of forces are determined by the history of the packing. Thus indeterminacy in rigid particles becomes memory in deformable ones. Furthermore, the torque needed to rotate the particle was calculated. Two different paths to motion were identified. In the first, contact forces change slowly, and the indeterminacy decreases continuously to zero, and vanishes precisely at the onset of motion, and the torque needed to rotate the disk is independent of method and packing history. In the second way, this torque depends on method and on the history of the packing, and the forces jump discontinuously at the onset of motion.Comment: 11 pages, 7 figures, submitted to Phys Rev

Hipoplasticidad Contra Elastoplasticidad (Parte I)

By means of simple questions and answers the article present the basic concepts of a hypoplastic constitutive model for the three-dimensional non-linear stress-strain and dilatant volume change behaviour of granular materials. The model is developed without recourse to the concept in elastoplasticity theory such as yield surface, plastic potencial and descomposition into elastic and plastic parts

Energetic Instability Unjams Sand and Suspension

Jamming is a phenomenon occurring in systems as diverse as traffic, colloidal suspensions and granular materials. A theory on the reversible elastic deformation of jammed states is presented. First, an explicit granular stress-strain relation is derived that captures many relevant features of sand, including especially the Coulomb yield surface and a third-order jamming transition. Then this approach is generalized, and employed to consider jammed magneto- and electro-rheological fluids, again producing results that compare well to experiments and simulations.Comment: 9 pages 2 fi

Hipoplasticidad Contra Elastoplasticidad (Parte II)

An alternative to elastoplastic models for the mathematical description of soil mechanical behaviour appeared in 1977, created by KOLYMBAS in his doctoral thesis at the University of Karlsruhe, Germany, and was named hypoplasticity. The article present the basic concepts of the hypoplastic constitutive model for the behaviour of granular materials. With a single constitutive equation, inspired by modern rational mechanics, without recorurse to yield or potential surfaces, important phenomena of soil mechanical behaviour can be represented. The development of the model is commented briefly.

Undrained Cavity-Contraction Analysis for Prediction of Soil Behavior around Tunnels

The cavity-contraction method has been used for decades for the design of tunneling and prediction of ground settlement by modeling the cavity-unloading process from an in situ stress state. Analytical solutions of undrained cavity contraction in a unified state-parameter model for clay and sand (CASM) are developed in this paper to predict soil behavior around tunnels. The overall behavior of clay and sand under both drained and undrained loading conditions could be properly captured by CASM, and the large-strain and effective-stress analyses of cavity contraction provide the distributions of stress/strain within the elastic, plastic, and critical-state regions around a tunnel. The effects of ground condition and soil model parameters are investigated from the results of stress paths and cavity-contraction curves. Comparisons of the ground-reaction curve and the excess pore pressure are also provided between the predicted and measured behavior of tunneling by using data of centrifuge tunnel tests in clay

Allen-Cahn and Cahn-Hilliard-like equations for dissipative dynamics of saturated porous media

We consider a saturated porous medium in the regime of solid-fluid segregation under an applied pressure on the solid constituent. We prove that, depending on the dissipation mechanism, the dynamics is described either by a Cahn-Hilliard or by an Allen-Cahn-like equation. More precisely, when the dissipation is modeled via the Darcy law we find that, for small deformation of the solid and small variations of the fluid density, the evolution equation is very similar to the Cahn-Hilliard equation. On the other hand, when only the Stokes dissipation term is considered, we find that the evolution is governed by an Allen-Cahn-like equation. We use this theory to describe the formation of interfaces inside porous media. We consider a recently developed model proposed to study the solid-liquid segregation in consolidation and we are able to fully describe the formation of an interface between the fluid-rich and the fluid-poor phase

Granular Elasticity without the Coulomb Condition

An self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.Comment: 4pages, 2 figure