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HyperelasticityOperator.cpp
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HyperelasticityOperator.cpp
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/************************************************************************
* Copyright © 2020 The Multiphysics Modeling and Computation (M2C) Lab
* <kevin.wgy@gmail.com> <kevinw3@vt.edu>
************************************************************************/
#include<HyperelasticityOperator.h>
#include<EmbeddedBoundaryDataSet.h>
#include<linear_algebra.h>
#include<trilinear_interpolation.h>
#include<Vector5D.h>
extern int INACTIVE_MATERIAL_ID;
//------------------------------------------------------------
HyperelasticityOperator::HyperelasticityOperator(MPI_Comm &comm_, DataManagers3D &dm_all_,
IoData &iod_, vector<VarFcnBase*> &varFcn_, SpaceVariable3D &coordinates_,
SpaceVariable3D &delta_xyz_, SpaceVariable3D &volume_,
GlobalMeshInfo &global_mesh_,
InterpolatorBase &interpolator_, GradientCalculatorBase &grad_,
std::vector<GhostPoint> &ghost_nodes_inner_,
std::vector<GhostPoint> &ghost_nodes_outer_)
: comm(comm_), iod(iod_), varFcn(varFcn_), global_mesh(global_mesh_),
coordinates(coordinates_), volume(volume_),
interpolator(interpolator_), grad(grad_),
refmap(comm_, dm_all_, iod_, coordinates_, delta_xyz_,
global_mesh_, ghost_nodes_inner_, ghost_nodes_outer_),
F(comm_, &(dm_all_.ghosted1_9dof)),
J(comm_, &(dm_all_.ghosted1_1dof)),
Var1(comm_, &(dm_all_.ghosted1_3dof)),
Var2(comm_, &(dm_all_.ghosted1_3dof)),
Var3(comm_, &(dm_all_.ghosted1_3dof)),
dXidx_i_minus_half(comm_, &(dm_all_.ghosted1_3dof)),
dXidx_j_minus_half(comm_, &(dm_all_.ghosted1_3dof)),
dXidx_k_minus_half(comm_, &(dm_all_.ghosted1_3dof)),
dXidy_i_minus_half(comm_, &(dm_all_.ghosted1_3dof)),
dXidy_j_minus_half(comm_, &(dm_all_.ghosted1_3dof)),
dXidy_k_minus_half(comm_, &(dm_all_.ghosted1_3dof)),
dXidz_i_minus_half(comm_, &(dm_all_.ghosted1_3dof)),
dXidz_j_minus_half(comm_, &(dm_all_.ghosted1_3dof)),
dXidz_k_minus_half(comm_, &(dm_all_.ghosted1_3dof))
{
coordinates_.GetCornerIndices(&i0, &j0, &k0, &imax, &jmax, &kmax);
coordinates_.GetGhostedCornerIndices(&ii0, &jj0, &kk0, &iimax, &jjmax, &kkmax);
cylindrical_symmetry = false;
if(iod.mesh.type == MeshData::CYLINDRICAL) {
cylindrical_symmetry = true;
if(!global_mesh.two_dimensional_xy) {
print_error("*** Error: HyperelasticityOperator detected incorrect mesh, "
"with cylindrical symmetry requested.\n");
exit_mpi();
}
} else if(iod.mesh.type != MeshData::THREEDIMENSIONAL) {
print_error("*** Error: HyperelasticityOperator cannot handle user-specified domain/mesh type.\n");
exit_mpi();
}
// Create a HyperelasticityFcn for each material.
// For problems involving multiple materials, it could happen that the user specified
// hyperelasticity model for only some of the materials, but not all. In this case, we
// still create a dummy (i.e. base) function for those unspecified materials.
for(auto it = iod.eqs.materials.dataMap.begin(); it != iod.eqs.materials.dataMap.end(); it++) {
hyperFcn.push_back(NULL); //allocate space
deviator_only.push_back(true); //default is true
}
for(auto it = iod.eqs.materials.dataMap.begin(); it != iod.eqs.materials.dataMap.end(); it++) {
int matid = it->first;
if(matid < 0 || matid >= (int)hyperFcn.size()) {
print_error("*** Error: Detected error in the specification of material indices (id = %d).\n", matid);
exit_mpi();
}
deviator_only[matid] = (it->second->hyperelasticity.stress_option
== HyperelasticityModelData::DEVIATOR_ONLY);
switch (it->second->hyperelasticity.type) {
case HyperelasticityModelData::NONE :
if(cylindrical_symmetry)
hyperFcn[matid] = new HyperelasticityFcnBase2DCyl(*varFcn[matid]);
else
hyperFcn[matid] = new HyperelasticityFcnBase(*varFcn[matid]);
break;
case HyperelasticityModelData::SAINTVENANT_KIRCHHOFF :
if(cylindrical_symmetry)
hyperFcn[matid] = new HyperelasticityFcnSaintVenantKirchhoff2DCyl
(it->second->hyperelasticity, *varFcn[matid]);
else
hyperFcn[matid] = new HyperelasticityFcnSaintVenantKirchhoff
(it->second->hyperelasticity, *varFcn[matid]);
break;
case HyperelasticityModelData::MODIFIED_SAINTVENANT_KIRCHHOFF :
if(cylindrical_symmetry)
hyperFcn[matid] = new HyperelasticityFcnModifiedSaintVenantKirchhoff2DCyl
(it->second->hyperelasticity, *varFcn[matid]);
else
hyperFcn[matid] = new HyperelasticityFcnModifiedSaintVenantKirchhoff
(it->second->hyperelasticity, *varFcn[matid]);
break;
case HyperelasticityModelData::NEO_HOOKEAN :
if(cylindrical_symmetry)
hyperFcn[matid] = new HyperelasticityFcnNeoHookean2DCyl
(it->second->hyperelasticity, *varFcn[matid]);
else
hyperFcn[matid] = new HyperelasticityFcnNeoHookean
(it->second->hyperelasticity, *varFcn[matid]);
break;
case HyperelasticityModelData::MOONEY_RIVLIN :
if(cylindrical_symmetry)
hyperFcn[matid] = new HyperelasticityFcnMooneyRivlin2DCyl
(it->second->hyperelasticity, *varFcn[matid]);
else
hyperFcn[matid] = new HyperelasticityFcnMooneyRivlin
(it->second->hyperelasticity, *varFcn[matid]);
break;
default :
print_error("*** Error: HyperelasticityOperator detected unknown model type.\n");
exit_mpi();
}
}
}
//------------------------------------------------------------
HyperelasticityOperator::~HyperelasticityOperator()
{
for(int i=0; i<(int)hyperFcn.size(); i++)
delete hyperFcn[i];
}
//------------------------------------------------------------
void
HyperelasticityOperator::Destroy()
{
refmap.Destroy();
F.Destroy();
J.Destroy();
Var1.Destroy();
Var2.Destroy();
Var3.Destroy();
dXidx_i_minus_half.Destroy();
dXidx_j_minus_half.Destroy();
dXidx_k_minus_half.Destroy();
dXidy_i_minus_half.Destroy();
dXidy_j_minus_half.Destroy();
dXidy_k_minus_half.Destroy();
dXidz_i_minus_half.Destroy();
dXidz_j_minus_half.Destroy();
dXidz_k_minus_half.Destroy();
}
//------------------------------------------------------------
void
HyperelasticityOperator::InitializeReferenceMap(SpaceVariable3D &Xi)
{
refmap.SetInitialCondition(Xi);
}
//------------------------------------------------------------
void
HyperelasticityOperator::ApplyBoundaryConditionsToReferenceMap(SpaceVariable3D &Xi)
{
refmap.ApplyBoundaryConditions(Xi);
}
//------------------------------------------------------------
void
HyperelasticityOperator::ComputeReferenceMapResidual(SpaceVariable3D &V, SpaceVariable3D &Xi,
SpaceVariable3D &R, [[maybe_unused]] double time)
{
#ifdef HYPERELASTICITY_TEST
PrescribeVelocityForTesting(V, time);
#endif
refmap.ComputeResidual(V,Xi,R);
}
//------------------------------------------------------------
void
HyperelasticityOperator::ComputeDeformationGradientAtNodes(SpaceVariable3D &Xi)
{
if(cylindrical_symmetry)
ComputeDeformGradAtNodes2DCylindrical(Xi);
else
ComputeDeformGradAtNodes3D(Xi);
}
//------------------------------------------------------------
void
HyperelasticityOperator::ComputeDeformGradAtNodes3D(SpaceVariable3D &Xi)
{
// NOTE: This function computes deformation gradient (F) ONLY WITHIN THE PHYSICAL DOMAIN,
// NOT in the ghost boundary layer.
// ------------------------------------
// Step 1: Calculate the Jacobian of Xi
// ------------------------------------
std::vector<int> i012{0,1,2};
// dxi/dx
grad.CalculateFirstDerivativeAtNodes(0 /*dx*/, Xi, i012, Var1, i012);
// dxi/dy
grad.CalculateFirstDerivativeAtNodes(1 /*dy*/, Xi, i012, Var2, i012);
// dxi/dz
grad.CalculateFirstDerivativeAtNodes(2 /*dz*/, Xi, i012, Var3, i012);
// ------------------------------------
// Step 2: Calculate the deformation gradient: F = inv(grad.Xi) and its determinant
// ------------------------------------
double*** f = F.GetDataPointer(); //column-first (aka. column-major)
double*** Jloc = J.GetDataPointer();
Vec3D*** dXidx = (Vec3D***)Var1.GetDataPointer();
Vec3D*** dXidy = (Vec3D***)Var2.GetDataPointer();
Vec3D*** dXidz = (Vec3D***)Var3.GetDataPointer();
double gradxi[9]; //local values of Jacobian of Xi
bool invertible = false;
for(int k=k0; k<kmax; k++)
for(int j=j0; j<jmax; j++)
for(int i=i0; i<imax; i++) {
for(int dim=0; dim<3; dim++)
gradxi[dim] = dXidx[k][j][i][dim];
for(int dim=0; dim<3; dim++)
gradxi[3+dim] = dXidy[k][j][i][dim];
for(int dim=0; dim<3; dim++)
gradxi[6+dim] = dXidz[k][j][i][dim];
invertible = MathTools::LinearAlgebra::
CalculateMatrixInverseAndDeterminant3x3(gradxi, &f[k][j][9*i], &Jloc[k][j][i]);
if(!invertible)
fprintf(stdout,"\033[0;35mWarning: Jacobian of ref. map at (%d,%d,%d) is not invertible."
" determinant = %e.\033[0m\n", i,j,k, Jloc[k][j][i]);
Jloc[k][j][i] = 1.0/Jloc[k][j][i]; // we want the determinant of F, not grad-xi!
if(Jloc[k][j][i]<=0.0)
fprintf(stdout,"\033[0;35mWarning: Determinant of deformation gradient at (%d,%d,%d)"
" is negative (%e).\033[0m\n", i,j,k, Jloc[k][j][i]);
}
F.RestoreDataPointerAndInsert();
J.RestoreDataPointerAndInsert();
Var1.RestoreDataPointerToLocalVector();
Var2.RestoreDataPointerToLocalVector();
Var3.RestoreDataPointerToLocalVector();
}
//------------------------------------------------------------
void
HyperelasticityOperator::ComputeDeformGradAtNodes2DCylindrical(SpaceVariable3D &Xi)
{
// NOTE: This function computes deformation gradient (F) ONLY WITHIN THE PHYSICAL DOMAIN,
// NOT in the ghost boundary layer.
// ------------------------------------
// Step 1: Calculate the Jacobian of Xi
// ------------------------------------
std::vector<int> i01{0,1};
// dxi/dx (i.e., dxi/dz in cylindrical coords)
grad.CalculateFirstDerivativeAtNodes(0 /*dx*/, Xi, i01, Var1, i01);
// dxi/dy (i.e., dxi/dr in cylindrical coords)
grad.CalculateFirstDerivativeAtNodes(1 /*dy*/, Xi, i01, Var2, i01);
// ------------------------------------
// Step 2: Calculate the deformation gradient: F = inv(grad.Xi) and its determinant
// ------------------------------------
double*** f = F.GetDataPointer(); //column-first (aka. column-major)
double*** Jloc = J.GetDataPointer();
Vec3D*** xi = (Vec3D***)Xi.GetDataPointer();
Vec3D*** dXidx = (Vec3D***)Var1.GetDataPointer();
Vec3D*** dXidy = (Vec3D***)Var2.GetDataPointer();
double gradxi[4]; //local values of Jacobian of Xi
double f2[4], Jloc2, r0;
bool invertible = false;
for(int k=k0; k<kmax; k++) {
for(int j=j0; j<jmax; j++) {
double r = global_mesh.GetY(j);
for(int i=i0; i<imax; i++) {
for(int dim=0; dim<2; dim++)
gradxi[dim] = dXidx[k][j][i][dim];
for(int dim=0; dim<2; dim++)
gradxi[2+dim] = dXidy[k][j][i][dim];
invertible = MathTools::LinearAlgebra::
CalculateMatrixInverseAndDeterminant2x2(gradxi, f2, &Jloc2);
if(!invertible)
fprintf(stdout,"\033[0;35mWarning: Jacobian of ref. map at (%d,%d,%d) is not invertible."
" determinant = %e.\033[0m\n", i,j,k, Jloc2);
// Note: f = [dz/dZ 0 dz/dR; 0 r/R 0; dr/dZ 0 dr/dR]; //"x = z", "y = r"!
r0 = xi[k][j][i][1];
double* floc(&f[k][j][9*i]);
floc[0] = f2[0]; floc[3] = 0.0; floc[6] = f2[2];
floc[1] = 0.0; floc[4] = r/r0; floc[7] = 0.0;
floc[2] = f2[1]; floc[5] = 0.0; floc[8] = f2[3];
Jloc[k][j][i] = 1.0/Jloc2*r/r0; // we want the determinant of F, not grad-xi!
if(Jloc[k][j][i]<=0.0)
fprintf(stdout,"\033[0;35mWarning: Determinant of deformation gradient at (%d,%d,%d)"
" is negative (%e).\033[0m\n", i,j,k, Jloc[k][j][i]);
}
}
}
F.RestoreDataPointerAndInsert();
J.RestoreDataPointerAndInsert();
Xi.RestoreDataPointerToLocalVector();
Var1.RestoreDataPointerToLocalVector();
Var2.RestoreDataPointerToLocalVector();
}
//------------------------------------------------------------
void
HyperelasticityOperator::ComputePrincipalStresses(SpaceVariable3D &Xi, SpaceVariable3D &V,
SpaceVariable3D &ID, SpaceVariable3D &PS)
{
if(cylindrical_symmetry)
ComputePrincipalStresses2DCylindrical(Xi,V,ID,PS);
else
ComputePrincipalStresses3D(Xi,V,ID,PS);
}
//------------------------------------------------------------
void
HyperelasticityOperator::ComputePrincipalStresses3D(SpaceVariable3D &Xi, SpaceVariable3D &V,
SpaceVariable3D &ID, SpaceVariable3D &PS)
{
ComputeDeformGradAtNodes3D(Xi); //fill F
double*** f = F.GetDataPointer();
double*** id = ID.GetDataPointer();
Vec5D*** v = (Vec5D***)V.GetDataPointer();
Vec3D*** ps = (Vec3D***)PS.GetDataPointer();
bool success;
int myid;
double sigma6[6], sigma9[9]; //Cauchy stress tensor, column-first, symmetric
for(int k=k0; k<kmax; k++)
for(int j=j0; j<jmax; j++)
for(int i=i0; i<imax; i++) {
myid = id[k][j][i];
if(myid == INACTIVE_MATERIAL_ID) {
ps[k][j][i] = 0.0;
continue;
}
assert(myid>=0 && myid<(int)hyperFcn.size());
double* floc(&f[k][j][9*i]);
hyperFcn[myid]->GetCauchyStressTensor(floc, v[k][j][i], sigma6);
// Get a general 3x3 matrix
sigma9[0] = sigma6[0]; sigma9[3] = sigma6[1]; sigma9[6] = sigma6[2];
sigma9[1] = sigma6[1]; sigma9[4] = sigma6[3]; sigma9[7] = sigma6[4];
sigma9[2] = sigma6[2]; sigma9[5] = sigma6[4]; sigma9[8] = sigma6[5];
success = MathTools::LinearAlgebra::
CalculateEigenSymmetricMatrix3x3(sigma9, ps[k][j][i]);
if(!success) {
fprintf(stdout,"\033[0;31m*** Error: Unable to calculate matrix "
"eigenvalues in HyperelasticityOperator.\n");
exit(-1);
}
std::swap(ps[k][j][i][0], ps[k][j][i][2]); // should be in descending order
/*
if(k==75) {
double r = sqrt(global_mesh.GetX(i)*global_mesh.GetX(i)+global_mesh.GetY(j)*global_mesh.GetY(j));
if(fabs(r-0.205)<1e-4)
fprintf(stdout,"At (x,y,z) = (%e,%e,%e), r = %e, phi = %e, F = [%e %e %e; %e %e %e; %e %e %e;]. "
"sigma6 = %e %e %e %e %e %e. ps = %e %e %e.\n",
global_mesh.GetX(i), global_mesh.GetY(j), global_mesh.GetZ(k), r,
atan(global_mesh.GetY(j)/global_mesh.GetX(i)), floc[0], floc[3], floc[6],
floc[1], floc[4], floc[7], floc[2], floc[5], floc[8],
sigma6[0], sigma6[1], sigma6[2], sigma6[3], sigma6[4], sigma6[5],
ps[k][j][i][0], ps[k][j][i][1], ps[k][j][i][2]);
}
*/
}
F.RestoreDataPointerToLocalVector();
ID.RestoreDataPointerToLocalVector();
V.RestoreDataPointerToLocalVector();
PS.RestoreDataPointerAndInsert();
}
//------------------------------------------------------------
void
HyperelasticityOperator::ComputePrincipalStresses2DCylindrical(SpaceVariable3D &Xi, SpaceVariable3D &V,
SpaceVariable3D &ID, SpaceVariable3D &PS)
{
ComputeDeformGradAtNodes2DCylindrical(Xi); //fills F
double*** f = F.GetDataPointer();
double*** id = ID.GetDataPointer();
Vec5D*** v = (Vec5D***)V.GetDataPointer();
Vec3D*** ps = (Vec3D***)PS.GetDataPointer();
bool success;
int myid = 0;
double sigma2d[3], sigma9[9] = {0.0}, sigma_phiphi; //"sigma_2D" and \sigma_{\phi\phi}
for(int k=k0; k<kmax; k++)
for(int j=j0; j<jmax; j++)
for(int i=i0; i<imax; i++) {
myid = id[k][j][i];
if(myid == INACTIVE_MATERIAL_ID) {
ps[k][j][i] = 0.0;
continue;
}
assert(myid>=0 && myid<(int)hyperFcn.size());
// Get sigma_2D and sigma_phiphi
double* floc(&f[k][j][9*i]);
dynamic_cast<HyperelasticityFcnBase2DCyl*>
(hyperFcn[myid])->GetCauchyStressTensor(floc, v[k][j][i], sigma2d, sigma_phiphi);
// Get a general 3x3 matrix
sigma9[0] = sigma2d[0]; sigma9[6] = sigma2d[1];
sigma9[4] = sigma_phiphi;
sigma9[2] = sigma2d[1]; sigma9[8] = sigma2d[2];
success = MathTools::LinearAlgebra::
CalculateEigenSymmetricMatrix3x3(sigma9, ps[k][j][i]);
if(!success) {
fprintf(stdout,"\033[0;31m*** Error: Unable to calculate matrix "
"eigenvalues in HyperelasticityOperator.\n");
exit(-1);
}
std::swap(ps[k][j][i][0], ps[k][j][i][2]); // should be in descending order
/*
if(i==75 && j==20)
fprintf(stdout,"At (z,r) = (%e,%e), F = [%e %e %e; %e %e %e; %e %e %e;]. sigma2d = [%e %e; %e %e]"
". sigma_phiphi = %e. ps = %e %e %e.\n",
global_mesh.GetX(i), global_mesh.GetY(j), floc[0], floc[3], floc[6],
floc[1], floc[4], floc[7], floc[2], floc[5], floc[8],
sigma2d[0], sigma2d[1], sigma2d[1], sigma2d[2], sigma_phiphi,
ps[k][j][i][0], ps[k][j][i][1], ps[k][j][i][2]);
*/
}
F.RestoreDataPointerToLocalVector();
ID.RestoreDataPointerToLocalVector();
V.RestoreDataPointerToLocalVector();
PS.RestoreDataPointerAndInsert();
}
//------------------------------------------------------------
void
HyperelasticityOperator::ComputePrincipalStressesAtProbes(SpaceVariable3D &Xi, SpaceVariable3D &ID,
std::vector<Int3> &ijk, std::vector<std::pair<int, std::array<bool,8> > > &ijk_valid,
std::vector<Vec3D> &trilinear_coords, Vec5D*** v, vector<Vec3D> &sol)
{
int nProbes = ijk.size();
if(nProbes == 0) {
sol.clear();
return; //no probes
}
ComputeDeformationGradientAtNodes(Xi); // fill "F"
double*** id = ID.GetDataPointer();
double*** f = F.GetDataPointer();
sol.assign(nProbes, 0.0);
int dim = 5;
for(int iProbe=0; iProbe<nProbes; iProbe++) {
int i = ijk[iProbe][0], j = ijk[iProbe][1], k = ijk[iProbe][2];
if(!coordinates.IsHere(i,j,k,true))
continue;
//NOTE: Unlike other space variables, "Xi" is only populated within the physical domain.
// Therefore, we should calculate stresses only at nodes within the physical domain
//this probe node is in the current subdomain (including ghost)
// c000
Vec3D c000 = 0.0;
vector<bool> valid(8,false);
int valid_count = 0;
if(ijk_valid[iProbe].second[0] && coordinates.IsHereOrInternalGhost(i,j,k)) {
valid[0] = true;
valid_count++;
c000 = ComputePrincipalStressesAtPoint(&f[k][j][i*9], v[k][j][i*dim], id[k][j][i]);
}
// c100
Vec3D c100 = 0.0;
if(ijk_valid[iProbe].second[1] && coordinates.IsHereOrInternalGhost(i+1,j,k)) {
valid[1] = true;
valid_count++;
c100 = ComputePrincipalStressesAtPoint(&f[k][j][(i+1)*9], v[k][j][(i+1)*dim], id[k][j][i+1]);
}
// c010
Vec3D c010 = 0.0;
if(ijk_valid[iProbe].second[2] && coordinates.IsHereOrInternalGhost(i,j+1,k)) {
valid[2] = true;
valid_count++;
c010 = ComputePrincipalStressesAtPoint(&f[k][j+1][i*9], v[k][j+1][i*dim], id[k][j+1][i]);
}
// c110
Vec3D c110 = 0.0;
if(ijk_valid[iProbe].second[3] && coordinates.IsHereOrInternalGhost(i+1,j+1,k)) {
valid[3] = true;
valid_count++;
c110 = ComputePrincipalStressesAtPoint(&f[k][j+1][(i+1)*9], v[k][j+1][(i+1)*dim], id[k][j+1][i+1]);
}
// c001
Vec3D c001 = 0.0;
if(ijk_valid[iProbe].second[4] && coordinates.IsHereOrInternalGhost(i,j,k+1)) {
valid[4] = true;
valid_count++;
c001 = ComputePrincipalStressesAtPoint(&f[k+1][j][i*9], v[k+1][j][i*dim], id[k+1][j][i]);
}
// c101
Vec3D c101 = 0.0;
if(ijk_valid[iProbe].second[5] && coordinates.IsHereOrInternalGhost(i+1,j,k+1)) {
valid[5] = true;
valid_count++;
c101 = ComputePrincipalStressesAtPoint(&f[k+1][j][(i+1)*9], v[k+1][j][(i+1)*dim], id[k+1][j][i+1]);
}
// c011
Vec3D c011 = 0.0;
if(ijk_valid[iProbe].second[6] && coordinates.IsHereOrInternalGhost(i,j+1,k+1)) {
valid[6] = true;
valid_count++;
c011 = ComputePrincipalStressesAtPoint(&f[k+1][j+1][i*9], v[k+1][j+1][i*dim], id[k+1][j+1][i]);
}
// c111
Vec3D c111 = 0.0;
if(ijk_valid[iProbe].second[7] && coordinates.IsHereOrInternalGhost(i+1,j+1,k+1)) {
valid[7] = true;
valid_count++;
c111 = ComputePrincipalStressesAtPoint(&f[k+1][j+1][(i+1)*9], v[k+1][j+1][(i+1)*dim],
id[k+1][j+1][i+1]);
}
if(valid_count<8) {//fill invalid slots with average value
Vec3D c_avg = (c000+c100+c010+c110+c001+c101+c011+c111)/valid_count;
if(!valid[0]) c000 = c_avg;
if(!valid[1]) c100 = c_avg;
if(!valid[2]) c010 = c_avg;
if(!valid[3]) c110 = c_avg;
if(!valid[4]) c001 = c_avg;
if(!valid[5]) c101 = c_avg;
if(!valid[6]) c011 = c_avg;
if(!valid[7]) c111 = c_avg;
}
sol[iProbe] = MathTools::trilinear_interpolation(trilinear_coords[iProbe], c000, c100, c010, c110,
c001, c101, c011, c111);
}
MPI_Allreduce(MPI_IN_PLACE, (double*)sol.data(), 3*sol.size(), MPI_DOUBLE, MPI_SUM, comm);
F.RestoreDataPointerToLocalVector();
ID.RestoreDataPointerToLocalVector();
}
//------------------------------------------------------------
Vec3D
HyperelasticityOperator::ComputePrincipalStressesAtPoint(double *f, Vec5D &v, int id)
{
if(cylindrical_symmetry)
return ComputePrincipalStressesAtPoint2DCylindrical(f, v, id);
return ComputePrincipalStressesAtPoint3D(f, v, id);
}
//------------------------------------------------------------
Vec3D
HyperelasticityOperator::ComputePrincipalStressesAtPoint3D(double *f, Vec5D &v, int id)
{
Vec3D ps(0.0);
if(id == INACTIVE_MATERIAL_ID)
return ps;
assert(id>=0 && id<(int)hyperFcn.size());
double sigma6[6], sigma9[9]; //Cauchy stress tensor, column-first, symmetric
hyperFcn[id]->GetCauchyStressTensor(f, v, sigma6);
// Get a general 3x3 matrix
sigma9[0] = sigma6[0]; sigma9[3] = sigma6[1]; sigma9[6] = sigma6[2];
sigma9[1] = sigma6[1]; sigma9[4] = sigma6[3]; sigma9[7] = sigma6[4];
sigma9[2] = sigma6[2]; sigma9[5] = sigma6[4]; sigma9[8] = sigma6[5];
bool success = MathTools::LinearAlgebra::CalculateEigenSymmetricMatrix3x3(sigma9, ps);
if(!success) {
fprintf(stdout,"\033[0;31m*** Error: Unable to calculate matrix "
"eigenvalues in HyperelasticityOperator (1P3D).\n");
exit(-1);
}
std::swap(ps[0], ps[2]); // should be in descending order
return ps;
}
//------------------------------------------------------------
Vec3D
HyperelasticityOperator::ComputePrincipalStressesAtPoint2DCylindrical(double *f, Vec5D &v, int id)
{
Vec3D ps(0.0);
if(id == INACTIVE_MATERIAL_ID)
return ps;
assert(id>=0 && id<(int)hyperFcn.size());
// Get sigma_2D and sigma_phiphi
double sigma2d[3], sigma9[9] = {0.0}, sigma_phiphi; //"sigma_2D" and \sigma_{\phi\phi}
dynamic_cast<HyperelasticityFcnBase2DCyl*>
(hyperFcn[id])->GetCauchyStressTensor(f, v, sigma2d, sigma_phiphi);
// Get a general 3x3 matrix
sigma9[0] = sigma2d[0]; sigma9[6] = sigma2d[1];
sigma9[4] = sigma_phiphi;
sigma9[2] = sigma2d[1]; sigma9[8] = sigma2d[2];
bool success = MathTools::LinearAlgebra::CalculateEigenSymmetricMatrix3x3(sigma9, ps);
if(!success) {
fprintf(stdout,"\033[0;31m*** Error: Unable to calculate matrix "
"eigenvalues in HyperelasticityOperator (1P2DCyl).\n");
exit(-1);
}
std::swap(ps[0], ps[2]); // should be in descending order
return ps;
}
//------------------------------------------------------------
//Note: Fluxes are added on the left-hand-side of the Navier-Stokes equations
void
HyperelasticityOperator::AddHyperelasticityFluxes(SpaceVariable3D &V, SpaceVariable3D &ID, SpaceVariable3D &Xi,
vector<std::unique_ptr<EmbeddedBoundaryDataSet> > *EBDS,
SpaceVariable3D &R)
{
if(cylindrical_symmetry) {
AddFluxes2DCylindrical(V,ID,Xi,EBDS,R);
AddCylindricalSourceTerms(V,ID,Xi,EBDS,R);
} else
AddFluxes3D(V,ID,Xi,EBDS,R);
}
//------------------------------------------------------------
//Note: Fluxes are added on the left-hand-side of the Navier-Stokes equations
void
HyperelasticityOperator::AddFluxes3D(SpaceVariable3D &V, SpaceVariable3D &ID, SpaceVariable3D &Xi,
vector<std::unique_ptr<EmbeddedBoundaryDataSet> > *EBDS,
SpaceVariable3D &R)
{
if(EBDS)
print_warning("Warning: AddHyperelasticityFluxes: Not able to account for embedded surfaces.\n");
std::vector<int> i123{1,2,3}, i012{0,1,2};
//1. Calculate Xi derivatives at cell interfaces
grad.CalculateFirstDerivativeAtCellInterfaces(0, 0, Xi, i012, dXidx_i_minus_half, i012);
grad.CalculateFirstDerivativeAtCellInterfaces(0, 1, Xi, i012, dXidx_j_minus_half, i012);
grad.CalculateFirstDerivativeAtCellInterfaces(0, 2, Xi, i012, dXidx_k_minus_half, i012);
grad.CalculateFirstDerivativeAtCellInterfaces(1, 0, Xi, i012, dXidy_i_minus_half, i012);
grad.CalculateFirstDerivativeAtCellInterfaces(1, 1, Xi, i012, dXidy_j_minus_half, i012);
grad.CalculateFirstDerivativeAtCellInterfaces(1, 2, Xi, i012, dXidy_k_minus_half, i012);
grad.CalculateFirstDerivativeAtCellInterfaces(2, 0, Xi, i012, dXidz_i_minus_half, i012);
grad.CalculateFirstDerivativeAtCellInterfaces(2, 1, Xi, i012, dXidz_j_minus_half, i012);
grad.CalculateFirstDerivativeAtCellInterfaces(2, 2, Xi, i012, dXidz_k_minus_half, i012);
//2. Loop through cell interfaces and calculate fluxes
Vec3D*** dxidx_i = (Vec3D***)dXidx_i_minus_half.GetDataPointer();
Vec3D*** dxidx_j = (Vec3D***)dXidx_j_minus_half.GetDataPointer();
Vec3D*** dxidx_k = (Vec3D***)dXidx_k_minus_half.GetDataPointer();
Vec3D*** dxidy_i = (Vec3D***)dXidy_i_minus_half.GetDataPointer();
Vec3D*** dxidy_j = (Vec3D***)dXidy_j_minus_half.GetDataPointer();
Vec3D*** dxidy_k = (Vec3D***)dXidy_k_minus_half.GetDataPointer();
Vec3D*** dxidz_i = (Vec3D***)dXidz_i_minus_half.GetDataPointer();
Vec3D*** dxidz_j = (Vec3D***)dXidz_j_minus_half.GetDataPointer();
Vec3D*** dxidz_k = (Vec3D***)dXidz_k_minus_half.GetDataPointer();
Vec5D*** v = (Vec5D***)V.GetDataPointer();
Vec5D*** res = (Vec5D***)R.GetDataPointer();
double*** id = (double***)ID.GetDataPointer();
int myid = 0;
double gradxi[9], f[9]; //nabla xi and deformation gradient
double dx = 0.0, dy = 0.0, dz = 0.0;
Vec5D flux;
bool invertible;
for(int k=k0; k<kkmax; k++) {
dz = global_mesh.GetDz(k);
for(int j=j0; j<jjmax; j++) {
dy = global_mesh.GetDy(j);
for(int i=i0; i<iimax; i++) {
dx = global_mesh.GetDx(i);
myid = id[k][j][i];
if(myid == INACTIVE_MATERIAL_ID)
continue;
assert(myid>=0 && myid<(int)hyperFcn.size());
//*****************************************
//calculate flux function F_{i-1/2,j,k}
//*****************************************
if(k!=kkmax-1 && j!=jjmax-1) {
for(int dim=0; dim<3; dim++)
gradxi[dim] = dxidx_i[k][j][i][dim];
for(int dim=0; dim<3; dim++)
gradxi[3+dim] = dxidy_i[k][j][i][dim];
for(int dim=0; dim<3; dim++)
gradxi[6+dim] = dxidz_i[k][j][i][dim];
invertible = MathTools::LinearAlgebra::
CalculateMatrixInverseAndDeterminant3x3(gradxi, f);
if(!invertible)
fprintf(stdout,"\033[0;35mWarning: Jacobian of ref. map at (%d-1/2,%d,%d)"
" is not invertible.\033[0m\n", i,j,k);
hyperFcn[myid]->EvaluateHyperelasticFluxFunction_F(flux, f, v[k][j][i],
deviator_only[myid]);//TODO: multi-material
flux *= dy*dz;
res[k][j][i] += flux;
res[k][j][i-1] -= flux;
}
//*****************************************
//calculate flux function G_{i,j-1/2,k}
//*****************************************
if(i!=iimax-1 && k!=kkmax-1) {
for(int dim=0; dim<3; dim++)
gradxi[dim] = dxidx_j[k][j][i][dim];
for(int dim=0; dim<3; dim++)
gradxi[3+dim] = dxidy_j[k][j][i][dim];
for(int dim=0; dim<3; dim++)
gradxi[6+dim] = dxidz_j[k][j][i][dim];
invertible = MathTools::LinearAlgebra::
CalculateMatrixInverseAndDeterminant3x3(gradxi, f);
if(!invertible)
fprintf(stdout,"\033[0;35mWarning: Jacobian of ref. map at (%d,%d-1/2,%d)"
" is not invertible.\033[0m\n", i,j,k);
hyperFcn[myid]->EvaluateHyperelasticFluxFunction_G(flux, f, v[k][j][i],
deviator_only[myid]);//TODO: multi-material
flux *= dx*dz;
res[k][j][i] += flux;
res[k][j-1][i] -= flux;
}
//*****************************************
//calculate flux function H_{i,j,k-1/2}
//*****************************************
if(i!=iimax-1 && j!=jjmax-1) {
for(int dim=0; dim<3; dim++)
gradxi[dim] = dxidx_k[k][j][i][dim];
for(int dim=0; dim<3; dim++)
gradxi[3+dim] = dxidy_k[k][j][i][dim];
for(int dim=0; dim<3; dim++)
gradxi[6+dim] = dxidz_k[k][j][i][dim];
invertible = MathTools::LinearAlgebra::
CalculateMatrixInverseAndDeterminant3x3(gradxi, f);
if(!invertible)
fprintf(stdout,"\033[0;35mWarning: Jacobian of ref. map at (%d,%d,%d-1/2)"
" is not invertible.\033[0m\n", i,j,k);
hyperFcn[myid]->EvaluateHyperelasticFluxFunction_H(flux, f, v[k][j][i],
deviator_only[myid]);//TODO: multi-material
flux *= dx*dy;
res[k][j][i] += flux;
res[k-1][j][i] -= flux;
}
}
}
}
dXidx_i_minus_half.RestoreDataPointerToLocalVector();
dXidx_j_minus_half.RestoreDataPointerToLocalVector();
dXidx_k_minus_half.RestoreDataPointerToLocalVector();
dXidy_i_minus_half.RestoreDataPointerToLocalVector();
dXidy_j_minus_half.RestoreDataPointerToLocalVector();
dXidy_k_minus_half.RestoreDataPointerToLocalVector();
dXidz_i_minus_half.RestoreDataPointerToLocalVector();
dXidz_j_minus_half.RestoreDataPointerToLocalVector();
dXidz_k_minus_half.RestoreDataPointerToLocalVector();
ID.RestoreDataPointerToLocalVector();
V.RestoreDataPointerToLocalVector();
R.RestoreDataPointerToLocalVector(); //NOTE: although R has been updated, there is no need of
// cross-subdomain communications. So, no need to
// update the global vec.
}
//------------------------------------------------------------
//Note: Fluxes are added on the left-hand-side of the Navier-Stokes equations
void
HyperelasticityOperator::AddFluxes2DCylindrical(SpaceVariable3D &V, SpaceVariable3D &ID, SpaceVariable3D &Xi,
vector<std::unique_ptr<EmbeddedBoundaryDataSet> > *EBDS,
SpaceVariable3D &R)
{
if(EBDS)
print_warning("Warning: AddHyperelasticityFluxes: Not able to account for embedded surfaces.\n");
std::vector<int> i01{0,1};
//1. Calculate Xi derivatives at cell interfaces
grad.CalculateFirstDerivativeAtCellInterfaces(0, 0, Xi, i01, dXidx_i_minus_half, i01);
grad.CalculateFirstDerivativeAtCellInterfaces(0, 1, Xi, i01, dXidx_j_minus_half, i01);
grad.CalculateFirstDerivativeAtCellInterfaces(1, 0, Xi, i01, dXidy_i_minus_half, i01);
grad.CalculateFirstDerivativeAtCellInterfaces(1, 1, Xi, i01, dXidy_j_minus_half, i01);
//2. Loop through cell interfaces and calculate fluxes
Vec3D*** dxidx_i = (Vec3D***)dXidx_i_minus_half.GetDataPointer();
Vec3D*** dxidx_j = (Vec3D***)dXidx_j_minus_half.GetDataPointer();
Vec3D*** dxidy_i = (Vec3D***)dXidy_i_minus_half.GetDataPointer();
Vec3D*** dxidy_j = (Vec3D***)dXidy_j_minus_half.GetDataPointer();
Vec3D*** xi = (Vec3D***)Xi.GetDataPointer();
Vec5D*** v = (Vec5D***)V.GetDataPointer();
Vec5D*** res = (Vec5D***)R.GetDataPointer();
double*** id = (double***)ID.GetDataPointer();
int myid = 0;
double gradxi[4], f2[4], f[9] = {0.0}; //nabla xi and deformation gradient
double dx = 0.0, dy = 0.0, dz = 0.0, r0;
Vec5D flux;
bool invertible;
for(int k=k0; k<kkmax; k++) {
dz = global_mesh.GetDz(k);
for(int j=j0; j<jjmax; j++) {
dy = global_mesh.GetDy(j);
for(int i=i0; i<iimax; i++) {
dx = global_mesh.GetDx(i);
myid = id[k][j][i];
if(myid == INACTIVE_MATERIAL_ID)
continue;
assert(myid>=0 && myid<(int)hyperFcn.size());
//*****************************************
//calculate flux function F_{i-1/2,j,k}
//*****************************************
if(k!=kkmax-1 && j!=jjmax-1) {
for(int dim=0; dim<2; dim++)
gradxi[dim] = dxidx_i[k][j][i][dim];
for(int dim=0; dim<2; dim++)
gradxi[2+dim] = dxidy_i[k][j][i][dim];
invertible = MathTools::LinearAlgebra::
CalculateMatrixInverseAndDeterminant2x2(gradxi, f2);
if(!invertible)
fprintf(stdout,"\033[0;35mWarning: Jacobian of ref. map at (%d-1/2,%d,%d)"
" is not invertible.\033[0m\n", i,j,k);
// Note: f = [dz/dZ 0 dz/dR; 0 r/R 0; dr/dZ 0 dr/dR]; //"x = z", "y = r"!
double r = global_mesh.GetY(j);
r0 = (global_mesh.GetDx(i-1)*xi[k][j][i][1] + dx*xi[k][j][i-1][1])
/ (global_mesh.GetDx(i-1) + dx);
f[0] = f2[0]; f[6] = f2[2];
f[4] = r/r0;
f[2] = f2[1]; f[8] = f2[3];
hyperFcn[myid]->EvaluateHyperelasticFluxFunction_F(flux, f, v[k][j][i],
deviator_only[myid]);//TODO: multi-material
flux *= dy*dz;
res[k][j][i] += flux;
res[k][j][i-1] -= flux;
}
//*****************************************
//calculate flux function G_{i,j-1/2,k}
//*****************************************
if(i!=iimax-1 && k!=kkmax-1) {
for(int dim=0; dim<2; dim++)
gradxi[dim] = dxidx_j[k][j][i][dim];
for(int dim=0; dim<2; dim++)
gradxi[2+dim] = dxidy_j[k][j][i][dim];
invertible = MathTools::LinearAlgebra::
CalculateMatrixInverseAndDeterminant2x2(gradxi, f2);
if(!invertible)
fprintf(stdout,"\033[0;35mWarning: Jacobian of ref. map at (%d,%d-1/2,%d)"
" is not invertible.\033[0m\n", i,j,k);
// Note: f = [dz/dZ 0 dz/dR; 0 r/R 0; dr/dZ 0 dr/dR]; //"x = z", "y = r"!
double r = global_mesh.GetY(j) - 0.5*dy;
r0 = (global_mesh.GetDy(j-1)*xi[k][j][i][1] + dy*xi[k][j-1][i][1])
/ (global_mesh.GetDy(j-1) + dy);
f[0] = f2[0]; f[6] = f2[2];
f[4] = r/r0;
f[2] = f2[1]; f[8] = f2[3];
hyperFcn[myid]->EvaluateHyperelasticFluxFunction_G(flux, f, v[k][j][i],
deviator_only[myid]);//TODO: multi-material
flux *= dx*dz;
res[k][j][i] += flux;
res[k][j-1][i] -= flux;
}
}
}
}
dXidx_i_minus_half.RestoreDataPointerToLocalVector();
dXidx_j_minus_half.RestoreDataPointerToLocalVector();
dXidy_i_minus_half.RestoreDataPointerToLocalVector();
dXidy_j_minus_half.RestoreDataPointerToLocalVector();
ID.RestoreDataPointerToLocalVector();
V.RestoreDataPointerToLocalVector();
Xi.RestoreDataPointerToLocalVector();
R.RestoreDataPointerToLocalVector(); //NOTE: although R has been updated, there is no need of
// cross-subdomain communications. So, no need to
// update the global vec.
}
//------------------------------------------------------------
// Note: Source terms are placed on the left-hand-side of the Navier-Stokes equations
void
HyperelasticityOperator::AddCylindricalSourceTerms(SpaceVariable3D &V, SpaceVariable3D &ID,
SpaceVariable3D &Xi,
vector<std::unique_ptr<EmbeddedBoundaryDataSet> > *EBDS,
SpaceVariable3D &R)
{
if(EBDS)
print_warning("Warning: AddHyperelasticityFluxes: Not able to account for embedded surfaces.\n");
// NOTE: This function computes deformation gradient (F) ONLY WITHIN THE PHYSICAL DOMAIN,
// NOT in the ghost boundary layer.
// ------------------------------------
// Step 1: Calculate the Jacobian of Xi
// ------------------------------------
std::vector<int> i01{0,1};
// dxi/dx (i.e., dxi/dz in cylindrical coords)
grad.CalculateFirstDerivativeAtNodes(0 /*dx*/, Xi, i01, Var1, i01);
// dxi/dy (i.e., dxi/dr in cylindrical coords)
grad.CalculateFirstDerivativeAtNodes(1 /*dy*/, Xi, i01, Var2, i01);
// ------------------------------------
// Step 2: Calculate the deformation gradient: F = inv(grad.Xi), its determinant.
// Then, evaluate the source terms due to cylindrical symmetry.
// ------------------------------------
Vec3D*** xi = (Vec3D***)Xi.GetDataPointer();
Vec3D*** dXidx = (Vec3D***)Var1.GetDataPointer();
Vec3D*** dXidy = (Vec3D***)Var2.GetDataPointer();
double*** id = (double***)ID.GetDataPointer();
Vec5D*** v = (Vec5D***)V.GetDataPointer();
Vec5D*** res = (Vec5D***)R.GetDataPointer();
double*** cv = (double***)volume.GetDataPointer();
int myid = 0;
double gradxi[4]; //local values of Jacobian of Xi
double f2[4], f[9] = {0.0}; //deform. grad