void
Nonlinear3D::computeIncrementalDeformationGradient(std::vector<ColumnMajorMatrix> & Fhat)
{
// A = grad(u(k+1) - u(k))
// Fbar = 1 + grad(u(k))
// Fhat = 1 + A*(Fbar^-1)
ColumnMajorMatrix A;
ColumnMajorMatrix Fbar;
ColumnMajorMatrix Fbar_inverse;
ColumnMajorMatrix Fhat_average;
Real volume(0);
_Fbar.resize(_solid_model.qrule()->n_points());
for (unsigned qp = 0; qp < _solid_model.qrule()->n_points(); ++qp)
{
fillMatrix(qp, _grad_disp_x, _grad_disp_y, _grad_disp_z, A);
fillMatrix(qp, _grad_disp_x_old, _grad_disp_y_old, _grad_disp_z_old, Fbar);
A -= Fbar;
Fbar.addDiag(1);
_Fbar[qp] = Fbar;
// Get Fbar^(-1)
// Computing the inverse is generally a bad idea.
// It's better to compute LU factors. For now at least, we'll take
// a direct route.
invertMatrix(Fbar, Fbar_inverse);
Fhat[qp] = A * Fbar_inverse;
Fhat[qp].addDiag(1);
if (_volumetric_locking_correction)
{
// Now include the contribution for the integration of Fhat over the element
Fhat_average += Fhat[qp] * _solid_model.JxW(qp);
volume += _solid_model.JxW(qp); // Accumulate original configuration volume
}
}
if (_volumetric_locking_correction)
{
Fhat_average /= volume;
const Real det_Fhat_average(detMatrix(Fhat_average));
// Finalize volumetric locking correction
for (unsigned qp = 0; qp < _solid_model.qrule()->n_points(); ++qp)
{
const Real det_Fhat(detMatrix(Fhat[qp]));
const Real factor(std::cbrt(det_Fhat_average / det_Fhat));
Fhat[qp] *= factor;
}
}
// Moose::out << "Fhat(0,0)" << Fhat[0](0,0) << std::endl;
}
void
dataStore(std::ostream & stream, ColumnMajorMatrix & v, void * /*context*/)
{
for (unsigned int i = 0; i < v.m(); i++)
for (unsigned int j = 0; j < v.n(); j++)
{
Real r = v(i, j);
stream.write((char *) &r, sizeof(r));
}
}
void
dataLoad(std::istream & stream, ColumnMajorMatrix & v, void * /*context*/)
{
for (unsigned int i = 0; i < v.m(); i++)
for (unsigned int j = 0; j < v.n(); j++)
{
Real r = 0;
stream.read((char *) &r, sizeof(r));
v(i, j) = r;
}
}
void
ColumnMajorMatrixTest::zeroMatrix()
{
ColumnMajorMatrix mat = *two_mat;
mat.zero();
CPPUNIT_ASSERT( mat(0,0) == 0 );
CPPUNIT_ASSERT( mat(1,0) == 0 );
CPPUNIT_ASSERT( mat(0,1) == 0 );
CPPUNIT_ASSERT( mat(1,1) == 0 );
}
void
ColumnMajorMatrixTest::transposeMatrix()
{
ColumnMajorMatrix mat = *two_mat;
ColumnMajorMatrix test = mat.transpose();
CPPUNIT_ASSERT( test(0,0) == 1 );
CPPUNIT_ASSERT( test(1,0) == 3 );
CPPUNIT_ASSERT( test(0,1) == 2 );
CPPUNIT_ASSERT( test(1,1) == 4 );
}
void
ColumnMajorMatrixTest::numEntries()
{
//numEntries is tested in other functions, like after different
//constructors to make sure the number of entries copied over correctly
ColumnMajorMatrix mat = *two_mat;
ColumnMajorMatrix mat2(3, 4);
CPPUNIT_ASSERT( mat.numEntries() == 4 );
CPPUNIT_ASSERT( mat2.numEntries() == 12 );
}
void
ColumnMajorMatrixTest::identityMatrix()
{
ColumnMajorMatrix mat = *two_mat;
mat.identity();
CPPUNIT_ASSERT( mat(0,0) == 1 );
CPPUNIT_ASSERT( mat(1,0) == 0 );
CPPUNIT_ASSERT( mat(0,1) == 0 );
CPPUNIT_ASSERT( mat(1,1) == 1 );
}
void
ColumnMajorMatrixTest::setDiagMatrix()
{
ColumnMajorMatrix mat = *two_mat;
mat.setDiag( 9 );
CPPUNIT_ASSERT( mat(0,0) == 9 );
CPPUNIT_ASSERT( mat(1,0) == 2 );
CPPUNIT_ASSERT( mat(0,1) == 3 );
CPPUNIT_ASSERT( mat(1,1) == 9 );
}
void
ColumnMajorMatrixTest::contractionMatrix()
{
ColumnMajorMatrix mat = *two_mat;
ColumnMajorMatrix sec(2, 2);
sec(0, 0) = 4;
sec(1, 0) = 3;
sec(0, 1) = 2;
sec(1, 1) = 1;
CPPUNIT_ASSERT( mat.doubleContraction( sec ) == (1*4 + 2*3 + 3*2 + 4*1) );
}
void
PlaneStrain::computeDeformationGradient( unsigned int qp, ColumnMajorMatrix & F)
{
mooseAssert(F.n() == 3 && F.m() == 3, "computeDefGrad requires 3x3 matrix");
F(0,0) = _grad_disp_x[qp](0) + 1.0;
F(0,1) = _grad_disp_x[qp](1);
F(0,2) = 0.0;
F(1,0) = _grad_disp_y[qp](0);
F(1,1) = _grad_disp_y[qp](1) + 1.0;
F(1,2) = 0.0;
F(2,0) = 0.0;
F(2,1) = 0.0;
F(2,2) = 1.0;
}
void
Nonlinear3D::computeDeformationGradient( unsigned int qp, ColumnMajorMatrix & F)
{
mooseAssert(F.n() == 3 && F.m() == 3, "computeDefGrad requires 3x3 matrix");
F(0,0) = _grad_disp_x[qp](0) + 1;
F(0,1) = _grad_disp_x[qp](1);
F(0,2) = _grad_disp_x[qp](2);
F(1,0) = _grad_disp_y[qp](0);
F(1,1) = _grad_disp_y[qp](1) + 1;
F(1,2) = _grad_disp_y[qp](2);
F(2,0) = _grad_disp_z[qp](0);
F(2,1) = _grad_disp_z[qp](1);
F(2,2) = _grad_disp_z[qp](2) + 1;
}
void
ColumnMajorMatrixTest::copyConstructor()
{
ColumnMajorMatrix mat = *two_mat;
ColumnMajorMatrix test = mat;
test(1, 1) = 9;
CPPUNIT_ASSERT( test(0,0) == 1 );
CPPUNIT_ASSERT( test(1,0) == 2 );
CPPUNIT_ASSERT( test(0,1) == 3 );
CPPUNIT_ASSERT( test(1,1) == 9 );
CPPUNIT_ASSERT( mat(1,1) == 4 );
CPPUNIT_ASSERT( test.numEntries() == 4 );
}
void
NonlinearRZ::computeDeformationGradient( unsigned int qp, ColumnMajorMatrix & F)
{
mooseAssert(F.n() == 3 && F.m() == 3, "computeDefGrad requires 3x3 matrix");
F(0,0) = _grad_disp_r[qp](0) + 1;
F(0,1) = _grad_disp_r[qp](1);
F(0,2) = 0;
F(1,0) = _grad_disp_z[qp](0);
F(1,1) = _grad_disp_z[qp](1) + 1;
F(1,2) = 0;
F(2,0) = 0;
F(2,1) = 0;
F(2,2) = (_solid_model.q_point(qp)(0) != 0.0 ? _disp_r[qp]/_solid_model.q_point(qp)(0) : 0.0) + 1;
}
void
SymmElasticityTensor::convertFrom6x6(const ColumnMajorMatrix & input)
{
if (input.numEntries() != 36)
{
mooseError("Cannot convert from ColumnMajorMatrix (wrong size)");
}
_val[0] = input(0, 0);
_val[1] = input(0, 1);
_val[2] = input(0, 2);
_val[3] = input(0, 3);
_val[4] = input(0, 4);
_val[5] = input(0, 5);
_val[6] = input(1, 1);
_val[7] = input(1, 2);
_val[8] = input(1, 3);
_val[9] = input(1, 4);
_val[10] = input(1, 5);
_val[11] = input(2, 2);
_val[12] = input(2, 3);
_val[13] = input(2, 4);
_val[14] = input(2, 5);
_val[15] = input(3, 3);
_val[16] = input(3, 4);
_val[17] = input(3, 5);
_val[18] = input(4, 4);
_val[19] = input(4, 5);
_val[20] = input(5, 5);
}
Real
Element::detMatrix( const ColumnMajorMatrix & A )
{
mooseAssert(A.n() == 3 && A.m() == 3, "detMatrix requires 3x3 matrix");
Real Axx = A(0,0);
Real Axy = A(0,1);
Real Axz = A(0,2);
Real Ayx = A(1,0);
Real Ayy = A(1,1);
Real Ayz = A(1,2);
Real Azx = A(2,0);
Real Azy = A(2,1);
Real Azz = A(2,2);
return Axx*Ayy*Azz + Axy*Ayz*Azx + Axz*Ayx*Azy
- Azx*Ayy*Axz - Azy*Ayz*Axx - Azz*Ayx*Axy;
}
void
NonlinearPlaneStrain::fillMatrix( unsigned int qp,
const VariableGradient & grad_x,
const VariableGradient & grad_y,
const Real & strain_zz,
ColumnMajorMatrix & A) const
{
mooseAssert(A.n() == 3 && A.m() == 3, "computeDefGrad requires 3x3 matrix");
A(0,0) = grad_x[qp](0);
A(0,1) = grad_x[qp](1);
A(0,2) = 0;
A(1,0) = grad_y[qp](0);
A(1,1) = grad_y[qp](1);
A(1,2) = 0;
A(2,0) = 0;
A(2,1) = 0;
A(2,2) = strain_zz;
}
void
NonlinearRZ::fillMatrix( unsigned int qp,
const VariableGradient & grad_r,
const VariableGradient & grad_z,
const VariableValue & u,
ColumnMajorMatrix & A) const
{
mooseAssert(A.n() == 3 && A.m() == 3, "computeDefGrad requires 3x3 matrix");
A(0,0) = grad_r[qp](0);
A(0,1) = grad_r[qp](1);
A(0,2) = 0;
A(1,0) = grad_z[qp](0);
A(1,1) = grad_z[qp](1);
A(1,2) = 0;
A(2,0) = 0;
A(2,1) = 0;
A(2,2) = (_solid_model.q_point(qp)(0) != 0.0 ? u[qp]/_solid_model.q_point(qp)(0) : 0.0);
}
void
NonlinearPlaneStrain::computeDeformationGradient( unsigned int qp, ColumnMajorMatrix & F)
{
mooseAssert(F.n() == 3 && F.m() == 3, "computeDefGrad requires 3x3 matrix");
F(0,0) = _grad_disp_x[qp](0) + 1;
F(0,1) = _grad_disp_x[qp](1);
F(0,2) = 0;
F(1,0) = _grad_disp_y[qp](0);
F(1,1) = _grad_disp_y[qp](1) + 1;
F(1,2) = 0;
F(2,0) = 0;
F(2,1) = 0;
if (_have_strain_zz)
F(2,2) = _strain_zz[qp] + 1;
else if (_have_scalar_strain_zz && _scalar_strain_zz.size()>0)
F(2,2) = _scalar_strain_zz[qp] + 1;
else
F(2,2) = 1;
}
void
Element::polarDecompositionEigen( const ColumnMajorMatrix & Fhat, ColumnMajorMatrix & Rhat, SymmTensor & strain_increment )
{
const int ND = 3;
ColumnMajorMatrix eigen_value(ND,1), eigen_vector(ND,ND);
ColumnMajorMatrix invUhat(ND,ND), logVhat(ND,ND);
ColumnMajorMatrix n1(ND,1), n2(ND,1), n3(ND,1), N1(ND,1), N2(ND,1), N3(ND,1);
ColumnMajorMatrix Chat = Fhat.transpose() * Fhat;
Chat.eigen(eigen_value,eigen_vector);
for(int i = 0; i < ND; i++)
{
N1(i) = eigen_vector(i,0);
N2(i) = eigen_vector(i,1);
N3(i) = eigen_vector(i,2);
}
const Real lamda1 = std::sqrt(eigen_value(0));
const Real lamda2 = std::sqrt(eigen_value(1));
const Real lamda3 = std::sqrt(eigen_value(2));
const Real log1 = std::log(lamda1);
const Real log2 = std::log(lamda2);
const Real log3 = std::log(lamda3);
ColumnMajorMatrix Uhat = N1 * N1.transpose() * lamda1 + N2 * N2.transpose() * lamda2 + N3 * N3.transpose() * lamda3;
invertMatrix(Uhat,invUhat);
Rhat = Fhat * invUhat;
strain_increment = N1 * N1.transpose() * log1 + N2 * N2.transpose() * log2 + N3 * N3.transpose() * log3;
}
void AbaqusUmatMaterial::computeStress()
{
//Calculate deformation gradient - modeled from "solid_mechanics/src/materials/Nonlinear3D.C"
// Fbar = 1 + grad(u(k))
ColumnMajorMatrix Fbar;
Fbar(0,0) = _grad_disp_x[_qp](0);
Fbar(0,1) = _grad_disp_x[_qp](1);
Fbar(0,2) = _grad_disp_x[_qp](2);
Fbar(1,0) = _grad_disp_y[_qp](0);
Fbar(1,1) = _grad_disp_y[_qp](1);
Fbar(1,2) = _grad_disp_y[_qp](2);
Fbar(2,0) = _grad_disp_z[_qp](0);
Fbar(2,1) = _grad_disp_z[_qp](1);
Fbar(2,2) = _grad_disp_z[_qp](2);
Fbar.addDiag(1);
_Fbar[_qp] = Fbar;
Real myDFGRD0[9] = {_Fbar_old[_qp](0,0), _Fbar_old[_qp](1,0), _Fbar_old[_qp](2,0), _Fbar_old[_qp](0,1), _Fbar_old[_qp](1,1), _Fbar_old[_qp](2,1), _Fbar_old[_qp](0,2), _Fbar_old[_qp](1,2), _Fbar_old[_qp](2,2)};
Real myDFGRD1[9] = {_Fbar[_qp](0,0), _Fbar[_qp](1,0), _Fbar[_qp](2,0), _Fbar[_qp](0,1), _Fbar[_qp](1,1), _Fbar[_qp](2,1), _Fbar[_qp](0,2), _Fbar[_qp](1,2), _Fbar[_qp](2,2)};
for (unsigned int i=0; i<9; ++i)
{
_DFGRD0[i] = myDFGRD0[i];
_DFGRD1[i] = myDFGRD1[i];
}
//Recover "old" state variables
for (unsigned int i=0; i<_num_state_vars; ++i)
_STATEV[i]=_state_var_old[_qp][i];
//Pass through updated stress, total strain, and strain increment arrays
for (int i=0; i<_NTENS; ++i)
{
_STRESS[i] = _stress_old.component(i);
_STRAN[i] = _total_strain[_qp].component(i);
_DSTRAN[i] = _strain_increment.component(i);
}
//Pass through step , time, and coordinate system information
_KSTEP = _t_step; //Step number
_TIME[0] = _t; //Value of step time at the beginning of the current increment - Check
_TIME[1] = _t-_dt; //Value of total time at the beginning of the current increment - Check
_DTIME = _dt; //Time increment
for (unsigned int i=0; i<3; ++i) //Loop current coordinates in UMAT COORDS
_COORDS[i] = _coord[i];
//Connection to extern statement
_umat(_STRESS, _STATEV, _DDSDDE, &_SSE, &_SPD, &_SCD, &_RPL, _DDSDDT, _DRPLDE, &_DRPLDT, _STRAN, _DSTRAN, _TIME, &_DTIME, &_TEMP, &_DTEMP, _PREDEF, _DPRED, &_CMNAME, &_NDI, &_NSHR, &_NTENS, &_NSTATV, _PROPS, &_NPROPS, _COORDS, _DROT, &_PNEWDT, &_CELENT, _DFGRD0, _DFGRD1, &_NOEL, &_NPT, &_LAYER, &_KSPT, &_KSTEP, &_KINC);
//Energy outputs
_elastic_strain_energy[_qp] = _SSE;
_plastic_dissipation[_qp] = _SPD;
_creep_dissipation[_qp] = _SCD;
//Update state variables
for (unsigned int i=0; i<_num_state_vars; ++i)
_state_var[_qp][i]=_STATEV[i];
//Get new stress tensor - UMAT should update stress
SymmTensor stressnew(_STRESS[0], _STRESS[1], _STRESS[2], _STRESS[3], _STRESS[4], _STRESS[5]);
_stress[_qp] = stressnew;
}
void
SymmElasticityTensor::rotateFromGlobalToLocal(const ColumnMajorMatrix & R)
{
convertFrom9x9(R.transpose() * (columnMajorMatrix9x9() * R));
}
PiecewiseBilinear::PiecewiseBilinear(const InputParameters & parameters) :
Function(parameters),
_data_file_name(getParam<FileName>("data_file")),
_axis(getParam<int>("axis")),
_yaxis(getParam<int>("yaxis")),
_xaxis(getParam<int>("xaxis")),
_axisValid( _axis > -1 && _axis < 3 ),
_yaxisValid( _yaxis > -1 && _yaxis < 3 ),
_xaxisValid( _xaxis > -1 && _xaxis < 3 ),
_scale_factor( getParam<Real>("scale_factor") ),
_radial(getParam<bool>("radial"))
{
if (!_axisValid && !_yaxisValid && !_xaxisValid)
mooseError("In PiecewiseBilinear " << _name << ": None of axis, yaxis, or xaxis properly defined. Allowable range is 0-2");
if (_axisValid && (_yaxisValid || _xaxisValid))
mooseError("In PiecewiseBilinear " << _name << ": Cannot define axis with either yaxis or xaxis");
if (_radial && (!_yaxisValid || !_xaxisValid))
mooseError("In PiecewiseBilinear " << _name << ": yaxis and xaxis must be defined when radial = true");
std::vector<Real> x;
std::vector<Real> y;
ColumnMajorMatrix z;
std::vector<Real> z_vec;
if (!_data_file_name.empty())
{
if ( parameters.isParamValid("x") || parameters.isParamValid("y") || parameters.isParamValid("z") )
mooseError("In PiecewiseBilinear: Cannot specify 'data_file' and 'x', 'y', or 'z' together.");
else
parse( x, y, z );
}
else if ( !(parameters.isParamValid("x") && parameters.isParamValid("y") && parameters.isParamValid("z")) )
mooseError("In PiecewiseBilinear: 'x' and 'y' and 'z' must be specified if any one is specified.");
else
{
x = getParam<std::vector<Real> >("x");
y = getParam<std::vector<Real> >("y");
z_vec = getParam<std::vector<Real> >("z");
//check that size of z = (size of x)*(size of y)
if (z_vec.size() != x.size()*y.size())
mooseError("In PiecewiseBilinear: Size of z should be the size of x times the size of y.");
//reshape and populate z matrix
z.reshape(y.size(),x.size());
int idx = 0;
for (unsigned int i = 0; i < y.size(); i++)
for (unsigned int j = 0; j < x.size(); j++)
{
z(i,j) = z_vec[idx];
idx += 1;
}
}
_bilinear_interp = libmesh_make_unique<BilinearInterpolation>(x, y, z);
}
void
PiecewiseBilinear::parse( std::vector<Real> & x,
std::vector<Real> & y,
ColumnMajorMatrix & z)
{
std::ifstream file(_data_file_name.c_str());
if (!file.good())
mooseError("In PiecewiseBilinear " << _name << ": Error opening file '" + _data_file_name + "'.");
std::string line;
unsigned int linenum= 0;
unsigned int itemnum = 0;
unsigned int num_cols = 0;
std::vector<Real> data;
while (getline (file, line))
{
linenum++;
std::istringstream linestream(line);
std::string item;
itemnum = 0;
while (getline (linestream, item, ','))
{
itemnum++;
std::istringstream i(item);
Real d;
i >> d;
data.push_back(d);
}
if (linenum == 1)
num_cols = itemnum;
else if (num_cols+1 != itemnum)
mooseError("In PiecewiseBilinear " << _name << ": Read " << itemnum << " columns of data but expected " << num_cols+1
<< " columns while reading line " << linenum << " of '" << _data_file_name << "'.");
}
x.resize(itemnum-1);
y.resize(linenum-1);
z.reshape(linenum-1,itemnum-1);
unsigned int offset(0);
// Extract the first line's data (the x axis data)
for (unsigned int j = 0; j < itemnum-1; ++j)
{
x[j] = data[offset];
++offset;
}
for (unsigned int i = 0; i < linenum-1; ++i)
{
// Extract the y axis entry for this line
y[i] = data[offset];
++offset;
// Extract the function values for this row in the matrix
for (unsigned int j = 0; j < itemnum-1; ++j)
{
z(i,j) = data[offset];
++offset;
}
}
if (data.size() != offset)
mooseError("ERROR! Inconsistency in data read from '" + _data_file_name + "' for PiecewiseBilinear function.");
}
