Lees Edward

Problem description:

Now we study a more complex situation, in which a continuum formulation makes sense: granular media sheared at a constant rate The code can be found in LeesEdwardsSelfTest.cpp.

Granular media sheared.

Headers

#include "Mercury2D.h"
#include "Boundaries/LeesEdwardsBoundary.h"
#include "Species/LinearViscoelasticSlidingFrictionSpecies.h"

Before the main function

class LeesEdwardsSelfTest : public Mercury2D
{
    public:
 
    LeesEdwardsSelfTest() {
        //set parameters to define the species properties
 
        setName("LeesEdwardsSelfTest");
        dataFile.setFileType(FileType::ONE_FILE);
        fStatFile.setFileType(FileType::ONE_FILE);
 
        const Mdouble particleRadius = 0.5; // such that diameter is one
        const Mdouble collisionTime = 0.05; //relatively stiff particles
        const Mdouble restitution = 0.95; //restitution close to glass particles
        const Mdouble sizeDistribution = 1.5;
        const Mdouble volumeFraction = 0.82;
        const Mdouble velocity = 15.0;
 
        //define species
        auto species = speciesHandler.copyAndAddObject(LinearViscoelasticSlidingFrictionSpecies());
        species->setDensity(4.0 / constants::pi); //such that particle mass is one
        Mdouble mass = species->getMassFromRadius(particleRadius);
        species->setCollisionTimeAndNormalAndTangentialRestitutionCoefficient(
                collisionTime, restitution, restitution, mass); //set stiffness and dissipation
        species->setSlidingFrictionCoefficient(0.5);
 
        setTimeStep(0.02 * species->getCollisionTime(mass));
        setTimeMax(4.0); //run until the situation is static
        setSaveCount(100);
 
        //set domain size
        setMin({0, 0, 0});
        setMax({15, 15, 1});
        //set gravity
        setGravity({0, 0, 0});
 
 
        //define leesEdwardsBoundary
        LeesEdwardsBoundary leesEdwardsBoundary;
        leesEdwardsBoundary.set(
                [velocity](double time) { return time * velocity; },
                [velocity](double time UNUSED) { return velocity; },
                getXMin(), getXMax(), getYMin(), getYMax());
        boundaryHandler.copyAndAddObject(leesEdwardsBoundary);
 
        //define common particle properties
        SphericalParticle p;
        p.setSpecies(speciesHandler.getObject(0));
        p.setRadius(particleRadius);
        Mdouble rMin = 2.0 * particleRadius / (sizeDistribution + 1);
        Mdouble rMax = sizeDistribution * rMin;
        p.setRadius(rMax);
        logger(INFO, "Inserting particles of diameter % to %, volumeFraction %", 2.0 * rMin, 2.0 * rMax,
               volumeFraction);
 
        Mdouble particleVolumeMax = volumeFraction * (getXMax() - getXMin()) * (getYMax() - getYMin());
        Mdouble particleVolume = 0;
        Vec3D position = {0, 0, 0};
        while (particleVolume + 0.5 * p.getVolume() < particleVolumeMax) {
            position.X = random.getRandomNumber(getXMin(), getXMax());
            position.Y = random.getRandomNumber(getYMin(), getYMax());
            p.setPosition(position);
            particleHandler.copyAndAddObject(p);
            particleVolume += p.getVolume();
            p.setRadius(random.getRandomNumber(rMin, rMax));
        }
 
    }
 
 
};

Main function

int main(int argc, char *argv[])
{
    //instantiate the class
    LeesEdwardsSelfTest problem;
    //set output and time stepping properties
    problem.setXBallsAdditionalArguments("-w0 -v0 -solidf -cmode 5");
    //solve
    problem.solve(argc, argv);
 
    logger(INFO,"Execute 'source LeesEdwardsSelfTest.sh' to get coarse-grained statistics");
    helpers::writeToFile("LeesEdwardsSelfTest.sh","../MercuryCG/fstatistics LeesEdwardsSelfTest -stattype XY -w 0.25 -h 0.25 -tmin 2\n"
     "../MercuryCG/fstatistics LeesEdwardsSelfTest -stattype Y -w 0.25 -h 0.1 -tmin 2 -o LeesEdwardsSelfTest.Y.stat");
 
    logger(INFO,"Run 'LeesEdwardsSelfTest.m' in MATLAB/octave to visualise the statistical output");
    helpers::writeToFile("LeesEdwardsSelfTest.m","%% 2D velocity field v_x(x,y)\n"
     "addpath('../MercuryCG/')\n"
     "data = loadstatistics('LeesEdwardsSelfTest.stat');\n"
     "colormap(jet)\n"
     "contourf(data.x,data.y,data.VelocityX,20,'EdgeColor','none')\n"
     "c = colorbar\n"
     "c.Label.String = '\\rho';\n"
     "title('Velocity')\n"
     "xlabel('x')\n"
     "ylabel('z');\n"
     "axis equal\n"
     "%% 1D velocity field v_x(y)\n"
     "dataY = loadstatistics('LeesEdwardsSelfTest.Y.stat');\n"
     "plot(dataY.y,dataY.VelocityX)\n"
     "xlabel('y')\n"
     "ylabel('v_x');\n"
     "axis equal");
 
    return 0;
}

Reference:

Lees, A. W., & Edwards, S. F. (1972). The computer study of transport processes under extreme conditions. Journal of Physics C: Solid State Physics, 5(15), 1921.
Granular Flow: From Dilute to Jammed States.

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