Constitutive Laws For Granular Materials Research Articles

A review and analysis of granular shear experiments under low effective stress conditions

The constitutive law for granular materials is governed mainly by the intergranular friction, which depends strongly on the gravitational force or effective isotropic stress. Such experiments are mostly performed with relatively high effective isotropic stress. This fact poses serious limitations on the formulation of a materially objective constitutive model based on experiments performed on earth. This paper analyzes the limited experimental data of shear strength and rheology of granular materials, subject to low effective stress conditions obtained in microgravity μg as well as in 1 g conditions. Results from these experiments show that granular materials may have an extremely high macroscopic peak friction angle and clear nonlinear S-shape non-Bingham fluidity in low effective stress conditions. In this paper, the classical limit equilibrium method is employed, and a rheological constitutive model is used to study experimental data. The limit equilibrium method enables the authors to correlate the bearing capacity of sand foundation with high peak friction angles under varying effective stress conditions. The calibrated analytical solution for the rheological constitutive model under low effective stress conditions, predicts a clear S-shape correlation of the viscous shear stress and shear strain rate. The mutation or inflection point takes place around the in-situ Niigata earthquake shear strain rate. The results of this paper are of great relevance to the assessment of seismic liquefaction hazards of infrastructure on earth.

Towards a new approach for modeling the behavior of granular materials: A mesoscopic-macroscopic change of scale

This paper constitutes a preliminary demonstration of the feasibility of a multi-scale approach for the definition of a constitutive law for granular materials. The case of two-dimensional granular materials was considered and the reasoning was built on 2D Discrete Element Method (DEM) simulations of 2D biaxial tests performed on sample made of disks. The change of scale relied on an intermediary local scale called the meso-scale which was based on the existence of meso-domains defined as closed loops of particles in contact. At the meso-scale, six sets of meso-domains or phases, with different properties in terms of local texture, have been defined. Then, an elastic–hardening–plastic model was designed at the phase scale and the identification of the model parameters was performed on a stress path denoted compression stress path. The model parameters defined for each phase were found correlated with the initial meso-texture of the considered phase and with the orientation of the loading path with respect to the phase orientation. The change of scale allowed us to obtain a modeling at the sample scale in good agreement with the DEM results on the compression stress path. Finally, the relevance of the model and of the approach were tested on a different stress path denoted unloading stress path. This was performed both at the level of the six phases and at the sample scale. The results were found to be in good agreement with the DEM simulations, which tends to validate the general approach presented in this paper, including the definition of the phases at the meso-scale, the design of a constitutive model at this scale, and the change of scale process to obtain the behavior of the material at the sample scale.

Effects of crystal shape‐ and size‐modality on magma rheology

AbstractErupting magma often contains crystals over a wide range of sizes and shapes, potentially affecting magma viscosity over many orders of magnitude. A robust relation between viscosity and the modality of crystal sizes and shapes remains lacking, principally because of the dimensional complexity and size of the governing parameter space. We have performed a suite of shear viscosity measurements on liquid‐particle suspensions of dynamical similarity to crystal‐bearing magma. Our experiments encompass five suspension types, each consisting of unique mixtures of two different particle sizes and shapes. The experiments span two orthogonal subspaces of particle concentration, as well as particle size and shape for each suspension type, thereby providing insight into the topology of parameter space. For each suspension type, we determined the dry maximum packing fraction and measured shear rates across a range of applied shear stresses. The results were fitted using a Herschel‐Bulkley model and augment existing predictive capabilities. We demonstrate that our results are consistent with previous work, including friction‐based constitutive laws for granular materials. We conclude that predictions for ascent rates of crystal‐rich magmas must take the shear‐rate dependence of viscosity into account. Shear‐rate dependence depends first and foremost on the volume fraction of crystals, relative to the maximum packing fraction, which in turn depends on crystal size and shape distribution.

Soft Dynamics simulation. 2. Elastic spheres undergoing a T1 process in a viscous fluid

Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear localization, observed also in foams, emulsions, and block copolymer cubic phases, seem to involve other micro-timescales which may be related to the dynamics of local particle reorganizations. In the present work, we consider a T(1) process as an example of a rearrangement. Using the Soft Dynamics simulation method introduced in the first paper of this series, we describe theoretically and numerically the motion of four elastic spheres in a viscous fluid. Hydrodynamic interactions are described at the level of lubrication (Poiseuille squeezing and Couette shear flow) and the elastic deflection of the particle surface is modeled as Hertzian. The duration of the simulated T(1) process can vary substantially as a consequence of minute changes in the initial separations, consistently with predictions. For the first time, a collective behaviour is thus found to depend on a parameter other than the typical volume fraction of particles.

A thermomicromechanical approach to multiscale continuum modeling of dense granular materials

A new method is proposed for the development of a class of elastoplastic thermomicromechanical constitutive laws for granular materials. The method engenders physical transparency in the constitutive formulation of multiscale phenomena from the particle to bulk. We demonstrate this approach for dense, cohesionless granular media under quasi-static loading conditions. The resulting constitutive law—expressed solely in terms of particle scale properties—is the first of its kind. Micromechanical relations for the internal variables, tied to nonaffine deformation, and their evolution laws, are derived from a structural mechanical analysis of a particular mesoscopic event: confined, elastoplastic buckling of a force chain. It is shown that the constitutive law can reproduce the defining behavior of strain-softening under dilatation in both the mesoscopic and macroscopic scales, and reliably predict the formation and evolution of shear bands. The thickness and angle of the shear band, the distribution of particle rotation and the evolution of the normal contact force anisotropy inside the band, are consistent with those observed in discrete element simulations and physical experiments.

Multi-mechanism anisotropic model for granular materials

By representing the assembly by a simplified column model, a constitutive theory, referred to as sliding–rolling theory, was recently developed for a two-dimensional assembly of rods subjected to biaxial loading, and then extended to a three-dimensional assembly of spheres subjected to triaxial (equibiaxial) loading. The sliding–rolling theory provides a framework for developing a phenomenological constitutive law for granular materials, which is the objective of the present work. The sliding–rolling theory provides information concerning yield and flow directions during radial and non-radial loading. In addition, the theory provides information on the role of fabric anisotropy on the stress–strain behavior and critical state shear strength. In the present paper, a multi-axial phenomenological model is developed within the sliding–rolling framework by utilizing the concepts of critical state, classical elasto-plasticity and bounding surface. The resulting theory involves two yield surfaces and falls within the definition of the multi-mechanism models. Computational issues concerning the solution uniqueness for stress states at the corner of yield surfaces are addressed. The effect of initial and induced fabric anisotropy on the constitutive behavior is incorporated. It is shown that the model is capable of simulating the effect of anisotropy, and the behavior of loose and dense sands under drained and undrained loading.

Transition to movement in granular chute flows

This experimental investigation deals with the observation of the behaviour that dense granular materials present when they flow in steady regime on a rough chute, focusing the attention on the transition to movement of the bed and on quantities involved as the internal friction angle. An important aspect of the study is the identification of parameters that distinguish granular from fluid flows, aiming to verify the possibility to describe a granular bed as it was a pseudo-fluid having a particular rheological behaviour. In the experiments we have not used idealised particles (spheres, rods or disks) but sieved powders of ethylenediaminetetraacetic acid (EDTA), constituted of non-spherical particles with polydisperse size distribution and surface roughness. A static and a flowing (dynamic) layer are clearly identified. The thickness of the observed layers (static and dynamic) along the chute has been measured for different inclination, finding out that they collapse into a single curve when considered in non-dimensional scale. On the ground of the experimental data we propose a direct way of measuring the dynamic friction angle from chute observations and a simple constitutive law for granular materials in the frictional regime of motion. The law has been tested using velocity profiles obtained by filming the flowing granular bed.

微視力学に基づく粒状体の構成則の定式化

微視力学に基づく粒状体の構成則の定式化

Micromechanical modeling of deformation and failure for granulates with frictional contacts

Perceiving granular material as a collection of particles, a constitutive law for granular material is derived based on micromechanics approach, taking into account the mechanisms of sliding and separation of particles under large deformation. The derived constitutive law is explicitly in terms of inter—particle contact properties. In deriving the overall stress-strain relationship, heterogeneity of the material is considered by a newly introduced distributive tensor. The distributive tensor describes the strain fluctuation in the system and facilitates an averaging process for obtaining the overall deformation behavior. Predicted results from the present model are compared with that obtained from computer simulation and experiments on sands. Unique features of the present theory are discussed to show their usefulness in comprehensive modelling of complex behavior for granular material.

Elastoplastic Deformation for Particulates with Frictional Contacts

Perceiving granular material as a collection of particles, a constitutive law for granular material is derived based on a micromechanics approach, taking into account the mechanisms of sliding and separation of particles under large deformation. One of the major obstacles to account for the particle sliding associated with large deformation is the nonuniform strain field. In this paper, we tackle this problem by using a self‐consistent method to account for the heterogeneous field of strain. The micromechanical approach is described to illustrate the three levels of granular material, namely, representative unit, microelement and inter‐particle contact. The overall stress‐strain relationship is expressed in explicit terms of interparticle contact properties. The present theory is evaluated by comparing the predicted stress‐strain behavior of a granular packing with that obtained from computer simulation. The unique features of the present theory are discussed to show its usefulness in comprehensive modeling of complex behavior for granular material.