1704 lines
54 KiB
C++
1704 lines
54 KiB
C++
/* ----------------------------------------------------------------------
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LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
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https://lammps.sandia.gov/, Sandia National Laboratories
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Steve Plimpton, sjplimp@sandia.gov
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Copyright (2003) Sandia Corporation. Under the terms of Contract
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DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
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certain rights in this software. This software is distributed under
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the GNU General Public License.
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See the README file in the top-level LAMMPS directory.
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------------------------------------------------------------------------- */
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/* ----------------------------------------------------------------------
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Contributing authors: Leo Silbert (SNL), Gary Grest (SNL),
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Dan Bolintineanu (SNL)
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------------------------------------------------------------------------- */
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#include "fix_wall_gran.h"
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#include "atom.h"
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#include "domain.h"
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#include "error.h"
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#include "force.h"
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#include "math_const.h"
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#include "memory.h"
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#include "modify.h"
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#include "neighbor.h"
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#include "respa.h"
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#include "update.h"
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#include <cmath>
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#include <cstring>
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using namespace LAMMPS_NS;
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using namespace FixConst;
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using namespace MathConst;
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#define PI27SQ 266.47931882941264802866 // 27*PI**2
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#define THREEROOT3 5.19615242270663202362 // 3*sqrt(3)
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#define SIXROOT6 14.69693845669906728801 // 6*sqrt(6)
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#define INVROOT6 0.40824829046386307274 // 1/sqrt(6)
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#define FOURTHIRDS 1.333333333333333 // 4/3
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#define THREEQUARTERS 0.75 // 3/4
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#define TWOPI 6.28318530717959 // 2*PI
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#define BIG 1.0e20
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#define EPSILON 1e-10
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// XYZ PLANE need to be 0,1,2
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enum {XPLANE=0,YPLANE=1,ZPLANE=2,ZCYLINDER,REGION};
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enum {NONE,CONSTANT,EQUAL};
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enum {DAMPING_NONE, VELOCITY, MASS_VELOCITY, VISCOELASTIC, TSUJI};
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enum {TANGENTIAL_NONE, TANGENTIAL_NOHISTORY, TANGENTIAL_HISTORY,
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TANGENTIAL_MINDLIN, TANGENTIAL_MINDLIN_RESCALE,
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TANGENTIAL_MINDLIN_FORCE, TANGENTIAL_MINDLIN_RESCALE_FORCE};
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enum {TWIST_NONE, TWIST_SDS, TWIST_MARSHALL};
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enum {ROLL_NONE, ROLL_SDS};
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/* ---------------------------------------------------------------------- */
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FixWallGran::FixWallGran(LAMMPS *lmp, int narg, char **arg) :
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Fix(lmp, narg, arg), idregion(nullptr), history_one(nullptr),
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fix_rigid(nullptr), mass_rigid(nullptr)
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{
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if (narg < 4) error->all(FLERR,"Illegal fix wall/gran command");
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if (!atom->sphere_flag)
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error->all(FLERR,"Fix wall/gran requires atom style sphere");
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create_attribute = 1;
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limit_damping = 0;
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// set interaction style
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// disable bonded/history option for now
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if (strcmp(arg[3],"hooke") == 0) pairstyle = HOOKE;
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else if (strcmp(arg[3],"hooke/history") == 0) pairstyle = HOOKE_HISTORY;
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else if (strcmp(arg[3],"hertz/history") == 0) pairstyle = HERTZ_HISTORY;
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else if (strcmp(arg[3],"granular") == 0) pairstyle = GRANULAR;
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else error->all(FLERR,"Invalid fix wall/gran interaction style");
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use_history = restart_peratom = 1;
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if (pairstyle == HOOKE) use_history = restart_peratom = 0;
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tangential_history = roll_history = twist_history = 0;
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normal_model = NORMAL_NONE;
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tangential_model = TANGENTIAL_NONE;
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damping_model = DAMPING_NONE;
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// wall/particle coefficients
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int iarg;
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if (pairstyle != GRANULAR) {
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size_history = 3;
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if (narg < 11) error->all(FLERR,"Illegal fix wall/gran command");
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kn = utils::numeric(FLERR,arg[4],false,lmp);
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if (strcmp(arg[5],"NULL") == 0) kt = kn * 2.0/7.0;
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else kt = utils::numeric(FLERR,arg[5],false,lmp);
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gamman = utils::numeric(FLERR,arg[6],false,lmp);
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if (strcmp(arg[7],"NULL") == 0) gammat = 0.5 * gamman;
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else gammat = utils::numeric(FLERR,arg[7],false,lmp);
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xmu = utils::numeric(FLERR,arg[8],false,lmp);
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int dampflag = utils::inumeric(FLERR,arg[9],false,lmp);
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if (dampflag == 0) gammat = 0.0;
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if (kn < 0.0 || kt < 0.0 || gamman < 0.0 || gammat < 0.0 ||
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xmu < 0.0 || xmu > 10000.0 || dampflag < 0 || dampflag > 1)
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error->all(FLERR,"Illegal fix wall/gran command");
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// convert Kn and Kt from pressure units to force/distance^2 if Hertzian
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if (pairstyle == HERTZ_HISTORY) {
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kn /= force->nktv2p;
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kt /= force->nktv2p;
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}
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iarg = 10;
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if (strcmp(arg[iarg],"limit_damping") == 0) {
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limit_damping = 1;
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iarg += 1;
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}
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} else {
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iarg = 4;
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damping_model = VISCOELASTIC;
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roll_model = twist_model = NONE;
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while (iarg < narg) {
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if (strcmp(arg[iarg], "hooke") == 0) {
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if (iarg + 2 >= narg)
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error->all(FLERR,"Illegal fix wall/gran command, "
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"not enough parameters provided for Hooke option");
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normal_model = NORMAL_HOOKE;
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normal_coeffs[0] = utils::numeric(FLERR,arg[iarg+1],false,lmp); //kn
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normal_coeffs[1] = utils::numeric(FLERR,arg[iarg+2],false,lmp); //damping
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iarg += 3;
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} else if (strcmp(arg[iarg], "hertz") == 0) {
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int num_coeffs = 2;
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if (iarg + num_coeffs >= narg)
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error->all(FLERR,"Illegal fix wall/gran command, "
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"not enough parameters provided for Hertz option");
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normal_model = NORMAL_HERTZ;
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normal_coeffs[0] = utils::numeric(FLERR,arg[iarg+1],false,lmp); //kn
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normal_coeffs[1] = utils::numeric(FLERR,arg[iarg+2],false,lmp); //damping
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iarg += num_coeffs+1;
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} else if (strcmp(arg[iarg], "hertz/material") == 0) {
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int num_coeffs = 3;
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if (iarg + num_coeffs >= narg)
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error->all(FLERR,"Illegal fix wall/gran command, "
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"not enough parameters provided for Hertz option");
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normal_model = HERTZ_MATERIAL;
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Emod = utils::numeric(FLERR,arg[iarg+1],false,lmp); //E
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normal_coeffs[1] = utils::numeric(FLERR,arg[iarg+2],false,lmp); //damping
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poiss = utils::numeric(FLERR,arg[iarg+3],false,lmp); //Poisson's ratio
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normal_coeffs[0] = Emod/(2*(1-poiss))*FOURTHIRDS;
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normal_coeffs[2] = poiss;
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iarg += num_coeffs+1;
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} else if (strcmp(arg[iarg], "dmt") == 0) {
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if (iarg + 4 >= narg)
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error->all(FLERR,"Illegal fix wall/gran command, "
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"not enough parameters provided for Hertz option");
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normal_model = DMT;
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Emod = utils::numeric(FLERR,arg[iarg+1],false,lmp); //E
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normal_coeffs[1] = utils::numeric(FLERR,arg[iarg+2],false,lmp); //damping
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poiss = utils::numeric(FLERR,arg[iarg+3],false,lmp); //Poisson's ratio
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normal_coeffs[0] = Emod/(2*(1-poiss))*FOURTHIRDS;
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normal_coeffs[2] = poiss;
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normal_coeffs[3] = utils::numeric(FLERR,arg[iarg+4],false,lmp); //cohesion
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iarg += 5;
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} else if (strcmp(arg[iarg], "jkr") == 0) {
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if (iarg + 4 >= narg)
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error->all(FLERR,"Illegal wall/gran command, "
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"not enough parameters provided for JKR option");
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normal_model = JKR;
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Emod = utils::numeric(FLERR,arg[iarg+1],false,lmp); //E
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normal_coeffs[1] = utils::numeric(FLERR,arg[iarg+2],false,lmp); //damping
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poiss = utils::numeric(FLERR,arg[iarg+3],false,lmp); //Poisson's ratio
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normal_coeffs[0] = Emod/(2*(1-poiss))*FOURTHIRDS;
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normal_coeffs[2] = poiss;
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normal_coeffs[3] = utils::numeric(FLERR,arg[iarg+4],false,lmp); //cohesion
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iarg += 5;
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} else if (strcmp(arg[iarg], "damping") == 0) {
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if (iarg+1 >= narg)
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error->all(FLERR, "Illegal wall/gran command, "
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"not enough parameters provided for damping model");
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if (strcmp(arg[iarg+1], "velocity") == 0) {
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damping_model = VELOCITY;
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iarg += 1;
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} else if (strcmp(arg[iarg+1], "mass_velocity") == 0) {
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damping_model = MASS_VELOCITY;
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iarg += 1;
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} else if (strcmp(arg[iarg+1], "viscoelastic") == 0) {
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damping_model = VISCOELASTIC;
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iarg += 1;
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} else if (strcmp(arg[iarg+1], "tsuji") == 0) {
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damping_model = TSUJI;
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iarg += 1;
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} else error->all(FLERR, "Illegal wall/gran command, "
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"unrecognized damping model");
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iarg += 1;
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} else if (strcmp(arg[iarg], "tangential") == 0) {
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if (iarg + 1 >= narg)
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error->all(FLERR,"Illegal pair_coeff command, "
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"must specify tangential model after tangential keyword");
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if (strcmp(arg[iarg+1], "linear_nohistory") == 0) {
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if (iarg + 3 >= narg)
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error->all(FLERR,"Illegal pair_coeff command, "
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"not enough parameters provided for tangential model");
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tangential_model = TANGENTIAL_NOHISTORY;
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tangential_coeffs[0] = 0;
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// gammat and friction coeff
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tangential_coeffs[1] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
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tangential_coeffs[2] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
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iarg += 4;
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} else if ((strcmp(arg[iarg+1], "linear_history") == 0) ||
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(strcmp(arg[iarg+1], "mindlin") == 0) ||
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(strcmp(arg[iarg+1], "mindlin_rescale") == 0) ||
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(strcmp(arg[iarg+1], "mindlin/force") == 0) ||
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(strcmp(arg[iarg+1], "mindlin_rescale/force") == 0)) {
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if (iarg + 4 >= narg)
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error->all(FLERR,"Illegal pair_coeff command, "
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"not enough parameters provided for tangential model");
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if (strcmp(arg[iarg+1], "linear_history") == 0)
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tangential_model = TANGENTIAL_HISTORY;
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else if (strcmp(arg[iarg+1], "mindlin") == 0)
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tangential_model = TANGENTIAL_MINDLIN;
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else if (strcmp(arg[iarg+1], "mindlin_rescale") == 0)
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tangential_model = TANGENTIAL_MINDLIN_RESCALE;
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else if (strcmp(arg[iarg+1], "mindlin/force") == 0)
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tangential_model = TANGENTIAL_MINDLIN_FORCE;
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else if (strcmp(arg[iarg+1], "mindlin_rescale/force") == 0)
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tangential_model = TANGENTIAL_MINDLIN_RESCALE_FORCE;
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if ((tangential_model == TANGENTIAL_MINDLIN ||
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tangential_model == TANGENTIAL_MINDLIN_RESCALE ||
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tangential_model == TANGENTIAL_MINDLIN_FORCE ||
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tangential_model == TANGENTIAL_MINDLIN_RESCALE_FORCE) &&
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(strcmp(arg[iarg+2], "NULL") == 0)) {
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if (normal_model == NORMAL_HERTZ || normal_model == NORMAL_HOOKE) {
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error->all(FLERR, "NULL setting for Mindlin tangential "
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"stiffness requires a normal contact model "
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"that specifies material properties");
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}
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tangential_coeffs[0] = Emod/4*(2-poiss)*(1+poiss);
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} else {
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tangential_coeffs[0] = utils::numeric(FLERR,arg[iarg+2],false,lmp); //kt
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}
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tangential_history = 1;
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// gammat and friction coeff
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tangential_coeffs[1] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
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tangential_coeffs[2] = utils::numeric(FLERR,arg[iarg+4],false,lmp);
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iarg += 5;
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} else {
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error->all(FLERR, "Illegal pair_coeff command, "
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"tangential model not recognized");
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}
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} else if (strcmp(arg[iarg], "rolling") == 0) {
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if (iarg + 1 >= narg)
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error->all(FLERR, "Illegal wall/gran command, not enough parameters");
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if (strcmp(arg[iarg+1], "none") == 0) {
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roll_model = ROLL_NONE;
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iarg += 2;
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} else if (strcmp(arg[iarg+1], "sds") == 0) {
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if (iarg + 4 >= narg)
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error->all(FLERR,"Illegal wall/gran command, "
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"not enough parameters provided for rolling model");
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roll_model = ROLL_SDS;
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roll_history = 1;
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// kR, gammaR, rolling friction coeff
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roll_coeffs[0] = utils::numeric(FLERR,arg[iarg+2],false,lmp);
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roll_coeffs[1] = utils::numeric(FLERR,arg[iarg+3],false,lmp);
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roll_coeffs[2] = utils::numeric(FLERR,arg[iarg+4],false,lmp);
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iarg += 5;
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} else {
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error->all(FLERR, "Illegal wall/gran command, "
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"rolling friction model not recognized");
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}
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} else if (strcmp(arg[iarg], "twisting") == 0) {
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if (iarg + 1 >= narg)
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error->all(FLERR, "Illegal wall/gran command, not enough parameters");
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if (strcmp(arg[iarg+1], "none") == 0) {
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twist_model = TWIST_NONE;
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iarg += 2;
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} else if (strcmp(arg[iarg+1], "marshall") == 0) {
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twist_model = TWIST_MARSHALL;
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twist_history = 1;
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iarg += 2;
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} else if (strcmp(arg[iarg+1], "sds") == 0) {
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if (iarg + 4 >= narg)
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error->all(FLERR,"Illegal wall/gran command, "
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"not enough parameters provided for twist model");
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twist_model = TWIST_SDS;
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twist_history = 1;
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twist_coeffs[0] = utils::numeric(FLERR,arg[iarg+2],false,lmp); //kt
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twist_coeffs[1] = utils::numeric(FLERR,arg[iarg+3],false,lmp); //gammat
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twist_coeffs[2] = utils::numeric(FLERR,arg[iarg+4],false,lmp); //friction coeff.
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iarg += 5;
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} else {
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error->all(FLERR, "Illegal wall/gran command, "
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"twisting friction model not recognized");
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}
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} else if (strcmp(arg[iarg], "xplane") == 0 ||
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strcmp(arg[iarg], "yplane") == 0 ||
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strcmp(arg[iarg], "zplane") == 0 ||
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strcmp(arg[iarg], "zcylinder") == 0 ||
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strcmp(arg[iarg], "region") == 0) {
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break;
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} else if (strcmp(arg[iarg],"limit_damping") == 0) {
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limit_damping = 1;
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iarg += 1;
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} else {
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error->all(FLERR, "Illegal fix wall/gran command");
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}
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}
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size_history = 3*tangential_history + 3*roll_history + twist_history;
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//Unlike the pair style, the wall style does not have a 'touch'
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//array. Hence, an additional entry in the history is used to
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//determine if particles previously contacted for JKR cohesion purposes.
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if (normal_model == JKR) size_history += 1;
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if (tangential_model == TANGENTIAL_MINDLIN_RESCALE ||
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tangential_model == TANGENTIAL_MINDLIN_RESCALE_FORCE) size_history += 1;
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if (limit_damping && normal_model == JKR)
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error->all(FLERR,"Illegal pair_coeff command, "
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"cannot limit damping with JRK model");
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if (limit_damping && normal_model == DMT)
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error->all(FLERR,"Illegal pair_coeff command, "
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"Cannot limit damping with DMT model");
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}
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// wallstyle args
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idregion = nullptr;
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if (strcmp(arg[iarg],"xplane") == 0) {
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if (narg < iarg+3) error->all(FLERR,"Illegal fix wall/gran command");
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wallstyle = XPLANE;
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if (strcmp(arg[iarg+1],"NULL") == 0) lo = -BIG;
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else lo = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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if (strcmp(arg[iarg+2],"NULL") == 0) hi = BIG;
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else hi = utils::numeric(FLERR,arg[iarg+2],false,lmp);
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iarg += 3;
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} else if (strcmp(arg[iarg],"yplane") == 0) {
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if (narg < iarg+3) error->all(FLERR,"Illegal fix wall/gran command");
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wallstyle = YPLANE;
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if (strcmp(arg[iarg+1],"NULL") == 0) lo = -BIG;
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else lo = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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if (strcmp(arg[iarg+2],"NULL") == 0) hi = BIG;
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else hi = utils::numeric(FLERR,arg[iarg+2],false,lmp);
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iarg += 3;
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} else if (strcmp(arg[iarg],"zplane") == 0) {
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if (narg < iarg+3) error->all(FLERR,"Illegal fix wall/gran command");
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wallstyle = ZPLANE;
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if (strcmp(arg[iarg+1],"NULL") == 0) lo = -BIG;
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else lo = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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if (strcmp(arg[iarg+2],"NULL") == 0) hi = BIG;
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else hi = utils::numeric(FLERR,arg[iarg+2],false,lmp);
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iarg += 3;
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} else if (strcmp(arg[iarg],"zcylinder") == 0) {
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if (narg < iarg+2) error->all(FLERR,"Illegal fix wall/gran command");
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wallstyle = ZCYLINDER;
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lo = hi = 0.0;
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cylradius = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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iarg += 2;
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} else if (strcmp(arg[iarg],"region") == 0) {
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if (narg < iarg+2) error->all(FLERR,"Illegal fix wall/gran command");
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wallstyle = REGION;
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idregion = utils::strdup(arg[iarg+1]);
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iarg += 2;
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}
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// optional args
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wiggle = 0;
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wshear = 0;
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peratom_flag = 0;
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while (iarg < narg) {
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if (strcmp(arg[iarg],"wiggle") == 0) {
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if (iarg+4 > narg) error->all(FLERR,"Illegal fix wall/gran command");
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if (strcmp(arg[iarg+1],"x") == 0) axis = 0;
|
|
else if (strcmp(arg[iarg+1],"y") == 0) axis = 1;
|
|
else if (strcmp(arg[iarg+1],"z") == 0) axis = 2;
|
|
else error->all(FLERR,"Illegal fix wall/gran command");
|
|
amplitude = utils::numeric(FLERR,arg[iarg+2],false,lmp);
|
|
period = utils::numeric(FLERR,arg[iarg+3],false,lmp);
|
|
wiggle = 1;
|
|
iarg += 4;
|
|
} else if (strcmp(arg[iarg],"shear") == 0) {
|
|
if (iarg+3 > narg) error->all(FLERR,"Illegal fix wall/gran command");
|
|
if (strcmp(arg[iarg+1],"x") == 0) axis = 0;
|
|
else if (strcmp(arg[iarg+1],"y") == 0) axis = 1;
|
|
else if (strcmp(arg[iarg+1],"z") == 0) axis = 2;
|
|
else error->all(FLERR,"Illegal fix wall/gran command");
|
|
vshear = utils::numeric(FLERR,arg[iarg+2],false,lmp);
|
|
wshear = 1;
|
|
iarg += 3;
|
|
} else if (strcmp(arg[iarg],"contacts") == 0) {
|
|
peratom_flag = 1;
|
|
size_peratom_cols = 8;
|
|
peratom_freq = 1;
|
|
iarg += 1;
|
|
} else error->all(FLERR,"Illegal fix wall/gran command");
|
|
}
|
|
|
|
if (wallstyle == XPLANE && domain->xperiodic)
|
|
error->all(FLERR,"Cannot use wall in periodic dimension");
|
|
if (wallstyle == YPLANE && domain->yperiodic)
|
|
error->all(FLERR,"Cannot use wall in periodic dimension");
|
|
if (wallstyle == ZPLANE && domain->zperiodic)
|
|
error->all(FLERR,"Cannot use wall in periodic dimension");
|
|
if (wallstyle == ZCYLINDER && (domain->xperiodic || domain->yperiodic))
|
|
error->all(FLERR,"Cannot use wall in periodic dimension");
|
|
|
|
if (wiggle && wshear)
|
|
error->all(FLERR,"Cannot wiggle and shear fix wall/gran");
|
|
if (wiggle && wallstyle == ZCYLINDER && axis != 2)
|
|
error->all(FLERR,"Invalid wiggle direction for fix wall/gran");
|
|
if (wshear && wallstyle == XPLANE && axis == 0)
|
|
error->all(FLERR,"Invalid shear direction for fix wall/gran");
|
|
if (wshear && wallstyle == YPLANE && axis == 1)
|
|
error->all(FLERR,"Invalid shear direction for fix wall/gran");
|
|
if (wshear && wallstyle == ZPLANE && axis == 2)
|
|
error->all(FLERR,"Invalid shear direction for fix wall/gran");
|
|
if ((wiggle || wshear) && wallstyle == REGION)
|
|
error->all(FLERR,"Cannot wiggle or shear with fix wall/gran/region");
|
|
|
|
// setup oscillations
|
|
|
|
if (wiggle) omega = 2.0*MY_PI / period;
|
|
|
|
// perform initial allocation of atom-based arrays
|
|
// register with Atom class
|
|
|
|
history_one = nullptr;
|
|
grow_arrays(atom->nmax);
|
|
atom->add_callback(Atom::GROW);
|
|
atom->add_callback(Atom::RESTART);
|
|
|
|
nmax = 0;
|
|
mass_rigid = nullptr;
|
|
|
|
// initialize history as if particle is not touching region
|
|
// history_one will be a null pointer for wallstyle = REGION
|
|
|
|
if (use_history && history_one) {
|
|
int nlocal = atom->nlocal;
|
|
for (int i = 0; i < nlocal; i++)
|
|
for (int j = 0; j < size_history; j++)
|
|
history_one[i][j] = 0.0;
|
|
}
|
|
|
|
if (peratom_flag) {
|
|
clear_stored_contacts();
|
|
}
|
|
|
|
time_origin = update->ntimestep;
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
FixWallGran::~FixWallGran()
|
|
{
|
|
// unregister callbacks to this fix from Atom class
|
|
|
|
atom->delete_callback(id,Atom::GROW);
|
|
atom->delete_callback(id,Atom::RESTART);
|
|
|
|
// delete local storage
|
|
|
|
delete [] idregion;
|
|
memory->destroy(history_one);
|
|
memory->destroy(mass_rigid);
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
int FixWallGran::setmask()
|
|
{
|
|
int mask = 0;
|
|
mask |= POST_FORCE;
|
|
mask |= POST_FORCE_RESPA;
|
|
return mask;
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::init()
|
|
{
|
|
int i;
|
|
|
|
dt = update->dt;
|
|
|
|
if (utils::strmatch(update->integrate_style,"^respa"))
|
|
nlevels_respa = ((Respa *) update->integrate)->nlevels;
|
|
|
|
// check for FixRigid so can extract rigid body masses
|
|
|
|
fix_rigid = nullptr;
|
|
for (i = 0; i < modify->nfix; i++)
|
|
if (modify->fix[i]->rigid_flag) break;
|
|
if (i < modify->nfix) fix_rigid = modify->fix[i];
|
|
|
|
if(pairstyle == GRANULAR) {
|
|
tangential_history_index = 0;
|
|
if (roll_history) {
|
|
if (tangential_history) roll_history_index = 3;
|
|
else roll_history_index = 0;
|
|
}
|
|
if (twist_history) {
|
|
if (tangential_history) {
|
|
if (roll_history) twist_history_index = 6;
|
|
else twist_history_index = 3;
|
|
}
|
|
else{
|
|
if (roll_history) twist_history_index = 3;
|
|
else twist_history_index = 0;
|
|
}
|
|
}
|
|
if (normal_model == JKR) {
|
|
tangential_history_index += 1;
|
|
roll_history_index += 1;
|
|
twist_history_index += 1;
|
|
}
|
|
if (tangential_model == TANGENTIAL_MINDLIN_RESCALE ||
|
|
tangential_model == TANGENTIAL_MINDLIN_RESCALE_FORCE) {
|
|
roll_history_index += 1;
|
|
twist_history_index += 1;
|
|
}
|
|
|
|
if (damping_model == TSUJI) {
|
|
double cor = normal_coeffs[1];
|
|
normal_coeffs[1] = 1.2728-4.2783*cor+11.087*pow(cor,2)-22.348*pow(cor,3)+
|
|
27.467*pow(cor,4)-18.022*pow(cor,5)+
|
|
4.8218*pow(cor,6);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::setup(int vflag)
|
|
{
|
|
if (utils::strmatch(update->integrate_style,"^verlet"))
|
|
post_force(vflag);
|
|
else {
|
|
((Respa *) update->integrate)->copy_flevel_f(nlevels_respa-1);
|
|
post_force_respa(vflag,nlevels_respa-1,0);
|
|
((Respa *) update->integrate)->copy_f_flevel(nlevels_respa-1);
|
|
}
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::post_force(int /*vflag*/)
|
|
{
|
|
int i,j;
|
|
double dx,dy,dz,del1,del2,delxy,delr,rsq,rwall,meff;
|
|
double vwall[3];
|
|
|
|
// do not update history during setup
|
|
|
|
history_update = 1;
|
|
if (update->setupflag) history_update = 0;
|
|
|
|
// if just reneighbored:
|
|
// update rigid body masses for owned atoms if using FixRigid
|
|
// body[i] = which body atom I is in, -1 if none
|
|
// mass_body = mass of each rigid body
|
|
|
|
if (neighbor->ago == 0 && fix_rigid) {
|
|
int tmp;
|
|
int *body = (int *) fix_rigid->extract("body",tmp);
|
|
double *mass_body = (double *) fix_rigid->extract("masstotal",tmp);
|
|
if (atom->nmax > nmax) {
|
|
memory->destroy(mass_rigid);
|
|
nmax = atom->nmax;
|
|
memory->create(mass_rigid,nmax,"wall/gran:mass_rigid");
|
|
}
|
|
int nlocal = atom->nlocal;
|
|
for (i = 0; i < nlocal; i++) {
|
|
if (body[i] >= 0) mass_rigid[i] = mass_body[body[i]];
|
|
else mass_rigid[i] = 0.0;
|
|
}
|
|
}
|
|
|
|
// set position of wall to initial settings and velocity to 0.0
|
|
// if wiggle or shear, set wall position and velocity accordingly
|
|
|
|
double wlo = lo;
|
|
double whi = hi;
|
|
vwall[0] = vwall[1] = vwall[2] = 0.0;
|
|
if (wiggle) {
|
|
double arg = omega * (update->ntimestep - time_origin) * dt;
|
|
if (wallstyle == axis) {
|
|
wlo = lo + amplitude - amplitude*cos(arg);
|
|
whi = hi + amplitude - amplitude*cos(arg);
|
|
}
|
|
vwall[axis] = amplitude*omega*sin(arg);
|
|
} else if (wshear) vwall[axis] = vshear;
|
|
|
|
// loop over all my atoms
|
|
// rsq = distance from wall
|
|
// dx,dy,dz = signed distance from wall
|
|
// for rotating cylinder, reset vwall based on particle position
|
|
// skip atom if not close enough to wall
|
|
// if wall was set to a null pointer, it's skipped since lo/hi are infinity
|
|
// compute force and torque on atom if close enough to wall
|
|
// via wall potential matched to pair potential
|
|
// set history if pair potential stores history
|
|
|
|
double **x = atom->x;
|
|
double **v = atom->v;
|
|
double **f = atom->f;
|
|
double **omega = atom->omega;
|
|
double **torque = atom->torque;
|
|
double *radius = atom->radius;
|
|
double *rmass = atom->rmass;
|
|
int *mask = atom->mask;
|
|
int nlocal = atom->nlocal;
|
|
|
|
rwall = 0.0;
|
|
|
|
if (peratom_flag) {
|
|
clear_stored_contacts();
|
|
}
|
|
|
|
for (int i = 0; i < nlocal; i++) {
|
|
if (mask[i] & groupbit) {
|
|
|
|
dx = dy = dz = 0.0;
|
|
|
|
if (wallstyle == XPLANE) {
|
|
del1 = x[i][0] - wlo;
|
|
del2 = whi - x[i][0];
|
|
if (del1 < del2) dx = del1;
|
|
else dx = -del2;
|
|
} else if (wallstyle == YPLANE) {
|
|
del1 = x[i][1] - wlo;
|
|
del2 = whi - x[i][1];
|
|
if (del1 < del2) dy = del1;
|
|
else dy = -del2;
|
|
} else if (wallstyle == ZPLANE) {
|
|
del1 = x[i][2] - wlo;
|
|
del2 = whi - x[i][2];
|
|
if (del1 < del2) dz = del1;
|
|
else dz = -del2;
|
|
} else if (wallstyle == ZCYLINDER) {
|
|
delxy = sqrt(x[i][0]*x[i][0] + x[i][1]*x[i][1]);
|
|
delr = cylradius - delxy;
|
|
if (delr > radius[i]) {
|
|
dz = cylradius;
|
|
rwall = 0.0;
|
|
} else {
|
|
dx = -delr/delxy * x[i][0];
|
|
dy = -delr/delxy * x[i][1];
|
|
// rwall = -2r_c if inside cylinder, 2r_c outside
|
|
rwall = (delxy < cylradius) ? -2*cylradius : 2*cylradius;
|
|
if (wshear && axis != 2) {
|
|
vwall[0] += vshear * x[i][1]/delxy;
|
|
vwall[1] += -vshear * x[i][0]/delxy;
|
|
vwall[2] = 0.0;
|
|
}
|
|
}
|
|
}
|
|
|
|
rsq = dx*dx + dy*dy + dz*dz;
|
|
|
|
double rad;
|
|
if (pairstyle == GRANULAR && normal_model == JKR) {
|
|
rad = radius[i] + pulloff_distance(radius[i]);
|
|
}
|
|
else
|
|
rad = radius[i];
|
|
|
|
if (rsq > rad*rad) {
|
|
if (use_history)
|
|
for (j = 0; j < size_history; j++)
|
|
history_one[i][j] = 0.0;
|
|
}
|
|
else {
|
|
if (pairstyle == GRANULAR && normal_model == JKR && use_history) {
|
|
if ((history_one[i][0] == 0) && (rsq > radius[i]*radius[i])) {
|
|
// Particles have not contacted yet,
|
|
// and are outside of contact distance
|
|
for (j = 0; j < size_history; j++)
|
|
history_one[i][j] = 0.0;
|
|
continue;
|
|
}
|
|
}
|
|
|
|
// meff = effective mass of sphere
|
|
// if I is part of rigid body, use body mass
|
|
|
|
meff = rmass[i];
|
|
if (fix_rigid && mass_rigid[i] > 0.0) meff = mass_rigid[i];
|
|
|
|
// store contact info
|
|
if (peratom_flag) {
|
|
array_atom[i][0] = 1.0;
|
|
array_atom[i][4] = x[i][0] - dx;
|
|
array_atom[i][5] = x[i][1] - dy;
|
|
array_atom[i][6] = x[i][2] - dz;
|
|
array_atom[i][7] = radius[i];
|
|
}
|
|
|
|
// invoke sphere/wall interaction
|
|
double *contact;
|
|
if (peratom_flag)
|
|
contact = array_atom[i];
|
|
else
|
|
contact = nullptr;
|
|
|
|
if (pairstyle == HOOKE)
|
|
hooke(rsq,dx,dy,dz,vwall,v[i],f[i],
|
|
omega[i],torque[i],radius[i],meff, contact);
|
|
else if (pairstyle == HOOKE_HISTORY)
|
|
hooke_history(rsq,dx,dy,dz,vwall,v[i],f[i],
|
|
omega[i],torque[i],radius[i],meff,history_one[i],
|
|
contact);
|
|
else if (pairstyle == HERTZ_HISTORY)
|
|
hertz_history(rsq,dx,dy,dz,vwall,rwall,v[i],f[i],
|
|
omega[i],torque[i],radius[i],meff,history_one[i],
|
|
contact);
|
|
else if (pairstyle == GRANULAR)
|
|
granular(rsq,dx,dy,dz,vwall,rwall,v[i],f[i],
|
|
omega[i],torque[i],radius[i],meff,history_one[i],
|
|
contact);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void FixWallGran::clear_stored_contacts() {
|
|
const int nlocal = atom->nlocal;
|
|
for (int i = 0; i < nlocal; i++) {
|
|
for (int m = 0; m < size_peratom_cols; m++) {
|
|
array_atom[i][m] = 0.0;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::post_force_respa(int vflag, int ilevel, int /*iloop*/)
|
|
{
|
|
if (ilevel == nlevels_respa-1) post_force(vflag);
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::hooke(double rsq, double dx, double dy, double dz,
|
|
double *vwall, double *v,
|
|
double *f, double *omega, double *torque,
|
|
double radius, double meff, double* contact)
|
|
{
|
|
double r,vr1,vr2,vr3,vnnr,vn1,vn2,vn3,vt1,vt2,vt3;
|
|
double wr1,wr2,wr3,damp,ccel,vtr1,vtr2,vtr3,vrel;
|
|
double fn,fs,ft,fs1,fs2,fs3,fx,fy,fz,tor1,tor2,tor3,rinv,rsqinv;
|
|
|
|
r = sqrt(rsq);
|
|
rinv = 1.0/r;
|
|
rsqinv = 1.0/rsq;
|
|
|
|
// relative translational velocity
|
|
|
|
vr1 = v[0] - vwall[0];
|
|
vr2 = v[1] - vwall[1];
|
|
vr3 = v[2] - vwall[2];
|
|
|
|
// normal component
|
|
|
|
vnnr = vr1*dx + vr2*dy + vr3*dz;
|
|
vn1 = dx*vnnr * rsqinv;
|
|
vn2 = dy*vnnr * rsqinv;
|
|
vn3 = dz*vnnr * rsqinv;
|
|
|
|
// tangential component
|
|
|
|
vt1 = vr1 - vn1;
|
|
vt2 = vr2 - vn2;
|
|
vt3 = vr3 - vn3;
|
|
|
|
// relative rotational velocity
|
|
|
|
wr1 = radius*omega[0] * rinv;
|
|
wr2 = radius*omega[1] * rinv;
|
|
wr3 = radius*omega[2] * rinv;
|
|
|
|
// normal forces = Hookian contact + normal velocity damping
|
|
|
|
damp = meff*gamman*vnnr*rsqinv;
|
|
ccel = kn*(radius-r)*rinv - damp;
|
|
if (limit_damping && (ccel < 0.0)) ccel = 0.0;
|
|
|
|
// relative velocities
|
|
|
|
vtr1 = vt1 - (dz*wr2-dy*wr3);
|
|
vtr2 = vt2 - (dx*wr3-dz*wr1);
|
|
vtr3 = vt3 - (dy*wr1-dx*wr2);
|
|
vrel = vtr1*vtr1 + vtr2*vtr2 + vtr3*vtr3;
|
|
vrel = sqrt(vrel);
|
|
|
|
// force normalization
|
|
|
|
fn = xmu * fabs(ccel*r);
|
|
fs = meff*gammat*vrel;
|
|
if (vrel != 0.0) ft = MIN(fn,fs) / vrel;
|
|
else ft = 0.0;
|
|
|
|
// tangential force due to tangential velocity damping
|
|
|
|
fs1 = -ft*vtr1;
|
|
fs2 = -ft*vtr2;
|
|
fs3 = -ft*vtr3;
|
|
|
|
// forces & torques
|
|
|
|
fx = dx*ccel + fs1;
|
|
fy = dy*ccel + fs2;
|
|
fz = dz*ccel + fs3;
|
|
|
|
if (peratom_flag) {
|
|
contact[1] = fx;
|
|
contact[2] = fy;
|
|
contact[3] = fz;
|
|
}
|
|
|
|
f[0] += fx;
|
|
f[1] += fy;
|
|
f[2] += fz;
|
|
|
|
tor1 = rinv * (dy*fs3 - dz*fs2);
|
|
tor2 = rinv * (dz*fs1 - dx*fs3);
|
|
tor3 = rinv * (dx*fs2 - dy*fs1);
|
|
torque[0] -= radius*tor1;
|
|
torque[1] -= radius*tor2;
|
|
torque[2] -= radius*tor3;
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::hooke_history(double rsq, double dx, double dy, double dz,
|
|
double *vwall, double *v,
|
|
double *f, double *omega, double *torque,
|
|
double radius, double meff, double *history,
|
|
double *contact)
|
|
{
|
|
double r,vr1,vr2,vr3,vnnr,vn1,vn2,vn3,vt1,vt2,vt3;
|
|
double wr1,wr2,wr3,damp,ccel,vtr1,vtr2,vtr3,vrel;
|
|
double fn,fs,fs1,fs2,fs3,fx,fy,fz,tor1,tor2,tor3;
|
|
double shrmag,rsht,rinv,rsqinv;
|
|
|
|
r = sqrt(rsq);
|
|
rinv = 1.0/r;
|
|
rsqinv = 1.0/rsq;
|
|
|
|
// relative translational velocity
|
|
|
|
vr1 = v[0] - vwall[0];
|
|
vr2 = v[1] - vwall[1];
|
|
vr3 = v[2] - vwall[2];
|
|
|
|
// normal component
|
|
|
|
vnnr = vr1*dx + vr2*dy + vr3*dz;
|
|
vn1 = dx*vnnr * rsqinv;
|
|
vn2 = dy*vnnr * rsqinv;
|
|
vn3 = dz*vnnr * rsqinv;
|
|
|
|
// tangential component
|
|
|
|
vt1 = vr1 - vn1;
|
|
vt2 = vr2 - vn2;
|
|
vt3 = vr3 - vn3;
|
|
|
|
// relative rotational velocity
|
|
|
|
wr1 = radius*omega[0] * rinv;
|
|
wr2 = radius*omega[1] * rinv;
|
|
wr3 = radius*omega[2] * rinv;
|
|
|
|
// normal forces = Hookian contact + normal velocity damping
|
|
|
|
damp = meff*gamman*vnnr*rsqinv;
|
|
ccel = kn*(radius-r)*rinv - damp;
|
|
if (limit_damping && (ccel < 0.0)) ccel = 0.0;
|
|
|
|
// relative velocities
|
|
|
|
vtr1 = vt1 - (dz*wr2-dy*wr3);
|
|
vtr2 = vt2 - (dx*wr3-dz*wr1);
|
|
vtr3 = vt3 - (dy*wr1-dx*wr2);
|
|
vrel = vtr1*vtr1 + vtr2*vtr2 + vtr3*vtr3;
|
|
vrel = sqrt(vrel);
|
|
|
|
// shear history effects
|
|
|
|
if (history_update) {
|
|
history[0] += vtr1*dt;
|
|
history[1] += vtr2*dt;
|
|
history[2] += vtr3*dt;
|
|
}
|
|
shrmag = sqrt(history[0]*history[0] + history[1]*history[1] +
|
|
history[2]*history[2]);
|
|
|
|
// rotate shear displacements
|
|
|
|
rsht = history[0]*dx + history[1]*dy + history[2]*dz;
|
|
rsht = rsht*rsqinv;
|
|
if (history_update) {
|
|
history[0] -= rsht*dx;
|
|
history[1] -= rsht*dy;
|
|
history[2] -= rsht*dz;
|
|
}
|
|
|
|
// tangential forces = shear + tangential velocity damping
|
|
|
|
fs1 = - (kt*history[0] + meff*gammat*vtr1);
|
|
fs2 = - (kt*history[1] + meff*gammat*vtr2);
|
|
fs3 = - (kt*history[2] + meff*gammat*vtr3);
|
|
|
|
// rescale frictional displacements and forces if needed
|
|
|
|
fs = sqrt(fs1*fs1 + fs2*fs2 + fs3*fs3);
|
|
fn = xmu * fabs(ccel*r);
|
|
|
|
if (fs > fn) {
|
|
if (shrmag != 0.0) {
|
|
history[0] = (fn/fs) * (history[0] + meff*gammat*vtr1/kt) -
|
|
meff*gammat*vtr1/kt;
|
|
history[1] = (fn/fs) * (history[1] + meff*gammat*vtr2/kt) -
|
|
meff*gammat*vtr2/kt;
|
|
history[2] = (fn/fs) * (history[2] + meff*gammat*vtr3/kt) -
|
|
meff*gammat*vtr3/kt;
|
|
fs1 *= fn/fs ;
|
|
fs2 *= fn/fs;
|
|
fs3 *= fn/fs;
|
|
} else fs1 = fs2 = fs3 = 0.0;
|
|
}
|
|
|
|
// forces & torques
|
|
|
|
fx = dx*ccel + fs1;
|
|
fy = dy*ccel + fs2;
|
|
fz = dz*ccel + fs3;
|
|
|
|
f[0] += fx;
|
|
f[1] += fy;
|
|
f[2] += fz;
|
|
|
|
if (peratom_flag) {
|
|
contact[1] = fx;
|
|
contact[2] = fy;
|
|
contact[3] = fz;
|
|
}
|
|
|
|
tor1 = rinv * (dy*fs3 - dz*fs2);
|
|
tor2 = rinv * (dz*fs1 - dx*fs3);
|
|
tor3 = rinv * (dx*fs2 - dy*fs1);
|
|
torque[0] -= radius*tor1;
|
|
torque[1] -= radius*tor2;
|
|
torque[2] -= radius*tor3;
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::hertz_history(double rsq, double dx, double dy, double dz,
|
|
double *vwall, double rwall, double *v,
|
|
double *f, double *omega, double *torque,
|
|
double radius, double meff, double *history,
|
|
double *contact)
|
|
{
|
|
double r,vr1,vr2,vr3,vnnr,vn1,vn2,vn3,vt1,vt2,vt3;
|
|
double wr1,wr2,wr3,damp,ccel,vtr1,vtr2,vtr3,vrel;
|
|
double fn,fs,fs1,fs2,fs3,fx,fy,fz,tor1,tor2,tor3;
|
|
double shrmag,rsht,polyhertz,rinv,rsqinv;
|
|
|
|
r = sqrt(rsq);
|
|
rinv = 1.0/r;
|
|
rsqinv = 1.0/rsq;
|
|
|
|
// relative translational velocity
|
|
|
|
vr1 = v[0] - vwall[0];
|
|
vr2 = v[1] - vwall[1];
|
|
vr3 = v[2] - vwall[2];
|
|
|
|
// normal component
|
|
|
|
vnnr = vr1*dx + vr2*dy + vr3*dz;
|
|
vn1 = dx*vnnr / rsq;
|
|
vn2 = dy*vnnr / rsq;
|
|
vn3 = dz*vnnr / rsq;
|
|
|
|
// tangential component
|
|
|
|
vt1 = vr1 - vn1;
|
|
vt2 = vr2 - vn2;
|
|
vt3 = vr3 - vn3;
|
|
|
|
// relative rotational velocity
|
|
|
|
wr1 = radius*omega[0] * rinv;
|
|
wr2 = radius*omega[1] * rinv;
|
|
wr3 = radius*omega[2] * rinv;
|
|
|
|
// normal forces = Hertzian contact + normal velocity damping
|
|
// rwall = 0 is flat wall case
|
|
// rwall positive or negative is curved wall
|
|
// will break (as it should) if rwall is negative and
|
|
// its absolute value < radius of particle
|
|
|
|
damp = meff*gamman*vnnr*rsqinv;
|
|
ccel = kn*(radius-r)*rinv - damp;
|
|
if (rwall == 0.0) polyhertz = sqrt((radius-r)*radius);
|
|
else polyhertz = sqrt((radius-r)*radius*rwall/(rwall+radius));
|
|
ccel *= polyhertz;
|
|
if (limit_damping && (ccel < 0.0)) ccel = 0.0;
|
|
|
|
// relative velocities
|
|
|
|
vtr1 = vt1 - (dz*wr2-dy*wr3);
|
|
vtr2 = vt2 - (dx*wr3-dz*wr1);
|
|
vtr3 = vt3 - (dy*wr1-dx*wr2);
|
|
vrel = vtr1*vtr1 + vtr2*vtr2 + vtr3*vtr3;
|
|
vrel = sqrt(vrel);
|
|
|
|
// shear history effects
|
|
|
|
if (history_update) {
|
|
history[0] += vtr1*dt;
|
|
history[1] += vtr2*dt;
|
|
history[2] += vtr3*dt;
|
|
}
|
|
shrmag = sqrt(history[0]*history[0] + history[1]*history[1] +
|
|
history[2]*history[2]);
|
|
|
|
// rotate history displacements
|
|
|
|
rsht = history[0]*dx + history[1]*dy + history[2]*dz;
|
|
rsht = rsht*rsqinv;
|
|
if (history_update) {
|
|
history[0] -= rsht*dx;
|
|
history[1] -= rsht*dy;
|
|
history[2] -= rsht*dz;
|
|
}
|
|
|
|
// tangential forces = shear + tangential velocity damping
|
|
|
|
fs1 = -polyhertz * (kt*history[0] + meff*gammat*vtr1);
|
|
fs2 = -polyhertz * (kt*history[1] + meff*gammat*vtr2);
|
|
fs3 = -polyhertz * (kt*history[2] + meff*gammat*vtr3);
|
|
|
|
// rescale frictional displacements and forces if needed
|
|
|
|
fs = sqrt(fs1*fs1 + fs2*fs2 + fs3*fs3);
|
|
fn = xmu * fabs(ccel*r);
|
|
|
|
if (fs > fn) {
|
|
if (shrmag != 0.0) {
|
|
history[0] = (fn/fs) * (history[0] + meff*gammat*vtr1/kt) -
|
|
meff*gammat*vtr1/kt;
|
|
history[1] = (fn/fs) * (history[1] + meff*gammat*vtr2/kt) -
|
|
meff*gammat*vtr2/kt;
|
|
history[2] = (fn/fs) * (history[2] + meff*gammat*vtr3/kt) -
|
|
meff*gammat*vtr3/kt;
|
|
fs1 *= fn/fs ;
|
|
fs2 *= fn/fs;
|
|
fs3 *= fn/fs;
|
|
} else fs1 = fs2 = fs3 = 0.0;
|
|
}
|
|
|
|
// forces & torques
|
|
|
|
fx = dx*ccel + fs1;
|
|
fy = dy*ccel + fs2;
|
|
fz = dz*ccel + fs3;
|
|
|
|
if (peratom_flag) {
|
|
contact[1] = fx;
|
|
contact[2] = fy;
|
|
contact[3] = fz;
|
|
}
|
|
|
|
f[0] += fx;
|
|
f[1] += fy;
|
|
f[2] += fz;
|
|
|
|
tor1 = rinv * (dy*fs3 - dz*fs2);
|
|
tor2 = rinv * (dz*fs1 - dx*fs3);
|
|
tor3 = rinv * (dx*fs2 - dy*fs1);
|
|
torque[0] -= radius*tor1;
|
|
torque[1] -= radius*tor2;
|
|
torque[2] -= radius*tor3;
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::granular(double rsq, double dx, double dy, double dz,
|
|
double *vwall, double rwall, double *v,
|
|
double *f, double *omega, double *torque,
|
|
double radius, double meff, double *history,
|
|
double *contact)
|
|
{
|
|
double fx,fy,fz,nx,ny,nz;
|
|
double r,rinv;
|
|
double Reff, delta, dR, dR2;
|
|
|
|
double vr1,vr2,vr3,vnnr,vn1,vn2,vn3,vt1,vt2,vt3;
|
|
double wr1,wr2,wr3;
|
|
double vtr1,vtr2,vtr3,vrel;
|
|
|
|
double knfac, damp_normal, damp_normal_prefactor;
|
|
double k_tangential, damp_tangential;
|
|
double Fne, Ft, Fdamp, Fntot, Fncrit, Fscrit, Frcrit;
|
|
double fs, fs1, fs2, fs3;
|
|
|
|
double tor1,tor2,tor3;
|
|
double relrot1,relrot2,relrot3,vrl1,vrl2,vrl3;
|
|
|
|
// for JKR
|
|
double R2, coh, F_pulloff, a, a2, E;
|
|
double t0, t1, t2, t3, t4, t5, t6;
|
|
double sqrt1, sqrt2, sqrt3;
|
|
|
|
// rolling
|
|
double k_roll, damp_roll;
|
|
double torroll1, torroll2, torroll3;
|
|
double rollmag, rolldotn, scalefac;
|
|
double fr, fr1, fr2, fr3;
|
|
|
|
// twisting
|
|
double k_twist, damp_twist, mu_twist;
|
|
double signtwist, magtwist, magtortwist, Mtcrit;
|
|
double tortwist1, tortwist2, tortwist3;
|
|
|
|
double shrmag,rsht,prjmag;
|
|
bool frameupdate;
|
|
|
|
r = sqrt(rsq);
|
|
E = normal_coeffs[0];
|
|
|
|
if (rwall == 0) Reff = radius;
|
|
else Reff = radius*rwall/(radius+rwall);
|
|
|
|
rinv = 1.0/r;
|
|
|
|
nx = dx*rinv;
|
|
ny = dy*rinv;
|
|
nz = dz*rinv;
|
|
|
|
// relative translational velocity
|
|
|
|
vr1 = v[0] - vwall[0];
|
|
vr2 = v[1] - vwall[1];
|
|
vr3 = v[2] - vwall[2];
|
|
|
|
// normal component
|
|
|
|
vnnr = vr1*nx + vr2*ny + vr3*nz; //v_R . n
|
|
vn1 = nx*vnnr;
|
|
vn2 = ny*vnnr;
|
|
vn3 = nz*vnnr;
|
|
|
|
delta = radius - r;
|
|
dR = delta*Reff;
|
|
if (normal_model == JKR) {
|
|
history[0] = 1.0;
|
|
E *= THREEQUARTERS;
|
|
R2=Reff*Reff;
|
|
coh = normal_coeffs[3];
|
|
dR2 = dR*dR;
|
|
t0 = coh*coh*R2*R2*E;
|
|
t1 = PI27SQ*t0;
|
|
t2 = 8*dR*dR2*E*E*E;
|
|
t3 = 4*dR2*E;
|
|
sqrt1 = MAX(0, t0*(t1+2*t2)); // in case sqrt(0) < 0 due to precision issues
|
|
t4 = cbrt(t1+t2+THREEROOT3*MY_PI*sqrt(sqrt1));
|
|
t5 = t3/t4 + t4/E;
|
|
sqrt2 = MAX(0, 2*dR + t5);
|
|
t6 = sqrt(sqrt2);
|
|
sqrt3 = MAX(0, 4*dR - t5 + SIXROOT6*coh*MY_PI*R2/(E*t6));
|
|
a = INVROOT6*(t6 + sqrt(sqrt3));
|
|
a2 = a*a;
|
|
knfac = normal_coeffs[0]*a;
|
|
Fne = knfac*a2/Reff - TWOPI*a2*sqrt(4*coh*E/(MY_PI*a));
|
|
} else {
|
|
knfac = E; //Hooke
|
|
a = sqrt(dR);
|
|
Fne = knfac*delta;
|
|
if (normal_model != HOOKE) {
|
|
Fne *= a;
|
|
knfac *= a;
|
|
}
|
|
if (normal_model == DMT)
|
|
Fne -= 4*MY_PI*normal_coeffs[3]*Reff;
|
|
}
|
|
|
|
if (damping_model == VELOCITY) {
|
|
damp_normal = 1;
|
|
} else if (damping_model == MASS_VELOCITY) {
|
|
damp_normal = meff;
|
|
} else if (damping_model == VISCOELASTIC) {
|
|
damp_normal = a*meff;
|
|
} else if (damping_model == TSUJI) {
|
|
damp_normal = sqrt(meff*knfac);
|
|
} else damp_normal = 0.0;
|
|
|
|
damp_normal_prefactor = normal_coeffs[1]*damp_normal;
|
|
Fdamp = -damp_normal_prefactor*vnnr;
|
|
|
|
Fntot = Fne + Fdamp;
|
|
if (limit_damping && (Fntot < 0.0)) Fntot = 0.0;
|
|
|
|
//****************************************
|
|
// tangential force, including history effects
|
|
//****************************************
|
|
|
|
// For linear, mindlin, mindlin_rescale:
|
|
// history = cumulative tangential displacement
|
|
//
|
|
// For mindlin/force, mindlin_rescale/force:
|
|
// history = cumulative tangential elastic force
|
|
|
|
// tangential component
|
|
vt1 = vr1 - vn1;
|
|
vt2 = vr2 - vn2;
|
|
vt3 = vr3 - vn3;
|
|
|
|
// relative rotational velocity
|
|
wr1 = radius*omega[0];
|
|
wr2 = radius*omega[1];
|
|
wr3 = radius*omega[2];
|
|
|
|
// relative tangential velocities
|
|
vtr1 = vt1 - (nz*wr2-ny*wr3);
|
|
vtr2 = vt2 - (nx*wr3-nz*wr1);
|
|
vtr3 = vt3 - (ny*wr1-nx*wr2);
|
|
vrel = vtr1*vtr1 + vtr2*vtr2 + vtr3*vtr3;
|
|
vrel = sqrt(vrel);
|
|
|
|
if (normal_model == JKR) {
|
|
F_pulloff = 3*MY_PI*coh*Reff;
|
|
Fncrit = fabs(Fne + 2*F_pulloff);
|
|
}
|
|
else if (normal_model == DMT) {
|
|
F_pulloff = 4*MY_PI*coh*Reff;
|
|
Fncrit = fabs(Fne + 2*F_pulloff);
|
|
}
|
|
else{
|
|
Fncrit = fabs(Fntot);
|
|
}
|
|
|
|
//------------------------------
|
|
// tangential forces
|
|
//------------------------------
|
|
|
|
k_tangential = tangential_coeffs[0];
|
|
damp_tangential = tangential_coeffs[1]*damp_normal_prefactor;
|
|
Fscrit = tangential_coeffs[2] * Fncrit;
|
|
|
|
int thist0 = tangential_history_index;
|
|
int thist1 = thist0 + 1;
|
|
int thist2 = thist1 + 1;
|
|
|
|
if (tangential_history) {
|
|
if (tangential_model == TANGENTIAL_MINDLIN ||
|
|
tangential_model == TANGENTIAL_MINDLIN_FORCE) {
|
|
k_tangential *= a;
|
|
}
|
|
else if (tangential_model ==
|
|
TANGENTIAL_MINDLIN_RESCALE ||
|
|
tangential_model ==
|
|
TANGENTIAL_MINDLIN_RESCALE_FORCE){
|
|
k_tangential *= a;
|
|
// on unloading, rescale the shear displacements/force
|
|
if (a < history[thist2+1]) {
|
|
double factor = a/history[thist2+1];
|
|
history[thist0] *= factor;
|
|
history[thist1] *= factor;
|
|
history[thist2] *= factor;
|
|
}
|
|
}
|
|
|
|
|
|
// rotate and update displacements.
|
|
// see e.g. eq. 17 of Luding, Gran. Matter 2008, v10,p235
|
|
if (history_update) {
|
|
rsht = history[thist0]*nx + history[thist1]*ny + history[thist2]*nz;
|
|
if (tangential_model == TANGENTIAL_MINDLIN_FORCE ||
|
|
tangential_model == TANGENTIAL_MINDLIN_RESCALE_FORCE)
|
|
frameupdate = fabs(rsht) > EPSILON*Fscrit;
|
|
else
|
|
frameupdate = fabs(rsht)*k_tangential > EPSILON*Fscrit;
|
|
if (frameupdate) {
|
|
shrmag = sqrt(history[thist0]*history[thist0] +
|
|
history[thist1]*history[thist1] +
|
|
history[thist2]*history[thist2]);
|
|
// projection
|
|
history[thist0] -= rsht*nx;
|
|
history[thist1] -= rsht*ny;
|
|
history[thist2] -= rsht*nz;
|
|
|
|
// also rescale to preserve magnitude
|
|
prjmag = sqrt(history[thist0]*history[thist0] +
|
|
history[thist1]*history[thist1] + history[thist2]*history[thist2]);
|
|
if (prjmag > 0) scalefac = shrmag/prjmag;
|
|
else scalefac = 0;
|
|
history[thist0] *= scalefac;
|
|
history[thist1] *= scalefac;
|
|
history[thist2] *= scalefac;
|
|
}
|
|
// update history
|
|
if (tangential_model == TANGENTIAL_HISTORY ||
|
|
tangential_model == TANGENTIAL_MINDLIN ||
|
|
tangential_model == TANGENTIAL_MINDLIN_RESCALE) {
|
|
history[thist0] += vtr1*dt;
|
|
history[thist1] += vtr2*dt;
|
|
history[thist2] += vtr3*dt;
|
|
} else{
|
|
// tangential force
|
|
// see e.g. eq. 18 of Thornton et al, Pow. Tech. 2013, v223,p30-46
|
|
history[thist0] -= k_tangential*vtr1*dt;
|
|
history[thist1] -= k_tangential*vtr2*dt;
|
|
history[thist2] -= k_tangential*vtr3*dt;
|
|
}
|
|
if (tangential_model == TANGENTIAL_MINDLIN_RESCALE ||
|
|
tangential_model == TANGENTIAL_MINDLIN_RESCALE_FORCE)
|
|
history[thist2+1] = a;
|
|
}
|
|
|
|
// tangential forces = history + tangential velocity damping
|
|
if (tangential_model == TANGENTIAL_HISTORY ||
|
|
tangential_model == TANGENTIAL_MINDLIN ||
|
|
tangential_model == TANGENTIAL_MINDLIN_RESCALE) {
|
|
fs1 = -k_tangential*history[thist0] - damp_tangential*vtr1;
|
|
fs2 = -k_tangential*history[thist1] - damp_tangential*vtr2;
|
|
fs3 = -k_tangential*history[thist2] - damp_tangential*vtr3;
|
|
} else {
|
|
fs1 = history[thist0] - damp_tangential*vtr1;
|
|
fs2 = history[thist1] - damp_tangential*vtr2;
|
|
fs3 = history[thist2] - damp_tangential*vtr3;
|
|
}
|
|
|
|
// rescale frictional displacements and forces if needed
|
|
fs = sqrt(fs1*fs1 + fs2*fs2 + fs3*fs3);
|
|
if (fs > Fscrit) {
|
|
shrmag = sqrt(history[thist0]*history[thist0] +
|
|
history[thist1]*history[thist1] +
|
|
history[thist2]*history[thist2]);
|
|
if (shrmag != 0.0) {
|
|
if (tangential_model == TANGENTIAL_HISTORY ||
|
|
tangential_model == TANGENTIAL_MINDLIN ||
|
|
tangential_model ==
|
|
TANGENTIAL_MINDLIN_RESCALE) {
|
|
history[thist0] = -1.0/k_tangential*(Fscrit*fs1/fs +
|
|
damp_tangential*vtr1);
|
|
history[thist1] = -1.0/k_tangential*(Fscrit*fs2/fs +
|
|
damp_tangential*vtr2);
|
|
history[thist2] = -1.0/k_tangential*(Fscrit*fs3/fs +
|
|
damp_tangential*vtr3);
|
|
} else {
|
|
history[thist0] = Fscrit*fs1/fs + damp_tangential*vtr1;
|
|
history[thist1] = Fscrit*fs2/fs + damp_tangential*vtr2;
|
|
history[thist2] = Fscrit*fs3/fs + damp_tangential*vtr3;
|
|
}
|
|
fs1 *= Fscrit/fs;
|
|
fs2 *= Fscrit/fs;
|
|
fs3 *= Fscrit/fs;
|
|
} else fs1 = fs2 = fs3 = 0.0;
|
|
}
|
|
} else { // classic pair gran/hooke (no history)
|
|
fs = damp_tangential*vrel;
|
|
if (vrel != 0.0) Ft = MIN(Fscrit,fs) / vrel;
|
|
else Ft = 0.0;
|
|
fs1 = -Ft*vtr1;
|
|
fs2 = -Ft*vtr2;
|
|
fs3 = -Ft*vtr3;
|
|
}
|
|
|
|
//****************************************
|
|
// rolling resistance
|
|
//****************************************
|
|
|
|
if (roll_model != ROLL_NONE || twist_model != TWIST_NONE) {
|
|
relrot1 = omega[0];
|
|
relrot2 = omega[1];
|
|
relrot3 = omega[2];
|
|
}
|
|
if (roll_model != ROLL_NONE) {
|
|
// rolling velocity,
|
|
// see eq. 31 of Wang et al, Particuology v 23, p 49 (2015)
|
|
// This is different from the Marshall papers,
|
|
// which use the Bagi/Kuhn formulation
|
|
// for rolling velocity (see Wang et al for why the latter is wrong)
|
|
vrl1 = Reff*(relrot2*nz - relrot3*ny); //- 0.5*((radj-radi)/radsum)*vtr1;
|
|
vrl2 = Reff*(relrot3*nx - relrot1*nz); //- 0.5*((radj-radi)/radsum)*vtr2;
|
|
vrl3 = Reff*(relrot1*ny - relrot2*nx); //- 0.5*((radj-radi)/radsum)*vtr3;
|
|
|
|
int rhist0 = roll_history_index;
|
|
int rhist1 = rhist0 + 1;
|
|
int rhist2 = rhist1 + 1;
|
|
|
|
k_roll = roll_coeffs[0];
|
|
damp_roll = roll_coeffs[1];
|
|
Frcrit = roll_coeffs[2] * Fncrit;
|
|
|
|
if (history_update) {
|
|
rolldotn = history[rhist0]*nx + history[rhist1]*ny + history[rhist2]*nz;
|
|
frameupdate = fabs(rolldotn)*k_roll > EPSILON*Frcrit;
|
|
if (frameupdate) { // rotate into tangential plane
|
|
rollmag = sqrt(history[rhist0]*history[rhist0] +
|
|
history[rhist1]*history[rhist1] +
|
|
history[rhist2]*history[rhist2]);
|
|
// projection
|
|
history[rhist0] -= rolldotn*nx;
|
|
history[rhist1] -= rolldotn*ny;
|
|
history[rhist2] -= rolldotn*nz;
|
|
|
|
// also rescale to preserve magnitude
|
|
prjmag = sqrt(history[rhist0]*history[rhist0] +
|
|
history[rhist1]*history[rhist1] +
|
|
history[rhist2]*history[rhist2]);
|
|
|
|
if (prjmag > 0) scalefac = rollmag/prjmag;
|
|
else scalefac = 0;
|
|
history[rhist0] *= scalefac;
|
|
history[rhist1] *= scalefac;
|
|
history[rhist2] *= scalefac;
|
|
}
|
|
history[rhist0] += vrl1*dt;
|
|
history[rhist1] += vrl2*dt;
|
|
history[rhist2] += vrl3*dt;
|
|
}
|
|
|
|
fr1 = -k_roll*history[rhist0] - damp_roll*vrl1;
|
|
fr2 = -k_roll*history[rhist1] - damp_roll*vrl2;
|
|
fr3 = -k_roll*history[rhist2] - damp_roll*vrl3;
|
|
|
|
// rescale frictional displacements and forces if needed
|
|
fr = sqrt(fr1*fr1 + fr2*fr2 + fr3*fr3);
|
|
if (fr > Frcrit) {
|
|
rollmag = sqrt(history[rhist0]*history[rhist0] +
|
|
history[rhist1]*history[rhist1] +
|
|
history[rhist2]*history[rhist2]);
|
|
if (rollmag != 0.0) {
|
|
history[rhist0] = -1.0/k_roll*(Frcrit*fr1/fr + damp_roll*vrl1);
|
|
history[rhist1] = -1.0/k_roll*(Frcrit*fr2/fr + damp_roll*vrl2);
|
|
history[rhist2] = -1.0/k_roll*(Frcrit*fr3/fr + damp_roll*vrl3);
|
|
fr1 *= Frcrit/fr;
|
|
fr2 *= Frcrit/fr;
|
|
fr3 *= Frcrit/fr;
|
|
} else fr1 = fr2 = fr3 = 0.0;
|
|
}
|
|
}
|
|
|
|
//****************************************
|
|
// twisting torque, including history effects
|
|
//****************************************
|
|
|
|
if (twist_model != TWIST_NONE) {
|
|
magtwist = relrot1*nx + relrot2*ny + relrot3*nz; //Omega_T (eq 29 of Marshall)
|
|
if (twist_model == TWIST_MARSHALL) {
|
|
k_twist = 0.5*k_tangential*a*a;; // eq 32 of Marshall paper
|
|
damp_twist = 0.5*damp_tangential*a*a;
|
|
mu_twist = TWOTHIRDS*a*tangential_coeffs[2];
|
|
}
|
|
else{
|
|
k_twist = twist_coeffs[0];
|
|
damp_twist = twist_coeffs[1];
|
|
mu_twist = twist_coeffs[2];
|
|
}
|
|
if (history_update) {
|
|
history[twist_history_index] += magtwist*dt;
|
|
}
|
|
// M_t torque (eq 30)
|
|
magtortwist = -k_twist*history[twist_history_index] - damp_twist*magtwist;
|
|
signtwist = (magtwist > 0) - (magtwist < 0);
|
|
Mtcrit = mu_twist*Fncrit; // critical torque (eq 44)
|
|
if (fabs(magtortwist) > Mtcrit) {
|
|
history[twist_history_index] = 1.0/k_twist*(Mtcrit*signtwist -
|
|
damp_twist*magtwist);
|
|
magtortwist = -Mtcrit * signtwist; // eq 34
|
|
}
|
|
}
|
|
|
|
// apply forces & torques
|
|
|
|
fx = nx*Fntot + fs1;
|
|
fy = ny*Fntot + fs2;
|
|
fz = nz*Fntot + fs3;
|
|
|
|
if (peratom_flag) {
|
|
contact[1] = fx;
|
|
contact[2] = fy;
|
|
contact[3] = fz;
|
|
}
|
|
|
|
f[0] += fx;
|
|
f[1] += fy;
|
|
f[2] += fz;
|
|
|
|
tor1 = ny*fs3 - nz*fs2;
|
|
tor2 = nz*fs1 - nx*fs3;
|
|
tor3 = nx*fs2 - ny*fs1;
|
|
|
|
torque[0] -= radius*tor1;
|
|
torque[1] -= radius*tor2;
|
|
torque[2] -= radius*tor3;
|
|
|
|
if (twist_model != TWIST_NONE) {
|
|
tortwist1 = magtortwist * nx;
|
|
tortwist2 = magtortwist * ny;
|
|
tortwist3 = magtortwist * nz;
|
|
|
|
torque[0] += tortwist1;
|
|
torque[1] += tortwist2;
|
|
torque[2] += tortwist3;
|
|
}
|
|
|
|
if (roll_model != ROLL_NONE) {
|
|
torroll1 = Reff*(ny*fr3 - nz*fr2); //n cross fr
|
|
torroll2 = Reff*(nz*fr1 - nx*fr3);
|
|
torroll3 = Reff*(nx*fr2 - ny*fr1);
|
|
|
|
torque[0] += torroll1;
|
|
torque[1] += torroll2;
|
|
torque[2] += torroll3;
|
|
}
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
memory usage of local atom-based arrays
|
|
------------------------------------------------------------------------- */
|
|
|
|
double FixWallGran::memory_usage()
|
|
{
|
|
int nmax = atom->nmax;
|
|
double bytes = 0.0;
|
|
if (use_history) bytes += (double)nmax*size_history * sizeof(double); // shear history
|
|
if (fix_rigid) bytes += (double)nmax * sizeof(int); // mass_rigid
|
|
// store contacts
|
|
if (peratom_flag) bytes += (double)nmax*size_peratom_cols*sizeof(double);
|
|
return bytes;
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
allocate local atom-based arrays
|
|
------------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::grow_arrays(int nmax)
|
|
{
|
|
if (use_history) memory->grow(history_one,nmax,size_history,
|
|
"fix_wall_gran:history_one");
|
|
if (peratom_flag) {
|
|
memory->grow(array_atom,nmax,size_peratom_cols,"fix_wall_gran:array_atom");
|
|
}
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
copy values within local atom-based arrays
|
|
------------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::copy_arrays(int i, int j, int /*delflag*/)
|
|
{
|
|
if (use_history)
|
|
for (int m = 0; m < size_history; m++)
|
|
history_one[j][m] = history_one[i][m];
|
|
if (peratom_flag) {
|
|
for (int m = 0; m < size_peratom_cols; m++)
|
|
array_atom[j][m] = array_atom[i][m];
|
|
}
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
initialize one atom's array values, called when atom is created
|
|
------------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::set_arrays(int i)
|
|
{
|
|
if (use_history)
|
|
for (int m = 0; m < size_history; m++)
|
|
history_one[i][m] = 0;
|
|
if (peratom_flag) {
|
|
for (int m = 0; m < size_peratom_cols; m++)
|
|
array_atom[i][m] = 0;
|
|
}
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
pack values in local atom-based arrays for exchange with another proc
|
|
------------------------------------------------------------------------- */
|
|
|
|
int FixWallGran::pack_exchange(int i, double *buf)
|
|
{
|
|
int n = 0;
|
|
if (use_history) {
|
|
for (int m = 0; m < size_history; m++)
|
|
buf[n++] = history_one[i][m];
|
|
}
|
|
if (peratom_flag) {
|
|
for (int m = 0; m < size_peratom_cols; m++)
|
|
buf[n++] = array_atom[i][m];
|
|
}
|
|
return n;
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
unpack values into local atom-based arrays after exchange
|
|
------------------------------------------------------------------------- */
|
|
|
|
int FixWallGran::unpack_exchange(int nlocal, double *buf)
|
|
{
|
|
int n = 0;
|
|
if (use_history) {
|
|
for (int m = 0; m < size_history; m++)
|
|
history_one[nlocal][m] = buf[n++];
|
|
}
|
|
if (peratom_flag) {
|
|
for (int m = 0; m < size_peratom_cols; m++)
|
|
array_atom[nlocal][m] = buf[n++];
|
|
}
|
|
return n;
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
pack values in local atom-based arrays for restart file
|
|
------------------------------------------------------------------------- */
|
|
|
|
int FixWallGran::pack_restart(int i, double *buf)
|
|
{
|
|
if (!use_history) return 0;
|
|
|
|
int n = 0;
|
|
// pack buf[0] this way because other fixes unpack it
|
|
buf[n++] = size_history + 1;
|
|
for (int m = 0; m < size_history; m++)
|
|
buf[n++] = history_one[i][m];
|
|
return n;
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
unpack values from atom->extra array to restart the fix
|
|
------------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::unpack_restart(int nlocal, int nth)
|
|
{
|
|
if (!use_history) return;
|
|
|
|
double **extra = atom->extra;
|
|
|
|
// skip to Nth set of extra values
|
|
// unpack the Nth first values this way because other fixes pack them
|
|
|
|
int m = 0;
|
|
for (int i = 0; i < nth; i++) m += static_cast<int> (extra[nlocal][m]);
|
|
m++;
|
|
|
|
for (int i = 0; i < size_history; i++)
|
|
history_one[nlocal][i] = extra[nlocal][m++];
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
maxsize of any atom's restart data
|
|
------------------------------------------------------------------------- */
|
|
|
|
int FixWallGran::maxsize_restart()
|
|
{
|
|
if (!use_history) return 0;
|
|
return 1 + size_history;
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
size of atom nlocal's restart data
|
|
------------------------------------------------------------------------- */
|
|
|
|
int FixWallGran::size_restart(int /*nlocal*/)
|
|
{
|
|
if (!use_history) return 0;
|
|
return 1 + size_history;
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
void FixWallGran::reset_dt()
|
|
{
|
|
dt = update->dt;
|
|
}
|
|
|
|
double FixWallGran::pulloff_distance(double radius)
|
|
{
|
|
double coh, E, a, dist;
|
|
coh = normal_coeffs[3];
|
|
E = normal_coeffs[0]*THREEQUARTERS;
|
|
a = cbrt(9*MY_PI*coh*radius/(4*E));
|
|
dist = a*a/radius - 2*sqrt(MY_PI*coh*a/E);
|
|
return dist;
|
|
}
|
|
|