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 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;
}