Basic features of plastic strains: From micro-mechanics to incrementally nonlinear models

Most rate-independent constitutive relations for granular materials are based on the existence of a regular flow rule. This assumption states that once the mechanical state of a material point belongs to the yield surface, then the direction of the plastic strains is independent of the loading direction. In this paper, the notion of a regular flow rule is shown to exist only for two-dimensional and axisymmetric loading conditions. By considering our incrementally nonlinear constitutive model, it is established that this notion disappears as soon as more general loading conditions are applied, as also predicted from discrete element simulations. Moreover, a sound micro-mechanical interpretation of the vanishing of a regular flow rule in three-dimensional loading conditions is given from a multi-scale perspective using the micro-directional model. This model highlights the great influence of the loading history on the shape of the plastic Gudehus response-envelope.     

Static bending of granular beam: exact discrete and nonlocal solutions

Meccanica - This study is an attempt towards a better understanding of the length scale effects on the bending response of the granular beams. To this aim, a unidimensional discrete granular chain...     

On the definition of the stress tensor in granular media

This paper investigates the definition of the stress tensor within a granular assembly, when inertial effects are likely to occur. It is shown that the stress tensor can be expressed as a sum of two terms. A first term corresponds to the standard definition of the stress, according to the Love–Weber formula; this term is related to the contact forces existing within adjoining particles. A second term accounts for dynamic effects related to rotation velocities and accelerations of the particles. These results are checked from discrete numerical simulations in order to examine in which context the contribution of inertial effects should not be omitted. With this aim, the simulation of a granular specimen collapse and then a silo discharge is considered.     

Some micromechanical aspects of failure in granular materials based on second-order work

This paper discusses the notion of failure in a granular assembly by examining the key microstructural mechanisms which are most likely to trigger the nucleation and propagation of instabilities within a granular material. For this purpose, the key variable to predict the occurrence of failure, known as second-order work, is expressed from variables on the grain scale. The local behaviour incidents (where contacts may open or slide), compared to the global response of the assembly, are analysed by two approaches. First, numerical computations made by a discrete element model confirm the microscopic definition of the second-order work. Secondly, a micromechanical model, based on a homogenization procedure, relating the macroscopic behaviour to microscopic ingredients, namely contact planes, points to a close link between the occurrence of failure on the macroscopic scale as well as on the contact planes.     

Evolution of the micromechanical properties of impacted granular materials

The impact of a projectile on a granular material induces important changes in the micromechanical properties of the impacted material. These changes are studied using a Discrete Element Method model of the impact. The numerical results show that the impact first entails an energy propagation from the impact point to the limit of the sample through the existing force chains. A significant kinetic energy and a total breakage of the existing contact force chains are the main consequences of the energy propagation. During the long recovery balance phase observed after the energy propagation phase, frictional processes cause the kinetic energy dissipation. The motions of the particles and the numerous contact openings first prevent the formation of stable force chains. However, for long durations after the beginning of the impact, contact openings stop. The balance recovery phase therefore finally results in the creation of new stable contact force networks.     

Bifurcation in granular materials: An attempt for a unified framework

Sudden collapse mechanisms strictly inside the Mohr–Coulomb plastic limit condition have been observed in granular materials in the laboratory as well as in the field. The purpose of this paper is to show that the theoretical framework of loss of sustainability is convenient to describe such mechanisms. In this context, the notions of both loading and response variables, which characterize the loading path applied to the specimen considered and its response path, are fundamental. Moreover, by investigating the relation between loading and response parameters, it is established that this framework also embeds the notions of loss of constitutive uniqueness and loss of controllability. Therefore, a unified approach is attempted. Finally, by highlighting the basic role played by the loading parameters, the vanishing of the second-order work is shown to be a proper criterion to detect the occurrence of a bifurcation from a quasi-static regime to a dynamic regime leading to the collapse of the material.     

Ion-pair extraction and high-performance liquid chromatographic determination of tianeptine and its metabolites in human plasma, urine and tissues

An isocratic reversed-phase ion-pair liquid chromatographic method for the determination of tianeptine and its two main metabolites in plasma, urine and tissues, using an internal standard, is reported. The influence of two stationary phases on the retention of the drugs was studied. The drugs were extracted as ion pairs, using a heptane-octanol-tetraheptylammonium bromide mixture (98:2:0.5, v/v/w) as extraction solvent. This extraction procedure yielded plasma drug recoveries of greater than 60% and allowed UV detection at 220 nm without interference from endogenous components of plasma, urine or tissues. Linear standard curves up to 1.00 micrograms/ml and drug determination down to 0.01 microgram/ml were observed. This method has been successfully applied to the analysis of human plasma and urine samples and of encephales from tianeptine-dosed rats.