fix_wall_gran.cpp
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Created: Sun, Nov 10, 19:23

fix_wall_gran.cpp
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	/* ----------------------------------------------------------------------
	LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
	http://lammps.sandia.gov, Sandia National Laboratories
	Steve Plimpton, sjplimp@sandia.gov

	Copyright (2003) Sandia Corporation. Under the terms of Contract
	DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
	certain rights in this software. This software is distributed under
	the GNU General Public License.

	See the README file in the top-level LAMMPS directory.
	------------------------------------------------------------------------- */

	/* ----------------------------------------------------------------------
	Contributing authors: Leo Silbert (SNL), Gary Grest (SNL),
	Dan Bolintineanu (SNL)
	------------------------------------------------------------------------- */

	#include <math.h>
	#include <stdlib.h>
	#include <string.h>
	#include "fix_wall_gran.h"
	#include "atom.h"
	#include "domain.h"
	#include "update.h"
	#include "force.h"
	#include "pair.h"
	#include "modify.h"
	#include "respa.h"
	#include "math_const.h"
	#include "memory.h"
	#include "error.h"

	using namespace LAMMPS_NS;
	using namespace FixConst;
	using namespace MathConst;

	// XYZ PLANE need to be 0,1,2

	enum{XPLANE=0,YPLANE=1,ZPLANE=2,ZCYLINDER,REGION};
	enum{HOOKE,HOOKE_HISTORY,HERTZ_HISTORY,BONDED_HISTORY};
	enum{NONE,CONSTANT,EQUAL};

	#define BIG 1.0e20

	/* ---------------------------------------------------------------------- */

	FixWallGran::FixWallGran(LAMMPS lmp, int narg, char *arg) :
	Fix(lmp, narg, arg), idregion(NULL), shearone(NULL), fix_rigid(NULL), mass_rigid(NULL)
	{
	if (narg < 4) error->all(FLERR,"Illegal fix wall/gran command");

	if (!atom->sphere_flag)
	error->all(FLERR,"Fix wall/gran requires atom style sphere");

	create_attribute = 1;

	// set interaction style
	// disable bonded/history option for now

	if (strcmp(arg[3],"hooke") == 0) pairstyle = HOOKE;
	else if (strcmp(arg[3],"hooke/history") == 0) pairstyle = HOOKE_HISTORY;
	else if (strcmp(arg[3],"hertz/history") == 0) pairstyle = HERTZ_HISTORY;
	//else if (strcmp(arg[3],"bonded/history") == 0) pairstyle = BONDED_HISTORY;
	else error->all(FLERR,"Invalid fix wall/gran interaction style");

	history = restart_peratom = 1;
	if (pairstyle == HOOKE) history = restart_peratom = 0;

	// wall/particle coefficients

	int iarg;

	if (pairstyle != BONDED_HISTORY) {
	if (narg < 11) error->all(FLERR,"Illegal fix wall/gran command");

	kn = force->numeric(FLERR,arg[4]);
	if (strcmp(arg[5],"NULL") == 0) kt = kn * 2.0/7.0;
	else kt = force->numeric(FLERR,arg[5]);

	gamman = force->numeric(FLERR,arg[6]);
	if (strcmp(arg[7],"NULL") == 0) gammat = 0.5 * gamman;
	else gammat = force->numeric(FLERR,arg[7]);

	xmu = force->numeric(FLERR,arg[8]);
	int dampflag = force->inumeric(FLERR,arg[9]);
	if (dampflag == 0) gammat = 0.0;

	if (kn < 0.0 \|\| kt < 0.0 \|\| gamman < 0.0 \|\| gammat < 0.0 \|\|
	xmu < 0.0 \|\| xmu > 10000.0 \|\| dampflag < 0 \|\| dampflag > 1)
	error->all(FLERR,"Illegal fix wall/gran command");

	// convert Kn and Kt from pressure units to force/distance^2 if Hertzian

	if (pairstyle == HERTZ_HISTORY) {
	kn /= force->nktv2p;
	kt /= force->nktv2p;
	}

	iarg = 10;
	}

	else {
	if (narg < 10) error->all(FLERR,"Illegal fix wall/gran command");

	E = force->numeric(FLERR,arg[4]);
	G = force->numeric(FLERR,arg[5]);
	SurfEnergy = force->numeric(FLERR,arg[6]);
	// Note: this doesn't get used, check w/ Jeremy?
	gamman = force->numeric(FLERR,arg[7]);

	xmu = force->numeric(FLERR,arg[8]);
	// pois = E/(2.0*G) - 1.0;
	// kn = 2.0E/(3.0(1.0+pois)*(1.0-pois));
	// gammat=0.5*gamman;

	iarg = 9;
	}

	// wallstyle args

	idregion = NULL;

	if (strcmp(arg[iarg],"xplane") == 0) {
	if (narg < iarg+3) error->all(FLERR,"Illegal fix wall/gran command");
	wallstyle = XPLANE;
	if (strcmp(arg[iarg+1],"NULL") == 0) lo = -BIG;
	else lo = force->numeric(FLERR,arg[iarg+1]);
	if (strcmp(arg[iarg+2],"NULL") == 0) hi = BIG;
	else hi = force->numeric(FLERR,arg[iarg+2]);
	iarg += 3;
	} else if (strcmp(arg[iarg],"yplane") == 0) {
	if (narg < iarg+3) error->all(FLERR,"Illegal fix wall/gran command");
	wallstyle = YPLANE;
	if (strcmp(arg[iarg+1],"NULL") == 0) lo = -BIG;
	else lo = force->numeric(FLERR,arg[iarg+1]);
	if (strcmp(arg[iarg+2],"NULL") == 0) hi = BIG;
	else hi = force->numeric(FLERR,arg[iarg+2]);
	iarg += 3;
	} else if (strcmp(arg[iarg],"zplane") == 0) {
	if (narg < iarg+3) error->all(FLERR,"Illegal fix wall/gran command");
	wallstyle = ZPLANE;
	if (strcmp(arg[iarg+1],"NULL") == 0) lo = -BIG;
	else lo = force->numeric(FLERR,arg[iarg+1]);
	if (strcmp(arg[iarg+2],"NULL") == 0) hi = BIG;
	else hi = force->numeric(FLERR,arg[iarg+2]);
	iarg += 3;
	} else if (strcmp(arg[iarg],"zcylinder") == 0) {
	if (narg < iarg+2) error->all(FLERR,"Illegal fix wall/gran command");
	wallstyle = ZCYLINDER;
	lo = hi = 0.0;
	cylradius = force->numeric(FLERR,arg[iarg+1]);
	iarg += 2;
	} else if (strcmp(arg[iarg],"region") == 0) {
	if (narg < iarg+2) error->all(FLERR,"Illegal fix wall/gran command");
	wallstyle = REGION;
	int n = strlen(arg[iarg+1]) + 1;
	idregion = new char[n];
	strcpy(idregion,arg[iarg+1]);
	iarg += 2;
	}

	// optional args

	wiggle = 0;
	wshear = 0;

	while (iarg < narg) {
	if (strcmp(arg[iarg],"wiggle") == 0) {
	if (iarg+4 > 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");
	amplitude = force->numeric(FLERR,arg[iarg+2]);
	period = force->numeric(FLERR,arg[iarg+3]);
	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 = force->numeric(FLERR,arg[iarg+2]);
	wshear = 1;
	iarg += 3;
	} 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

	if (pairstyle == BONDED_HISTORY) sheardim = 7;
	else sheardim = 3;

	shearone = NULL;
	grow_arrays(atom->nmax);
	atom->add_callback(0);
	atom->add_callback(1);

	nmax = 0;
	mass_rigid = NULL;

	// initialize shear history as if particle is not touching region
	// shearone will be NULL for wallstyle = REGION

	if (history && shearone) {
	int nlocal = atom->nlocal;
	for (int i = 0; i < nlocal; i++)
	for (int j = 0; j < sheardim; j++)
	shearone[i][j] = 0.0;
	}

	time_origin = update->ntimestep;
	}

	/* ---------------------------------------------------------------------- */

	FixWallGran::~FixWallGran()
	{
	// unregister callbacks to this fix from Atom class

	atom->delete_callback(id,0);
	atom->delete_callback(id,1);

	// delete local storage

	delete [] idregion;
	memory->destroy(shearone);
	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 (strstr(update->integrate_style,"respa"))
	nlevels_respa = ((Respa *) update->integrate)->nlevels;

	// check for FixRigid so can extract rigid body masses

	fix_rigid = NULL;
	for (i = 0; i < modify->nfix; i++)
	if (modify->fix[i]->rigid_flag) break;
	if (i < modify->nfix) fix_rigid = modify->fix[i];
	}

	/* ---------------------------------------------------------------------- */

	void FixWallGran::setup(int vflag)
	{
	if (strstr(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 shear history during setup

	shearupdate = 1;
	if (update->setupflag) shearupdate = 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] = amplitudeomegasin(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 NULL, 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 shear 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;

	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) ? -2cylradius : 2cylradius;
	if (wshear && axis != 2) {
	vwall[0] += vshear * x[i][1]/delxy;
	vwall[1] += -vshear * x[i][0]/delxy;
	vwall[2] = 0.0;
	}
	}
	}

	rsq = dxdx + dydy + dz*dz;

	if (rsq > radius[i]*radius[i]) {
	if (history)
	for (j = 0; j < sheardim; j++)
	shearone[i][j] = 0.0;

	} else {

	// 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];

	// invoke sphere/wall interaction

	if (pairstyle == HOOKE)
	hooke(rsq,dx,dy,dz,vwall,v[i],f[i],
	omega[i],torque[i],radius[i],meff);
	else if (pairstyle == HOOKE_HISTORY)
	hooke_history(rsq,dx,dy,dz,vwall,v[i],f[i],
	omega[i],torque[i],radius[i],meff,shearone[i]);
	else if (pairstyle == HERTZ_HISTORY)
	hertz_history(rsq,dx,dy,dz,vwall,rwall,v[i],f[i],
	omega[i],torque[i],radius[i],meff,shearone[i]);
	else if (pairstyle == BONDED_HISTORY)
	bonded_history(rsq,dx,dy,dz,vwall,rwall,v[i],f[i],
	omega[i],torque[i],radius[i],meff,shearone[i]);
	}
	}
	}
	}

	/* ---------------------------------------------------------------------- */

	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 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 = vr1dx + vr2dy + vr3*dz;
	vn1 = dxvnnr rsqinv;
	vn2 = dyvnnr rsqinv;
	vn3 = dzvnnr rsqinv;

	// tangential component

	vt1 = vr1 - vn1;
	vt2 = vr2 - vn2;
	vt3 = vr3 - vn3;

	// relative rotational velocity

	wr1 = radiusomega[0] rinv;
	wr2 = radiusomega[1] rinv;
	wr3 = radiusomega[2] rinv;

	// normal forces = Hookian contact + normal velocity damping

	damp = meffgammanvnnr*rsqinv;
	ccel = kn(radius-r)rinv - damp;

	// relative velocities

	vtr1 = vt1 - (dzwr2-dywr3);
	vtr2 = vt2 - (dxwr3-dzwr1);
	vtr3 = vt3 - (dywr1-dxwr2);
	vrel = vtr1vtr1 + vtr2vtr2 + vtr3*vtr3;
	vrel = sqrt(vrel);

	// force normalization

	fn = xmu * fabs(ccel*r);
	fs = meffgammatvrel;
	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;

	f[0] += fx;
	f[1] += fy;
	f[2] += fz;

	tor1 = rinv * (dyfs3 - dzfs2);
	tor2 = rinv * (dzfs1 - dxfs3);
	tor3 = rinv * (dxfs2 - dyfs1);
	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 *shear)
	{
	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 = vr1dx + vr2dy + vr3*dz;
	vn1 = dxvnnr rsqinv;
	vn2 = dyvnnr rsqinv;
	vn3 = dzvnnr rsqinv;

	// tangential component

	vt1 = vr1 - vn1;
	vt2 = vr2 - vn2;
	vt3 = vr3 - vn3;

	// relative rotational velocity

	wr1 = radiusomega[0] rinv;
	wr2 = radiusomega[1] rinv;
	wr3 = radiusomega[2] rinv;

	// normal forces = Hookian contact + normal velocity damping

	damp = meffgammanvnnr*rsqinv;
	ccel = kn(radius-r)rinv - damp;

	// relative velocities

	vtr1 = vt1 - (dzwr2-dywr3);
	vtr2 = vt2 - (dxwr3-dzwr1);
	vtr3 = vt3 - (dywr1-dxwr2);
	vrel = vtr1vtr1 + vtr2vtr2 + vtr3*vtr3;
	vrel = sqrt(vrel);

	// shear history effects

	if (shearupdate) {
	shear[0] += vtr1*dt;
	shear[1] += vtr2*dt;
	shear[2] += vtr3*dt;
	}
	shrmag = sqrt(shear[0]shear[0] + shear[1]shear[1] + shear[2]*shear[2]);

	// rotate shear displacements

	rsht = shear[0]dx + shear[1]dy + shear[2]*dz;
	rsht = rsht*rsqinv;
	if (shearupdate) {
	shear[0] -= rsht*dx;
	shear[1] -= rsht*dy;
	shear[2] -= rsht*dz;
	}

	// tangential forces = shear + tangential velocity damping

	fs1 = - (ktshear[0] + meffgammat*vtr1);
	fs2 = - (ktshear[1] + meffgammat*vtr2);
	fs3 = - (ktshear[2] + meffgammat*vtr3);

	// rescale frictional displacements and forces if needed

	fs = sqrt(fs1fs1 + fs2fs2 + fs3*fs3);
	fn = xmu * fabs(ccel*r);

	if (fs > fn) {
	if (shrmag != 0.0) {
	shear[0] = (fn/fs) * (shear[0] + meffgammatvtr1/kt) -
	meffgammatvtr1/kt;
	shear[1] = (fn/fs) * (shear[1] + meffgammatvtr2/kt) -
	meffgammatvtr2/kt;
	shear[2] = (fn/fs) * (shear[2] + meffgammatvtr3/kt) -
	meffgammatvtr3/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;

	tor1 = rinv * (dyfs3 - dzfs2);
	tor2 = rinv * (dzfs1 - dxfs3);
	tor3 = rinv * (dxfs2 - dyfs1);
	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 *shear)
	{
	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 = vr1dx + vr2dy + 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 = radiusomega[0] rinv;
	wr2 = radiusomega[1] rinv;
	wr3 = radiusomega[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 = meffgammanvnnr*rsqinv;
	ccel = kn(radius-r)rinv - damp;
	if (rwall == 0.0) polyhertz = sqrt((radius-r)*radius);
	else polyhertz = sqrt((radius-r)radiusrwall/(rwall+radius));
	ccel *= polyhertz;

	// relative velocities

	vtr1 = vt1 - (dzwr2-dywr3);
	vtr2 = vt2 - (dxwr3-dzwr1);
	vtr3 = vt3 - (dywr1-dxwr2);
	vrel = vtr1vtr1 + vtr2vtr2 + vtr3*vtr3;
	vrel = sqrt(vrel);

	// shear history effects

	if (shearupdate) {
	shear[0] += vtr1*dt;
	shear[1] += vtr2*dt;
	shear[2] += vtr3*dt;
	}
	shrmag = sqrt(shear[0]shear[0] + shear[1]shear[1] + shear[2]*shear[2]);

	// rotate shear displacements

	rsht = shear[0]dx + shear[1]dy + shear[2]*dz;
	rsht = rsht*rsqinv;
	if (shearupdate) {
	shear[0] -= rsht*dx;
	shear[1] -= rsht*dy;
	shear[2] -= rsht*dz;
	}

	// tangential forces = shear + tangential velocity damping

	fs1 = -polyhertz * (ktshear[0] + meffgammat*vtr1);
	fs2 = -polyhertz * (ktshear[1] + meffgammat*vtr2);
	fs3 = -polyhertz * (ktshear[2] + meffgammat*vtr3);

	// rescale frictional displacements and forces if needed

	fs = sqrt(fs1fs1 + fs2fs2 + fs3*fs3);
	fn = xmu * fabs(ccel*r);

	if (fs > fn) {
	if (shrmag != 0.0) {
	shear[0] = (fn/fs) * (shear[0] + meffgammatvtr1/kt) -
	meffgammatvtr1/kt;
	shear[1] = (fn/fs) * (shear[1] + meffgammatvtr2/kt) -
	meffgammatvtr2/kt;
	shear[2] = (fn/fs) * (shear[2] + meffgammatvtr3/kt) -
	meffgammatvtr3/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;

	tor1 = rinv * (dyfs3 - dzfs2);
	tor2 = rinv * (dzfs1 - dxfs3);
	tor3 = rinv * (dxfs2 - dyfs1);
	torque[0] -= radius*tor1;
	torque[1] -= radius*tor2;
	torque[2] -= radius*tor3;
	}


	/* ---------------------------------------------------------------------- */

	void FixWallGran::bonded_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 *shear)
	{
	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;

	double pois,E_eff,G_eff,rad_eff;
	double a0,Fcrit,delcrit,delcritinv;
	double overlap,olapsq,olapcubed,sqrtterm,tmp,keyterm,keyterm2,keyterm3;
	double aovera0,foverFc;
	double gammatsuji;

	double ktwist,kroll,twistcrit,rollcrit;
	double relrot1,relrot2,relrot3,vrl1,vrl2,vrl3,vrlmag,vrlmaginv;
	double magtwist,magtortwist;
	double magrollsq,magroll,magrollinv,magtorroll;

	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 = vr1dx + vr2dy + 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 = radiusomega[0] rinv;
	wr2 = radiusomega[1] rinv;
	wr3 = radiusomega[2] rinv;

	// normal forces = Hertzian contact + normal velocity damping
	// material properties: currently assumes identical materials

	pois = E/(2.0*G) - 1.0;
	E_eff=0.5E/(1.0-poispois);
	G_eff=G/(4.0-2.0*pois);

	// rwall = 0 is infinite wall radius of curvature (flat wall)

	if (rwall == 0) rad_eff = radius;
	else rad_eff = radius*rwall/(radius+rwall);

	Fcrit = rad_eff * (3.0 * M_PI * SurfEnergy);
	a0=pow(9.0M_PISurfEnergyrad_effrad_eff/E_eff,1.0/3.0);
	delcrit = 1.0/rad_eff(0.5 a0*a0/pow(6.0,1.0/3.0));
	delcritinv = 1.0/delcrit;

	overlap = (radius-r) * delcritinv;
	olapsq = overlap*overlap;
	olapcubed = olapsq*overlap;
	sqrtterm = sqrt(1.0 + olapcubed);
	tmp = 2.0 + olapcubed + 2.0*sqrtterm;
	keyterm = pow(tmp,THIRD);
	keyterm2 = olapsq/keyterm;
	keyterm3 = sqrt(overlap + keyterm2 + keyterm);
	aovera0 = pow(6.0,-TWOTHIRDS) * (keyterm3 +
	sqrt(2.0*overlap - keyterm2 - keyterm + 4.0/keyterm3));
	foverFc = 4.0((aovera0aovera0*aovera0) - pow(aovera0,1.5));
	ccel = FcritfoverFcrinv;

	// damp = meffgammanvnnr*rsqinv;
	// ccel = kn(radius-r)rinv - damp;
	// polyhertz = sqrt((radius-r)*radius);
	// ccel *= polyhertz;

	// use Tsuji et al form

	polyhertz = 1.2728- 4.27830.9 + 11.0870.90.9 - 22.3480.90.90.9 +
	27.4670.90.90.90.9 - 18.0220.90.90.90.9*0.9 +
	4.82180.90.90.90.90.90.9;

	gammatsuji = 0.2sqrt(meffkn);
	damp = gammatsuji*vnnr/rsq;
	ccel = ccel - polyhertz * damp;

	// relative velocities

	vtr1 = vt1 - (dzwr2-dywr3);
	vtr2 = vt2 - (dxwr3-dzwr1);
	vtr3 = vt3 - (dywr1-dxwr2);
	vrel = vtr1vtr1 + vtr2vtr2 + vtr3*vtr3;
	vrel = sqrt(vrel);

	// shear history effects

	if (shearupdate) {
	shear[0] += vtr1*dt;
	shear[1] += vtr2*dt;
	shear[2] += vtr3*dt;
	}
	shrmag = sqrt(shear[0]shear[0] + shear[1]shear[1] + shear[2]*shear[2]);

	// rotate shear displacements

	rsht = shear[0]dx + shear[1]dy + shear[2]*dz;
	rsht = rsht*rsqinv;
	if (shearupdate) {
	shear[0] -= rsht*dx;
	shear[1] -= rsht*dy;
	shear[2] -= rsht*dz;
	}

	// tangential forces = shear + tangential velocity damping

	fs1 = -polyhertz * (ktshear[0] + meffgammat*vtr1);
	fs2 = -polyhertz * (ktshear[1] + meffgammat*vtr2);
	fs3 = -polyhertz * (ktshear[2] + meffgammat*vtr3);

	kt=8.0G_effa0*aovera0;

	// shear damping uses Tsuji et al form also

	fs1 = -ktshear[0] - polyhertzgammatsuji*vtr1;
	fs2 = -ktshear[1] - polyhertzgammatsuji*vtr2;
	fs3 = -ktshear[2] - polyhertzgammatsuji*vtr3;

	// rescale frictional displacements and forces if needed

	fs = sqrt(fs1fs1 + fs2fs2 + fs3*fs3);
	fn = xmu * fabs(ccelr + 2.0Fcrit);

	if (fs > fn) {
	if (shrmag != 0.0) {
	shear[0] = (fn/fs) * (shear[0] + polyhertzgammatsujivtr1/kt) -
	polyhertzgammatsujivtr1/kt;
	shear[1] = (fn/fs) * (shear[1] + polyhertzgammatsujivtr2/kt) -
	polyhertzgammatsujivtr2/kt;
	shear[2] = (fn/fs) * (shear[2] + polyhertzgammatsujivtr3/kt) -
	polyhertzgammatsujivtr3/kt;
	fs1 *= fn/fs ;
	fs2 *= fn/fs;
	fs3 *= fn/fs;
	} else fs1 = fs2 = fs3 = 0.0;
	}

	// calculate twisting and rolling components of torque
	// NOTE: this assumes spheres!

	relrot1 = omega[0];
	relrot2 = omega[1];
	relrot3 = omega[2];

	// rolling velocity
	// NOTE: this assumes mondisperse spheres!

	vrl1 = -rad_effrinv (relrot2dz - relrot3dy);
	vrl2 = -rad_effrinv (relrot3dx - relrot1dz);
	vrl3 = -rad_effrinv (relrot1dy - relrot2dx);
	vrlmag = sqrt(vrl1vrl1+vrl2vrl2+vrl3*vrl3);
	if (vrlmag != 0.0) vrlmaginv = 1.0/vrlmag;
	else vrlmaginv = 0.0;

	// bond history effects

	shear[3] += vrl1*dt;
	shear[4] += vrl2*dt;
	shear[5] += vrl3*dt;

	// rotate bonded displacements correctly

	double rlt = shear[3]dx + shear[4]dy + shear[5]*dz;
	rlt /= rsq;
	shear[3] -= rlt*dx;
	shear[4] -= rlt*dy;
	shear[5] -= rlt*dz;

	// twisting torque

	magtwist = rinv(relrot1dx + relrot2dy + relrot3dz);
	shear[6] += magtwist*dt;

	ktwist = 0.5kt(a0aovera0)(a0*aovera0);
	magtortwist = -ktwist*shear[6] -
	0.5polyhertzgammatsuji(a0aovera0)(a0aovera0)*magtwist;

	twistcrit=TWOTHIRDSa0aovera0*Fcrit;
	if (fabs(magtortwist) > twistcrit)
	magtortwist = -twistcrit * magtwist/fabs(magtwist);

	// rolling torque

	magrollsq = shear[3]shear[3] + shear[4]shear[4] + shear[5]*shear[5];
	magroll = sqrt(magrollsq);
	if (magroll != 0.0) magrollinv = 1.0/magroll;
	else magrollinv = 0.0;

	kroll = 1.04.0Fcrit*pow(aovera0,1.5);
	magtorroll = -krollmagroll - 0.1gammat*vrlmag;

	rollcrit = 0.01;
	if (magroll > rollcrit) magtorroll = -kroll*rollcrit;

	// forces & torques

	fx = dx*ccel + fs1;
	fy = dy*ccel + fs2;
	fz = dz*ccel + fs3;

	f[0] += fx;
	f[1] += fy;
	f[2] += fz;

	tor1 = rinv * (dyfs3 - dzfs2);
	tor2 = rinv * (dzfs1 - dxfs3);
	tor3 = rinv * (dxfs2 - dyfs1);
	torque[0] -= radius*tor1;
	torque[1] -= radius*tor2;
	torque[2] -= radius*tor3;

	torque[0] += magtortwist * dx*rinv;
	torque[1] += magtortwist * dy*rinv;
	torque[2] += magtortwist * dz*rinv;

	torque[0] += magtorroll * (shear[4]dz - shear[5]dy)rinvmagrollinv;
	torque[1] += magtorroll * (shear[5]dx - shear[3]dz)rinvmagrollinv;
	torque[2] += magtorroll * (shear[3]dy - shear[4]dx)rinvmagrollinv;
	}

	/* ----------------------------------------------------------------------
	memory usage of local atom-based arrays
	------------------------------------------------------------------------- */

	double FixWallGran::memory_usage()
	{
	int nmax = atom->nmax;
	double bytes = 0.0;
	if (history) bytes += nmaxsheardim sizeof(double); // shear history
	if (fix_rigid) bytes += nmax * sizeof(int); // mass_rigid
	return bytes;
	}

	/* ----------------------------------------------------------------------
	allocate local atom-based arrays
	------------------------------------------------------------------------- */

	void FixWallGran::grow_arrays(int nmax)
	{
	if (history) memory->grow(shearone,nmax,sheardim,"fix_wall_gran:shearone");
	}

	/* ----------------------------------------------------------------------
	copy values within local atom-based arrays
	------------------------------------------------------------------------- */

	void FixWallGran::copy_arrays(int i, int j, int delflag)
	{
	if (history)
	for (int m = 0; m < sheardim; m++)
	shearone[j][m] = shearone[i][m];
	}

	/* ----------------------------------------------------------------------
	initialize one atom's array values, called when atom is created
	------------------------------------------------------------------------- */

	void FixWallGran::set_arrays(int i)
	{
	if (history)
	for (int m = 0; m < sheardim; m++)
	shearone[i][m] = 0;
	}

	/* ----------------------------------------------------------------------
	pack values in local atom-based arrays for exchange with another proc
	------------------------------------------------------------------------- */

	int FixWallGran::pack_exchange(int i, double *buf)
	{
	if (!history) return 0;

	int n = 0;
	for (int m = 0; m < sheardim; m++)
	buf[n++] = shearone[i][m];
	return n;
	}

	/* ----------------------------------------------------------------------
	unpack values into local atom-based arrays after exchange
	------------------------------------------------------------------------- */

	int FixWallGran::unpack_exchange(int nlocal, double *buf)
	{
	if (!history) return 0;

	int n = 0;
	for (int m = 0; m < sheardim; m++)
	shearone[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 (!history) return 0;

	int n = 0;
	buf[n++] = sheardim + 1;
	for (int m = 0; m < sheardim; m++)
	buf[n++] = shearone[i][m];
	return n;
	}

	/* ----------------------------------------------------------------------
	unpack values from atom->extra array to restart the fix
	------------------------------------------------------------------------- */

	void FixWallGran::unpack_restart(int nlocal, int nth)
	{
	if (!history) return;

	double **extra = atom->extra;

	// skip to Nth set of extra values

	int m = 0;
	for (int i = 0; i < nth; i++) m += static_cast<int> (extra[nlocal][m]);
	m++;

	for (int i = 0; i < sheardim; i++)
	shearone[nlocal][i] = extra[nlocal][m++];
	}

	/* ----------------------------------------------------------------------
	maxsize of any atom's restart data
	------------------------------------------------------------------------- */

	int FixWallGran::maxsize_restart()
	{
	if (!history) return 0;
	return 1 + sheardim;
	}

	/* ----------------------------------------------------------------------
	size of atom nlocal's restart data
	------------------------------------------------------------------------- */

	int FixWallGran::size_restart(int nlocal)
	{
	if (!history) return 0;
	return 1 + sheardim;
	}

	/* ---------------------------------------------------------------------- */

	void FixWallGran::reset_dt()
	{
	dt = update->dt;
	}

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