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#include "CBLattice.h"
#include "CbPotential.h"
#include <fstream>
namespace ATC {
// removes any overlapping atoms (avoid calling because it scales n^2.)
INDEX AtomCluster::remove_overlap()
{
INDEX removed_count = 0;
std::vector<double>::iterator r(cur_bond_len_.begin());
std::vector<DENS_VEC>::iterator R(ref_coords_.begin()), Rp;
const double TOL = 1.0e-6 * R->dot(*R);
for (; R!=ref_coords_.end(); R++, r++) {
for (Rp=R+1; Rp!=ref_coords_.end(); Rp++) {
if (sum_difference_squared(*Rp, *R) < TOL) {
ref_coords_.erase(R--);
cur_bond_len_.erase(r--);
++removed_count;
break;
}
}
}
return removed_count;
}
//=========================================================================
// writes cluster to 3 column data format
//=========================================================================
void AtomCluster::write_to_dat(std::string path, bool current_config)
{
const int npts = int(ref_coords_.size());
if (path.substr(path.size()-5,4) != ".dat") path += ".dat";
std::fstream fid(path.c_str(), std::ios::out);
for (int i=0; i<npts; i++) {
DENS_VEC x (current_config ? r(i):R(i));
for (INDEX j=0; j<x.size(); j++) fid << x(j) << " ";
fid << " " << x.norm() << "\n";
}
}
//=========================================================================
// writes cluster to vtk format, (in either reference or current config)
//=========================================================================
void AtomCluster::write_to_vtk(std::string path, bool current_config)
{
const int npts = int(ref_coords_.size());
if (path.substr(path.size()-5,4) != ".vtk") path += ".vtk";
std::fstream fid(path.c_str(), std::ios::out);
// write header
fid << "# vtk DataFile Version 2.0\nWritten from FE-LAMMPS\n";
fid << "ASCII\nDATASET UNSTRUCTURED_GRID\n";
fid << "POINTS " << npts << " float\n";
for (int i=0; i<npts; i++) {
DENS_VEC x (current_config ? r(i):R(i));
for (INDEX j=0; j<x.size(); j++) fid << x(j) << " ";
fid << ((i+1)%3==0 ? "\n" : " ");
}
fid << "\nCELLS "<<npts<<" "<<2*npts<<"\n";
for (int i=0; i<npts; i++) fid << "1" << " " << i << "\n";
fid << "CELL_TYPES " << npts << "\n";
for (int i=0; i<npts; i++) fid << "1" << "\n";
}
//===========================================================================
// constructor
// @param N 3x3 DenseMatrix with each column as a base vector
// @param B 3xn DenseMatrix with each column being a basis vector
// @param R vector of 3D bond Vectors to representative atom in ref config
// @param r vector of bond lengths to representative atom in current config
// @param RC cutoff radius of bond potential
//===========================================================================
CBLattice::CBLattice(const MATRIX &N, const MATRIX &B)
: n_(N), b_(B), N_(N), B_(B)
{
// builds the default queue
for (int a=-1; a<2; a++)
for (int b=-1; b<2; b++)
for (int c=-1; c<2; c++)
if ( a!=0 || b!=0 || c!=0) queue0_.push(hash(a,b,c));
}
//=============================================================================
// writes out default lattice parameters
//=============================================================================
std::ostream & operator<<(std::ostream& o, const CBLattice& lattice)
{
o<<"cutoff radius = "<<sqrt(lattice.RC2_)<<"\n";
lattice.N_.print("Reference base vectors");
lattice.B_.print("Reference basis vectors");
return o;
}
//===========================================================================
// Constructs the virtual atom cluster of neighbors within cutoff
// @param F the deformation gradient tensor
//===========================================================================
void CBLattice::atom_cluster(const MATRIX &F, double cutoff, AtomCluster &v)
{
RC2_ = cutoff*cutoff;
// compute new base and basis vectors
v.clear();
v.F_ = F;
n_ = F*N_;
b_ = F*B_;
// add basis from the center cell (not including representative atom)
for (int i=1; i<B_.nCols(); i++) {
v.cur_bond_len_.push_back(b_.col_norm(i));
v.ref_coords_.push_back(column(B_,i));
}
_FindAtomsInCutoff(v);
}
//=============================================================================
// Computes forces on central atom, with atom I displaced by u.
//=============================================================================
DENS_VEC AtomCluster::perturbed_force(const CbPotential *p, int I, DENS_VEC *u) const
{
DENS_VEC f(3);
for (INDEX i=0; i<size(); i++) {
DENS_VEC ri = r(i);
if (u && i+1==I) ri += *u;
if (u && I==0) ri -= *u;
const double d = ri.norm();
f.add_scaled(ri, -p->phi_r(d)/d);
}
return f;
}
//=============================================================================
// Computes the force constant matrix between atoms I and 0.
//=============================================================================
DENS_MAT AtomCluster::force_constants(INDEX I, const CbPotential *p) const
{
DENS_MAT D(3,3);
for (INDEX i=0; i<3; i++) {
DENS_VEC du(3);
du(i) = 1.0e-6; // take central difference
row(D,i) = perturbed_force(p, I, &du);
du(i) = -du(i);
row(D,i) -= perturbed_force(p, I, &du);
}
D *= 0.5e6;
return D;
}
//=============================================================================
// performs an iterative search for all neighbors within cutoff
//=============================================================================
void CBLattice::_FindAtomsInCutoff(AtomCluster &v)
{
static const int dir[2] = {-1, 1};
int a, b, c, abc;
std::stack<int> queue(queue0_);
std::set<int> done;
// search in each direction
while (!queue.empty()) {
abc = queue.top();
queue.pop();
if (done.find(abc) == done.end()) { // value not in set
unhash(abc,a,b,c); // convert abc to a,b,c
if (_CheckUnitCell(a, b, c, v)) {
done.insert(abc);
// add direct 'outward' neighbors to queue
queue.push(hash(a+dir[a>0], b, c));
queue.push(hash(a, b+dir[b>0], c));
queue.push(hash(a, b, c+dir[c>0]));
}
}
}
}
//===========================================================================
// Computes \f$r^2 = \Vert a n_1 + b n_2 +c n_3 + b_d \Vert^2 \f$
// and adds atom (a,b,c,d) if \f$r^2 < r_{cutoff}^2 \f$
// @param a cell x-index
// @param b cell y-index
// @param c cell z-index
//===========================================================================
bool CBLattice::_CheckUnitCell(char a, char b, char c, AtomCluster &v)
{
const int nsd = n_.nRows(); // number of spatial dimensions
const double A=double(a), B=double(b), C=double(c);
bool found=false;
DENS_VEC r0(nsd,false), R0(nsd,false), Rd(nsd,false); // don't initialize
for (int i=0; i<nsd; i++) { // precompute locations of cell
R0(i) = A*N_(0,i) + B*N_(1,i) + C*N_(2,i); // reference
}
r0 = v.F_*R0; // deformed
for (int d=0; d<b_.nCols(); d++) {
double ri = r0(0) + b_(0,d);
double r2 = ri*ri;
for (int i=1; i<nsd; i++) {
ri = r0(i) + b_(i,d);
r2 += ri*ri;
}
if (r2 <= RC2_) {
v.ref_coords_.push_back(R0);
v.ref_coords_.back() += column(B_,d); // position is R0 + B_[d]
v.cur_bond_len_.push_back(sqrt(r2));
found = true;
}
}
return found;
}
} // end ATC
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