Constitutive relations for cohesionless frictional granular materials (original) (raw)
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Physical Review E
We present a systematic numerical investigation concerning the combined effects of sliding friction and particle shape (i.e., angularity) parameters on the shear strength and microstructure of granular packings. Sliding friction at contacts varied from 0 (frictionless particles) to 0.7, and the particles were irregular polygons with an increasing number of sides, ranging from triangles to disks. We find that the effect of local friction on shear strength follows the same trend for all shapes. Strength first increases with local friction and then saturates at a shape-dependent value. In contrast, the effect of angularity varies, depending on the level of sliding friction. For low friction values (i.e., under 0.3), the strength first increases with angularity and then declines for the most angular shapes. For high friction values, strength systematically increases with angularity. At the microscale, we focus on the connectivity and texture of the contact and force networks. In general terms, increasing local friction causes these networks to be less connected and more anisotropic. In contrast, increasing particle angularity may change the network topology in different directions, directly affecting the macroscopic shear strength. These analyses and data constitute a first step toward understanding the joint effect of local variables such as friction and grain shape on the macroscopic rheology of granular systems.
Taylor & Francis eBooks, 2003
The mechanical behaviour of a frictional granular material is strongly influenced by both fabric (anisotropy of grain packing) and grain contact force networks that develop during plastic deformations. When a sand body is sheared, an increase in volume (dilation) ensues as a consequence of geometrical constraints imposed by the fabric against applied stresses. This important phenomenon coined as stress-dilatancy hinges on particle kinematics (slip and spin) as the grains override each other against confinement. As such, both dilatancy and fabric control the nature of the deformation mode, e.g. the localization of deformations into a shear band, which usually signals incipient failure. It has been found that the dominant mechanism inside a shear band is that of particle rearrangement, including both rolling and translation leading into further fabric changes with respect to the region outside the shear band. In fact, Oda et al. (1998) and Desrues et al. (1996) both observed significant particle rotation and increase of voids within the shear band. Therefore, the proper description of stress-dilatancy with the inclusion of fabric information is a basic requisite for accurately modelling the stress-strain behaviour of sand leading to strain localization, see Wan & Guo (2001a). Stress dilatancy theories based on macroscopic observations can be traced as far back to the early works of Rowe (1962). While the importance of confinement, density and stress path has been clearly demonstrated (
Continuum Theory of Frictional Granular Matter
2002
In the present Letter, we derive a continuum description of stresses in granular matter, starting from the elastic deformations of individual grains about a preloaded equilibrium state. The assumed large intergrain friction ensures a well-defined contact network. Its texture is reflected in fabric tensors that relate strains to stresses. At odds with usual continuum media, here individual grains are free to reorient, thus relieving stress locally and contributing to the overall mechanical response.
Journal of Geophysical Research, 2005
1] By means of the contact dynamics discrete element method, we investigate the quasistatic behavior of granular media composed of rigid frictional particles. Eluding specific modeling of the contact rheology, this method is suitable for numerical simulation of the plastic deformations of granular materials. We studied the macroscopic stress-strain and volume-change behavior, as well as force transmission and shear instabilities, in a two-dimensional biaxial geometry for dense samples composed of 5000 rigid disks. The peak and residual strengths and shear bands were analyzed by varying the confining pressure and the coefficient of friction between particles. The results are consistent with well-known features of the plasticity of noncohesive granular media. The mechanical behavior is rigid-plastic governed by a Mohr-Coulomb yield criterion and showing strain hardening and softening. Conjugated shear bands characterize plastic failure. The volumetric strain is globally dilatant with considerable expansion observed along shear bands. The macroscopic coefficient of friction, determined from peak and residual strengths, increases nonlinearly and saturates to a constant value as a function of contact friction. The strong force chains are mostly parallel to the major principal stress axis, yet deviations are observed near the shear bands. These chains are often composed of particles that are larger than the average. The deviatoric stress shows small fluctuations often in the form of rapid falls that are correlated with tiny contractional events. This behavior is interpreted in terms of the propagation of dynamic shear instabilities along the shear bands, in close analogy with stick-slip behavior.
2014
This paper is concerned with micromechanics of Schneebeli material specimens composed of wooden roller stacks. Several laboratory tests are carried out to analyse the material behaviour under complex loading conditions, involving loading–unloading cycles and principal axes rotations. In order to characterize micromechanical deformation features and structure evolution, a series of pictures is taken during loading. Pictures are then digitized using a stereo device, obtaining the position of each roller. Starting from these data a number of computer programs, conceived for the purpose, allow us to measure micromechanical variables and to analyse their evolution. In the following, after the description of the devices employed in this research, macromechanical results are analysed to evaluate the reliability of the laboratory model. Then, local variables are introduced and the use of continuum mechanics to describe granular materials behaviour is discussed. Finally, the evolution of loc...
Towards a general state-variable constitutive relation to describe granular deformation
Earth and Planetary Science Letters, 2005
Triaxial-compression experiments were performed on cylindrical quartz sand-packs to explore the universality of statevariable constitutive relations used to describe granular deformation. Samples were subjected to relaxation-creep experiments similar to slide-hold-slide tests from friction studies. For relaxation-creep tests, a constant rate of axial shortening was interrupted by time intervals for which the applied shortening rate was set to zero. During holds, loadforce decayed exponentially with time and the total stress-relaxation scales with the logarithm of hold time, consistent with friction tests. On reloading after holds, stress monotonically increases to the pre-hold steady-state levels without displaying the restrengthening of static friction often observed from shear tests on granular layers. We find that the existing rate-and state-variable friction laws can model the transient strength behavior during relaxation creep and subsequent reloading by using simple assumptions about the deformation of cylindrical sand-packs in triaxial compression. By analogy with the rate-and state-friction constitutive relations, we propose a generalized state-variable expression for granular deformation in simple and pure shear. Although additional experiments under a variety of load boundary geometries and load paths will be needed, such a general constitutive relation may ultimately describe granular deformation under a broad range of conditions (e.g., for large variations in loading rate, shear stress, normal stress, mean stress) and may be applicable to a variety of research problems that involve deformation within granular media.
International Journal of Plasticity, 2006
The objective of this paper is to incorporate the effects of fabric and its evolution into the Dilatant Double Shearing Model . Initial planar deformation of dilatant granular materials. J. Mech. Phys. Solids 26, 269-284] for granular materials in order to capture the anisotropic behavior and the complex response of granular materials in cyclic shear loading. An important consequence of considering the fabric is that one can have unequal shearing rates along the two slip directions. This property leads to the non-coaxiality of the principal axes of stress and strain rate, which is more appropriate for a material that exhibits initial and induced anisotropy. In addition, we employ a fabric-dependent elasticity tensor with orthotropic symmetry. The model developed in this paper also predicts one of the experimentally observed characteristics of granular materials: the gradual concentration of the contact normals towards the maximum principal stress direction.
Unsteady Shear of Dense Assemblies of Cohesive Granular Materials under Constant Volume Conditions
Industrial & Engineering Chemistry Research, 2010
The response characteristics of dense assemblies of cohesive granular materials to unsteady simple shear in the quasi-static regime are investigated through discrete element method (DEM) simulations of monodisperse spherical and frictional particles in periodic domains at constant volume. The dynamics of the volume-averaged normal and shear stresses in materials, undergoing stop-and-go shearing and oscillatory shear, are studied in detail. Furthermore, the evolution of microstructure anisotropy has been quantified through a fabric tensor. The stresses and the microstructure anisotropy depend on the strain extent but not on the shear rate. They both undergo a transition following reversal of shear direction, which requires a shear strain of order unity to fully adapt. The results reveal a correlation between the stress evolution and the microstructure anisotropy development.
Stress Propagation in Two Dimensional Frictional Granular Matter
2002
The stress profile and reorientation of grains, in response to a point force applied to a preloaded two dimensional granular system, are calculated in the context of a continuum theory that incorporates the texture of the packing. When high friction prevents slip at the inter-grain contacts, an anisotropic packing propagates stress along two peaks which amalgamate into a single peak