arXiv subjects

P. Evesque

Publications and source records attributed to P. Evesque.

At least 37 records · Page 2Linked to original sources

arXiv2005

A new non linear mechanism able to generate avalanches based on soil mechanics

We propose a general mechanism based on soil mechanics concepts, such as dilatancy and friction, to explain the fact that avalanches stop at an angle smaller than they start: the mechanism involved is linked to the fact that the stress field near the free surface of a pile built with inclined strata obeys always the plasticity criteria, even when the slope is smaller than the friction angle. It results from this that the larger the slope angle the smaller the mean stress and the smaller the maximum principal stress. So when the pile rotates to generate the next instability the granular material is submitted to a decrease of the mean stress, resulting in an increase of its yielding angle, which becomes larger than the friction angle. The slope starts then flowing at an angle larger than the friction angle.

cond-mat.soft↗

arXiv2005

How to Fit simply Soil Mechanics Behaviour with Incremental Modelling and to Describe Drained Cyclic Behaviours

It has been proposed recently a new incremental modelling to describe the mechanics of soil. It is based on two parameters called the pseudo Young modulus E=1/Co and the pseudo Poisson coefficient n, which both evolve during compression. Evolution of n is known since it shall fit the Rowe's law of dilatancy, but Co has to be evaluated from experiment. In this paper we proposed a way to evaluate the Co variation from other mechanical modelling. The way cyclic behaviour of drained sample can be modelled is also described.

cond-mat.soft↗

arXiv2005

1-d granular gas with little dissipation in 0-g : A comment on "Resonance oscillations in Granular gases"

It is demonstrated that recent results on 1d granular gas in a container with a vibrating piston, which was modelled by a shock wave propagation, can be understood with a modelling using ideas coming from the "thermodynamics of a single particle". Defining e as the square root of the energetic-restitution coefficient of a single collision, and N as the total number of grains, the mean loss during a round trip of the momentum is calculated in the limit N(1-e)<<1. It is also demonstrated that the system cannot propagate sound waves nor shock waves in the limit of N(1-e)<<1 and that hydrodynamics equations cannot be defined when N(1-e)<<1. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

The Thermodynamics of a Single Bead in a Vibrating Container

Statistics of the 1d dynamics of a single particle in a box of length L is studied under different conditions of periodic excitation: vibrated container, or 1 wall moving periodically or two walls vibrating in opposite phases. Theoretical predictions for the mean typical speed are derived using some Random Phase Approximation (RPA) for small b/L ratio, as functions of the amplitude b and frequency f of vibration and of the collision restitution coefficient r=vout/vin. They are compared to numerical simulations. It is concluded that RPA is valid for b/L>0.005, that long time memory, i.e. non ergodicity, and/or resonance develop at large restitution coefficient r (r>0.95) and/or at large b/L, that scales always as f, and scales as b except for large b/L values, i.e. b/L>0.02, and that the relative velocity =[ /(bf)] is about 1 when r<0.4-0.5 . Relative standard deviation DV/V is found to be approximately constant, i.e. DV/V is about 0.3 except when resonance occurs; in this case, memory effect and non ergodicity effects are observed and become too important . Pacs # : 5.40 ; 45.70 ; 64 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

Phase transition or Maxwell's demon in Granular gas?

Dynamics of vibro-fluidised granular gas is investigated experimentally using the transfer of grains from a compartment through a horizontal slit at a given height h . It is demonstrated that the transfer rate j varies linearly with the grain number N in the box when N remains small; however j(N) becomes strongly non linear as soon as the number n of layers is larger than 0.3; dj/dN becomes negative for n>0.4.It is found also that the maximum of j(N) increases slightly with the acceleration af_ of the vibration which excites the granular gas. Using dynamical system theory, dynamics equations are written, and a critical bifurcation is found, which explains the existence of a condensation and of a phase transition. This explains how the pseudo " Maxwell's demon" works in granular gases. This experiments contradicts recent modeling . Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

Convection and motion in 2-d embankments under cyclic boundary conditions

The motion of grains in a 2d embankment under periodic horizontal forcing is studied theoretically using Coulomb-type modelling. Periodic conditions are used to determined the inclination of the free surface. It is shown that no periodic solution can be found in some domain of the bulk- and wall- friction parameters larger than 30 degrees. When a stable periodic solution exists, we show that the finite amplitude of motion leads to generate a flow localised (i) at the free surface, (ii) near the bulldozer wall and (iii) in the yield band; this may enforce a bulk convection too. At last, we argue why bulk convection is generated when the periodic solution is not stable. Results are compared to experimental data. Pacs # : 5.40.-a ; 5.45.-a ; 45.70.-n ; 62.20.-x ; 83.50.V

cond-mat.soft↗

arXiv2005

Distribution of contact forces in a homogeneous granular material of identical spheres under triaxial compression

The distribution P(F) of contact forces F in a homogeneous isotropic disordered granular sample subject to uniform triaxial stress field is studied using a model where forces propagate and collide. Collisions occur at grain and obey given rules which allow satisfying local static equilibrium. Analogy with Boltzmann's equation of density evolution is drawn and used to derive the parameters that control the distribution Ps(F) of contact forces F in the stationary state in case of a packing of mono-disperse spheres. Using symmetry argument and mean field approximation, it is found that stationarity is achieved when the density Ps(F) of force can be written as the product of exponentials of quantities whose sums are preserved during collisions. This introduces 3 parameters in 2d and 6 in 3d which are the mean force components {Fxo, Fyo, Fzo}, and the mean torques of the force on a grain {Mxo, Myo, Mzo} >. Astonishingly, it seems that the theory cannot include distribution of contact orientation implicitly. Extension of the model is possible with some care to case of anisotropic packing. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

Is Dissipative Granular Gas in Knudsen Regime Excited by Vibration Biphasic ?

Compatibility between a recent model (Poudres & Grains 15, 1-17, (2005)) of vibrated granular dissipative gas and recent experimental results in micro-gravity is investigated. It is found a good agreement for the distribution of impacts, which is found to vary exponentially as P(mv) = exp-(v/vo), both experimentally and theoretically; hence it confirms the distribution f(v) of speeds varying as (1/v) exp(-v/vo). However, some discrepancy is found for the variation of the total number of impacts with the number of balls contained in the cell. This is attributed to the existence of a second phase of balls "nearly at rest". Compatibility between results from granular gas experiments in micro-gravity and experiments on Maxwell's demon in 1-g is also discussed. The main idea, which allows understanding these results is to consider the piston as playing the role of an impact generator or of a "velostat" instead of a thermostat. It is shown also that the model predicts completely different behaviours in 1g and in 0g. Pacs # : 05.45.-a, 45.50.-j, 45.70.-n, 81.70.Bt, 81.70.Ha, 83.10.Pp

cond-mat.soft↗

arXiv2005

Experimental Stick-Slip Behaviour in Triaxial Test on Granular Matter

This paper is concerned with the quasi-static rheology of packings of glass spheres of diameter d (d=0.2mm, 0.7mm or 3mm). Stick-slip behaviour is observed on small spheres, i.e d=0.2mm & 0.7mm ; one observes also in this case a weakening of the rheology as the rate of deformation increases, and the larger the rate the larger the weakening; this generates macroscopic instabilities and stick-slip. Statistics of stick-slip events have been determined, which show that the larger the sample the more regular (i.e. "periodic") the sick-slip, the faster the strain rate the less periodic the events. One concludes that this stick-slip is generated at the macroscopic level and comes from the macroscopic rhelogical law. However when sample is small, local fluctuations perturb the macroscopic events and trigger them erratically. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

Macroscopic Continuous Approach versus Discrete Approach, Fluctuations, criticality and SOC. A state of the question based on articles in Powders & Grains 2001

The macroscopic continuous approach of the mechanics of granular media assumes that the whole system of discrete variables (contact locations, contact forces,...) can be replaced by continuous field equations relating stress and strain on macroscopic scale. On the contrary, recent approaches contest this validity on the basis that microscopic studies show the existence of large fluctuations of forces, of chains of forces,... This paper tries and establishes the state of this question using recent works reported at Powders & Grains 2001 which have studied the microscopic variables, their fluctuations and their evolution. This paper shows that these results validate the macroscopic approach despite the existence of these fluctuations. It concludes that the representative elementary volume is of few grains most of the time, except in some peculiar cases. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

Comparison between Classical-Gas behaviours and Granular-Gas ones in micro-gravity

Recent vibration experiments in microgravity are re-examined. We show that they demonstrate that "granular-gas" state exists only in the Knudsen regime, that its excitation is "supersonic" and that the probability density function of the pressure of the gas scales as (Af) to the power 3/2, with A and f being the excitation amplitude and frequency. This paper pursues the description of the experimental results. Then, it compares these ones to what can be predicted from few simple modelling, which are (i) the classical-gas theory and (ii) the thermodynamics of a single particle in a 1d box. The anomalous scaling of pressure fluctuations (Af) to the 3/2 is explained by the crossover from the regime of a single collision during the sampling time, which imposes p scales as_ (Af) at small speed, to a multiple collision imposing p scales as_(Af)_ . Air effect and effect of g-jitter are discussed and quantified. Influence of grain-grain collisions is described on the distribution of speed. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

Influence of boundary conditions on 2-fluid Systems under horizontal vibration

This paper is concerned with 2-phase systems under vibration in gravity condition, when the gravity is perpendicular to the direction of vibration. It tries and demonstrates that, even in such a restricted case, the patterns which can be formed are very sensitive to the cell shape, to the boundary conditions and to the direction and the mode of vibration, i.e. linear, rotational,... Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

The jamming surface of granular matter determined from soil mechanics results

Classical soil mechanics results are used to propose the equation of the jamming transition surface in the (stress, specific volume) space. Taking axis-ymmetric conditions, labelling q the deviatoric stress and p' the mean pressure applied on the granular skeleton, and considering normal range of pressure (10 kPa-10MPa) the equation of the surface of jamming transition is v = vo-m ln(p'/p'o)+ md ln(1+q q/(M' M' p' p')); M' is related to the friction angle, m and md are two constants which depend on soil characteristics; p'o is a "unit" pressure.

cond-mat.soft↗

arXiv2005

Are Temperature and other Thermodynamics Variables efficient Concepts for describing Granular Gases and/or Flows ?

Granular flows and vibro-fluidised granular gases have been extensively studied recently; most of the theoretical analyses and the experimental descriptions use temperature and other thermodynamics concepts. However, taking the very simple case of a vibro-fluidised gas made of identical particles, we show the lack of efficiency of such concepts for the understanding of the physics of such systems. This results from both (i) the fact that the vibrator does not transmit the same amount of energy to each particle, but an amount which depends on its mass and/or its size and (ii) from the fact that it is a strongly dissipative medium. We conclude that most experimental device works rather as velostat as a thermostat. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

On the role of Boundary Condition on the Speed- & Impact- Distributions in Dissipative Granular Gases in Knudsen Regime Excited by Vibration

Recent experimental results on granular gas in Knudsen regime excited by a vibrating piston in micro-gravity have measured distribution p(I) of impacts I with a fix target. They give p(I) scaling as exp(-I/Io). This distribution leads to a probability distribution function of speed v along z varying approximately as f(v) scaling as (1/v) exp(-v/vo); hence it diverges as 1/v at small speed and it is quite non Boltzmannian at large speed. Here, a model is proposed, which explains these experimental impact distributions; it takes account of the true role of the boundaries and of the dissipation in the gas. This validates the experimental data. Different approximations are discussed. Roles of boundaries and of 0-g condition are investigated theoretically. It is argued that the piston plays the role of an impact generator or a "velostat" for the Knudsen gas. These results cast a doubt on the efficiency of the notion of Boltzmann temperature and on the necessity to refer to Boltzman distribution in such dilute systems. The model shows also that the medium has to be considered as a whole, in global equilibrium: each part of the system is exchanging with the whole (at least in the direction of vibration); this is quite different from classic approach of dissipative systems based on local exchange and equilibrium, which leads to a "diffusive" Boltzmann equation; here the distribution f(z,t) is mainly propagative, i.e. f(z,v,t+dt)=f(z-vdt,v,t) instead of diffusive. Pacs # : 05.45.-a, 45.50.-j, 45.70.-n, 81.70.Bt, 81.70.Ha, 83.10.Pp

cond-mat.soft↗

arXiv2005

Fluctuations, Correlation and Representative Elementary Volume (REV) in Granular Materials

In general, the mechanics of granular matter is described using continuum mechanics approach; this requires to introduce the concepts of stress and strain, which are averaged quantities, so that this needs also to introduce the notion of representative elementary volume (REV) above which averaged quantities have some physical meaning. As local quantities fluctuate spatially in granular matter; a local measure of stress and strain shall exhibit fluctuations too, whose typical amplitude depends on the sampling size L. This paper discusses this problem and the causes for large scale correlation. The mean stress s applied to a plane surface of size L*L is calculated and its fluctuation amplitude Ds is found when local forces are not correlated; it is found that Ds/s scales as 1/L . It is shown also that large scale fluctuations of stress can always be interpreted as an inhomogeneous stress field and that static equilibrium modifies the mean stress applied to a rod (in 2d), even if it does not perturb the contact force distribution. This last result is compared to experiment, which indicates that the number N of contacts per rod (in 2d) is 2<N<3 . Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

Deformation Modes of a Packing of Rigid Grains: Rotation, Counter-rotation, dislocation field

The properties of the processes of deformation of a packing of rigid grains are analysed when the exact distribution of the normal forces at contacts is known. Importance of grain rotation and of counter-rotation of adjacent grains is stressed. It is shown that all deformation modes form an incomplete vectorial space D. This allows the statistics of fluctuation to be determined. Parallel with anti-ferromagnetism is then drawn and frustration of rotation is shown to be the leading dissipating mechanism. However this does not allow making the parallel with spinglass due to the structure of the space of deformation modes which is vectorial, which ensures response linearity. In order to demonstrate experimentally the validity of the approach and the existence of the incomplete vectorial space of deformation, experimental examples are studied starting from regular arrays. They do demonstrate the mechanism of counter-rotation and the existence of the vectorial space of deformation. This theory is applied to compare different experiment and simulation results on the deformation of square and triangular lattices of rods, which can only be done through a statistical approach based on existence of different modes of deformation. Non linear behaviour of the modes is demonstrated experimentally; link with the continuous theory of dislocation is made. Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

cond-mat.soft↗

arXiv2005

Three Comments on "A Simple Incremental Modelling of Granular-Media Mechanics"

Using the recent incremental modelling, it is shown that the trajectory of a sample in the phase space of soil mechanics in the vicinity of the critical state is not governed by the rigidity matrix, but by its variations. The characteristics are used to predict that pseudo Young modulus tends to 0 as B -M-1 tends to 0, i.e. near the critical point, where B is the vertical-to-lateral-stress ratio during an axi-symmetric test. An attempt to understand and predict unstable behaviours is done using the same modelling. Compatibility of this modelling with results on soil liquefaction is emphasised.

cond-mat.soft↗