Simple sintering process

Problem description:

This tutorial present a simple case of sintering between two particles. The code can be found in SinterPair.cpp.

Sintering of two particles.

Headers

#include "Mercury3D.h"
#include "Species/SinterSpecies.h"

Before the main function

class SinterPair : public Mercury3D
{
public:
    explicit SinterPair (Mdouble radius)
    {
        std::string r = helpers::toString(radius);
        setName("SinterPair"+r);
        helpers::writeToFile("SinterPair"+r+".gnu",
                             "set xlabel 'time [s]'\n"
                              "set ylabel 'x/a [nm]'\n"
                              "r="+r+"\n"
                              "plot 'SinterPair"+r+".fstat' u ($1):(sqrt($7/r)) w lp\n"
        );
 
        setGravity({0,0,0});
        setSaveCount(20000);
        setTimeMax(20);
        setMin({-2*radius,-radius,-radius});
        setMax({2*radius,radius,radius});
        setParticlesWriteVTK(true);
 
        const Mdouble stiffness = 1e-2 * radius;
        const Mdouble restitutionCoefficient = 0.1;
        const Mdouble density = 1005;
 
        SinterSpecies s;
        s.setHandler(&speciesHandler);
        s.setDensity(density);
        const Mdouble mass = s.getMassFromRadius(radius);
        s.setStiffnessAndRestitutionCoefficient(stiffness,restitutionCoefficient,mass);
        s.setPlasticParameters(stiffness, 10*stiffness, stiffness, 0.16);
        const Mdouble collisionTime = s.getCollisionTime(mass);
        logger(INFO,"Collision time %",collisionTime);
        s.setSinterType(SINTERTYPE::CONSTANT_RATE);
        s.setSinterRate(4e-10/radius);
        s.setSinterAdhesion(0.013*stiffness);
        //adhesiveForce = sinterAdhesion*radius;
        auto species = speciesHandler.copyAndAddObject(s);
 
        setTimeStep(0.02*collisionTime);
 
        SphericalParticle p;
        p.setSpecies(species);
        p.setRadius(radius);
        p.setPosition({-(1-1e-15)*radius,0,0});
        particleHandler.copyAndAddObject(p);
        p.setPosition(-p.getPosition());
        particleHandler.copyAndAddObject(p);
    }
 
    void printTime() const override
    {
        logger(INFO, "t=%3, tmax=%3, r=%3", getTime(), getTimeMax(), particleHandler.getLastObject()->getRadius());
         //<< ", Ekin=" << std::setprecision(3) << std::left << std::setw(6) << getKineticEnergy()/getElasticEnergy()
    }
 
};

Main function

There are three different radii for this tutorial: 1.5e-6, 2.0e-6, 5.0e-7

int main(int argc UNUSED, char *argv[] UNUSED)
{
    SinterPair sp0(2e-6);
    sp0.solve();
    SinterPair sp1(1.5e-6);
    sp1.solve();
    SinterPair sp2(5e-7);
    sp2.solve();
 
    helpers::writeToFile("SinterPair.gnu",
                         "set xlabel 'time [s]'\n"
                         "set ylabel 'x/a'\n"
                         "plot [0:200] 'SinterPair5e-07.fstat' u ($1):(sqrt($7/5e-07)) w lp lt rgb 'royalblue'\n"
                         "replot 'SinterPair1.5e-06.fstat' u ($1):(sqrt($7/1.5e-06)) w lp lt rgb 'light-red'\n"
                         "replot 'SinterPair2e-06.fstat' u ($1):(sqrt($7/2e-06)) w lp lt rgb 'sea-green'"
    );
    logger(INFO, "Execute 'gnuplot SinterPair.gnu' to view output");
}

Reference:

Fuchs, R., Weinhart, T., Ye, M., Luding, S., Butt, H. J., & Kappl, M. (2017). Initial stage sintering of polymer particles–Experiments and modelling of size-, temperature-and time-dependent contacts. In EPJ Web of Conferences (Vol. 140, p. 13012). EDP Sciences.

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