Mathematics and mechanics of granular materials

Journal of Engineering Mathematics, 2005

Initial response of a micro-polar hypoplastic material under plane shearing by E. Bauer 35-51 Some theoretical results about second-order work, uniqueness, existence and controllability independent of the constitutive equation by R. Chambon 53-61 Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers by G.M. Cox, S.W. McCue, N. Thamwattana and J.M. Hill 63-91 Micromechanical constitutive modelling of granular media: evolution and loss of contact in particle clusters by B.S. Gardiner and A. Tordesillas 93-106 A hyperbolic well-posed model for the flow of granular materials

International Journal for Numerical and Analytical Methods in Geomechanics, 2003

In this paper a micro-polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non-linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro-polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro-polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived.

2008

The friction effect in filling and unsteady/steady discharge of three-dimensional wedge-shaped hopper was considered numerically by the discrete element method. The presented model is based on contact mechanics of a single spherical particle involving Hooke's law of spring interaction, static and dynamic friction as well as viscous damping forces. The hopper filling process en masse was performed while the modeling of uncontrolled and controlled discharge was simulated. The evolution of the kinetic energy of filling, the distribution of stresses within granular material and stresses acting on the walls, as well as the change in fields of material porosity were investigated at the stages of filling and discharge of the hopper. The variation of flow velocities, the discharged mass fractions as well as discharge fraction rates were analyzed. The friction effect was analyzed by varying inter-particle friction coefficient over the range of 0-0.6. A comparison of the numerical results with available continuum-based predictions was also presented.

International Journal of Solids and Structures, 2012

The current study presents finite element simulations of shear localization along the interface between cohesionless granular soil and bounding structure under large shearing movement. Micro-polar (Cosserat) continuum approach is applied in the framework of elasto-plasticity in order to overcome the numerical problems of localization modeling seen in the conventional continuum mechanics. The effects of different micro-polar kinematic boundary conditions, along the interface, on the evolution and location of shear band are shown by the numerical results. Furthermore, shear band thickness is also investigated for its dependence on the initial void ratio, vertical pressure and mean grain size. Here, the distribution and evolution of static and kinematic quantities are the main focuses regarding infinite layer of micropolar material during plane shearing, especially with advanced large movement of bounding structure. The influence of such movement has not been investigated yet in the literature. Based on the results obtained from this study, shear localization appears parallel to the direction of shearing. It occurs either in the middle of granular layer or near boundaries, regarding the assumed micro-polar kinematic boundary conditions at the bottom and top surfaces of granular soil layer. Narrower shear band is observed in lower rotation resistance of soil particles along the interface. It is emphasized that the displacement magnitude of bounding structure has significant effect on the distribution and evolution of state variables and polar quantities in the granular soil layer. However, continuous displacement has no meaningful effect on the thickness of shear band. Here, smooth distributions of void ratio and shear stress components are obtained within the shear band, what the other previous numerical investigations did not receive. Despite indirect linking of Lade's model to the critical state soil mechanics, state variables tend towards asymptotical stationary condition in large shear deformation.

Acta Geotechnica, 2007

This paper focuses on the influence of the initial void ratio on the evolution of the passive earth pressure and the formation of shear zones in a dry sand body behind a retaining wall. For the numerical simulation a rigid and very rough retaining wall undergoing a horizontal translation against the backfill is considered. The essential mechanical properties of cohesionless granular soil are described with a micro-polar hypoplastic model which takes into account stresses and couple stresses, pressure dependent limit void ratios and the mean grain size as a characteristic length. Numerical investigations are carried out with an initially medium dense and initially loose sand using a homogeneous and random distribution of the initial void ratio. The geometry of calculated shear zones is discussed and compared with a corresponding laboratory model test.

Mechanics of Materials, 2002

A new formulation for polar extension of hypoplastic model is presented for cohesionless granular materials. The formulation is proposed based on the analysis of stationary states, which is a generalization of the concept of critical state in soil mechanics. The model includes stress, couple stress and void ratio as state variables and takes into account the mean grain diameter and inter-granular friction resistance to grain sliding and rotation. A coupled limit condition embedded in the model is derived from the analysis for stationary states and the physical interpretation of frictional parameters are provided. The performance of the model is studied by modeling the plane shearing of an infinite granular layer, which shows the capability of the model in capturing the phenomenon of shear localization with a finite thickness. Numerical results are presented to show the evolution of a localized zone and of the state variables. Parametric studies are performed to investigate the dependence of the thickness of shear bands on various factors. A correlation is proposed to correlate the thickness of shear bands with grain size, frictional parameters and pressuredependent relative density.

In this paper the mechanical behavior of a soilbag under an increasing vertical compression is numerically investigated using a micro-polar continuum approach. Particular attention is paid to the influence of the interaction between the filling material and the bag on the evolution of the stress strain behavior of the soilbag structure. The mechanical behavior of the cohesionless granular material is described with a micro-polar hypoplastic model and for the wrapping sack an elastic-ideally plastic behavior is assumed. Two different properties of the interface between the filling material and the wrapper are investigated: a frictionless and an interlocked interface. The numerical results show that the tensile stress in the bag material uniformly increases up to limit stress for the frictionless interface while a non-uniformity of the evolution of tensile stress is obtained for the interlocked interface. The deformation patterns, i.e. zones of intense strain localization, are also influenced by the prescribed interface behavior.

International Journal for Numerical and Analytical Methods in Geomechanics, 2012

Recently, the shear behavior of a cohesionless granular strip that is in contact with a very rough surface of a moving bounding structure has been numerically investigated by several authors by using a micropolar hypoplastic continuum model. It was shown that the micropolar boundary conditions assumed along the interface have a strong influence on the deformations within the granular layer. In previous investigations, only interface friction angles for very rough bounding structures were assumed. In contrast, the focus of the present paper is on the influence of the interface roughness on the deformation behavior of the granular strip when the interface friction angle is lower than the peak friction angle of the granular material. In addition to the interface friction angle, particular attention is also paid to the influence of the mean grain diameter, the solid hardness, the initial void ratio, and the vertical stress on the maximum horizontal shear displacement within the granular layer before sliding is started.

Granular Matter, 2006

The effect of transverse isotropy on shear localization in cohesionless granular materials is numerically investigated upon monotonous plane strain deformation paths using a hypoplastic constitutive model enhanced by micro-polar terms. In this model, a so-called density function is reformulated and made anisotropic. Dense sand specimens under constant lateral pressure are numerically tested for uniform and stochastic distributions of the initial void ratio and for two different mean grain diameters.

Granular Matter, 2005

In a recent paper, the effect of cyclic shearing on forced shear localization in an infinite granular strip between rough boundaries was numerically investigated. The present paper focuses on the evolution of spontaneous developed shear localization within an granular body under plane strain conditions, constant lateral pressure and cyclic vertical compression-extension. For a simulation of the mechanical behavior of a cohesionless granular material, a micro-polar hypoplastic constitutive is used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. For the calibration of the constitutive constants, the data of a medium quartz sand are used. The attention of numerical simulations is laid on the influence of the number of cycles, the magnitude of the vertical deformation amplitude and the initial density on the evolution of shear zones in an initially prismatic granular specimen.