Esempio n. 1
0
Real
InteractionIntegral::computeQpIntegral()
{
  Real scalar_q = 0.0;
  RealVectorValue grad_q(0.0, 0.0, 0.0);

  const std::vector<std::vector<Real>> & phi_curr_elem = *_phi_curr_elem;
  const std::vector<std::vector<RealGradient>> & dphi_curr_elem = *_dphi_curr_elem;

  for (unsigned int i = 0; i < _current_elem->n_nodes(); ++i)
  {
    scalar_q += phi_curr_elem[i][_qp] * _q_curr_elem[i];

    for (unsigned int j = 0; j < _current_elem->dim(); ++j)
      grad_q(j) += dphi_curr_elem[i][_qp](j) * _q_curr_elem[i];
  }

  // In the crack front coordinate system, the crack direction is (1,0,0)
  RealVectorValue crack_direction(0.0);
  crack_direction(0) = 1.0;

  // Calculate (r,theta) position of qp relative to crack front
  Point p(_q_point[_qp]);
  _crack_front_definition->calculateRThetaToCrackFront(p, _crack_front_point_index, _r, _theta);

  RankTwoTensor aux_stress;
  RankTwoTensor aux_du;

  if (_sif_mode == SifMethod::KI || _sif_mode == SifMethod::KII || _sif_mode == SifMethod::KIII)
    computeAuxFields(aux_stress, aux_du);
  else if (_sif_mode == SifMethod::T)
    computeTFields(aux_stress, aux_du);

  RankTwoTensor grad_disp((*_grad_disp[0])[_qp], (*_grad_disp[1])[_qp], (*_grad_disp[2])[_qp]);

  // Rotate stress, strain, displacement and temperature to crack front coordinate system
  RealVectorValue grad_q_cf =
      _crack_front_definition->rotateToCrackFrontCoords(grad_q, _crack_front_point_index);
  RankTwoTensor grad_disp_cf =
      _crack_front_definition->rotateToCrackFrontCoords(grad_disp, _crack_front_point_index);
  RankTwoTensor stress_cf =
      _crack_front_definition->rotateToCrackFrontCoords((*_stress)[_qp], _crack_front_point_index);
  RankTwoTensor strain_cf =
      _crack_front_definition->rotateToCrackFrontCoords((*_strain)[_qp], _crack_front_point_index);
  RealVectorValue grad_temp_cf =
      _crack_front_definition->rotateToCrackFrontCoords(_grad_temp[_qp], _crack_front_point_index);

  RankTwoTensor dq;
  dq(0, 0) = crack_direction(0) * grad_q_cf(0);
  dq(0, 1) = crack_direction(0) * grad_q_cf(1);
  dq(0, 2) = crack_direction(0) * grad_q_cf(2);

  // Calculate interaction integral terms

  // Term1 = stress * x1-derivative of aux disp * dq
  RankTwoTensor tmp1 = dq * stress_cf;
  Real term1 = aux_du.doubleContraction(tmp1);

  // Term2 = aux stress * x1-derivative of disp * dq
  RankTwoTensor tmp2 = dq * aux_stress;
  Real term2 = grad_disp_cf(0, 0) * tmp2(0, 0) + grad_disp_cf(1, 0) * tmp2(0, 1) +
               grad_disp_cf(2, 0) * tmp2(0, 2);

  // Term3 = aux stress * strain * dq_x   (= stress * aux strain * dq_x)
  Real term3 = dq(0, 0) * aux_stress.doubleContraction(strain_cf);

  // Term4 (thermal strain term) = q * aux_stress * alpha * dtheta_x
  // - the term including the derivative of alpha is not implemented
  Real term4 = 0.0;
  if (_has_temp)
  {
    Real sigma_alpha = aux_stress.doubleContraction((*_total_deigenstrain_dT)[_qp]);
    term4 = scalar_q * sigma_alpha * grad_temp_cf(0);
  }

  Real q_avg_seg = 1.0;
  if (!_crack_front_definition->treatAs2D())
  {
    q_avg_seg =
        (_crack_front_definition->getCrackFrontForwardSegmentLength(_crack_front_point_index) +
         _crack_front_definition->getCrackFrontBackwardSegmentLength(_crack_front_point_index)) /
        2.0;
  }

  Real eq = term1 + term2 - term3 + term4;

  if (_has_symmetry_plane)
    eq *= 2.0;

  return eq / q_avg_seg;
}
Esempio n. 2
0
Real
InteractionIntegralSM::computeQpIntegral()
{
  Real scalar_q = 0.0;
  RealVectorValue grad_q(0.0, 0.0, 0.0);

  const std::vector<std::vector<Real>> & phi_curr_elem = *_phi_curr_elem;
  const std::vector<std::vector<RealGradient>> & dphi_curr_elem = *_dphi_curr_elem;

  for (unsigned int i = 0; i < _current_elem->n_nodes(); ++i)
  {
    scalar_q += phi_curr_elem[i][_qp] * _q_curr_elem[i];

    for (unsigned int j = 0; j < _current_elem->dim(); ++j)
      grad_q(j) += dphi_curr_elem[i][_qp](j) * _q_curr_elem[i];
  }

  // In the crack front coordinate system, the crack direction is (1,0,0)
  RealVectorValue crack_direction(0.0);
  crack_direction(0) = 1.0;

  RankTwoTensor stress;
  stress(0, 0) = _stress[_qp].xx();
  stress(0, 1) = _stress[_qp].xy();
  stress(0, 2) = _stress[_qp].xz();
  stress(1, 0) = _stress[_qp].xy();
  stress(1, 1) = _stress[_qp].yy();
  stress(1, 2) = _stress[_qp].yz();
  stress(2, 0) = _stress[_qp].xz();
  stress(2, 1) = _stress[_qp].yz();
  stress(2, 2) = _stress[_qp].zz();

  RankTwoTensor strain;
  strain(0, 0) = _strain[_qp].xx();
  strain(0, 1) = _strain[_qp].xy();
  strain(0, 2) = _strain[_qp].xz();
  strain(1, 0) = _strain[_qp].xy();
  strain(1, 1) = _strain[_qp].yy();
  strain(1, 2) = _strain[_qp].yz();
  strain(2, 0) = _strain[_qp].xz();
  strain(2, 1) = _strain[_qp].yz();
  strain(2, 2) = _strain[_qp].zz();

  RankTwoTensor grad_disp;
  grad_disp(0, 0) = _grad_disp_x[_qp](0);
  grad_disp(0, 1) = _grad_disp_x[_qp](1);
  grad_disp(0, 2) = _grad_disp_x[_qp](2);
  grad_disp(1, 0) = _grad_disp_y[_qp](0);
  grad_disp(1, 1) = _grad_disp_y[_qp](1);
  grad_disp(1, 2) = _grad_disp_y[_qp](2);
  grad_disp(2, 0) = _grad_disp_z[_qp](0);
  grad_disp(2, 1) = _grad_disp_z[_qp](1);
  grad_disp(2, 2) = _grad_disp_z[_qp](2);

  // Rotate stress, strain, displacement and temperature to crack front coordinate system
  RealVectorValue grad_q_cf =
      _crack_front_definition->rotateToCrackFrontCoords(grad_q, _crack_front_point_index);
  RankTwoTensor grad_disp_cf =
      _crack_front_definition->rotateToCrackFrontCoords(grad_disp, _crack_front_point_index);
  RankTwoTensor stress_cf =
      _crack_front_definition->rotateToCrackFrontCoords(stress, _crack_front_point_index);
  RankTwoTensor strain_cf =
      _crack_front_definition->rotateToCrackFrontCoords(strain, _crack_front_point_index);
  RealVectorValue grad_temp_cf =
      _crack_front_definition->rotateToCrackFrontCoords(_grad_temp[_qp], _crack_front_point_index);

  RankTwoTensor dq;
  dq(0, 0) = crack_direction(0) * grad_q_cf(0);
  dq(0, 1) = crack_direction(0) * grad_q_cf(1);
  dq(0, 2) = crack_direction(0) * grad_q_cf(2);

  // Calculate interaction integral terms

  // Term1 = stress * x1-derivative of aux disp * dq
  RankTwoTensor tmp1 = dq * stress_cf;
  Real term1 = _aux_grad_disp[_qp].doubleContraction(tmp1);

  // Term2 = aux stress * x1-derivative of disp * dq
  RankTwoTensor tmp2 = dq * _aux_stress[_qp];
  Real term2 = grad_disp_cf(0, 0) * tmp2(0, 0) + grad_disp_cf(1, 0) * tmp2(0, 1) +
               grad_disp_cf(2, 0) * tmp2(0, 2);

  // Term3 = aux stress * strain * dq_x   (= stress * aux strain * dq_x)
  Real term3 = dq(0, 0) * _aux_stress[_qp].doubleContraction(strain_cf);

  // Term4 (thermal strain term) = q * aux_stress * alpha * dtheta_x
  // - the term including the derivative of alpha is not implemented
  Real term4 = 0.0;
  if (_has_temp)
  {
    Real aux_stress_trace =
        _aux_stress[_qp](0, 0) + _aux_stress[_qp](1, 1) + _aux_stress[_qp](2, 2);
    term4 = scalar_q * aux_stress_trace * (*_current_instantaneous_thermal_expansion_coef)[_qp] *
            grad_temp_cf(0);
  }

  Real q_avg_seg = 1.0;
  if (!_crack_front_definition->treatAs2D())
  {
    q_avg_seg =
        (_crack_front_definition->getCrackFrontForwardSegmentLength(_crack_front_point_index) +
         _crack_front_definition->getCrackFrontBackwardSegmentLength(_crack_front_point_index)) /
        2.0;
  }

  Real eq = term1 + term2 - term3 + term4;

  if (_has_symmetry_plane)
    eq *= 2.0;

  return eq / q_avg_seg;
}
Esempio n. 3
0
Real
InteractionIntegral::computeQpIntegral()
{

  RealVectorValue grad_q = _grad_of_scalar_q[_qp];

  //In the crack front coordinate system, the crack direction is (1,0,0)
  RealVectorValue crack_direction(0.0);
  crack_direction(0) = 1.0;

  ColumnMajorMatrix aux_du;
  aux_du(0,0) = _aux_grad_disp[_qp](0,0);
  aux_du(0,1) = _aux_grad_disp[_qp](0,1);
  aux_du(0,2) = _aux_grad_disp[_qp](0,2);

  ColumnMajorMatrix stress;
  stress(0,0) = _stress[_qp].xx();
  stress(0,1) = _stress[_qp].xy();
  stress(0,2) = _stress[_qp].xz();
  stress(1,0) = _stress[_qp].xy();
  stress(1,1) = _stress[_qp].yy();
  stress(1,2) = _stress[_qp].yz();
  stress(2,0) = _stress[_qp].xz();
  stress(2,1) = _stress[_qp].yz();
  stress(2,2) = _stress[_qp].zz();

  ColumnMajorMatrix strain;
  strain(0,0) = _strain[_qp].xx();
  strain(0,1) = _strain[_qp].xy();
  strain(0,2) = _strain[_qp].xz();
  strain(1,0) = _strain[_qp].xy();
  strain(1,1) = _strain[_qp].yy();
  strain(1,2) = _strain[_qp].yz();
  strain(2,0) = _strain[_qp].xz();
  strain(2,1) = _strain[_qp].yz();
  strain(2,2) = _strain[_qp].zz();

  ColumnMajorMatrix grad_disp;
  grad_disp(0,0) = _grad_disp_x[_qp](0);
  grad_disp(0,1) = _grad_disp_x[_qp](1);
  grad_disp(0,2) = _grad_disp_x[_qp](2);
  grad_disp(1,0) = _grad_disp_y[_qp](0);
  grad_disp(1,1) = _grad_disp_y[_qp](1);
  grad_disp(1,2) = _grad_disp_y[_qp](2);
  grad_disp(2,0) = _grad_disp_z[_qp](0);
  grad_disp(2,1) = _grad_disp_z[_qp](1);
  grad_disp(2,2) = _grad_disp_z[_qp](2);

  //Rotate stress, strain, and displacement to crack front coordinate system
  RealVectorValue grad_q_cf = _crack_front_definition->rotateToCrackFrontCoords(grad_q,_crack_front_point_index);
  ColumnMajorMatrix grad_disp_cf = _crack_front_definition->rotateToCrackFrontCoords(grad_disp,_crack_front_point_index);
  ColumnMajorMatrix stress_cf = _crack_front_definition->rotateToCrackFrontCoords(stress,_crack_front_point_index);
  ColumnMajorMatrix strain_cf = _crack_front_definition->rotateToCrackFrontCoords(strain,_crack_front_point_index);

  ColumnMajorMatrix dq;
  dq(0,0) = crack_direction(0)*grad_q_cf(0);
  dq(0,1) = crack_direction(0)*grad_q_cf(1);
  dq(0,2) = crack_direction(0)*grad_q_cf(2);

  //Calculate interaction integral terms

  // Term1 = stress * x1-derivative of aux disp * dq
  ColumnMajorMatrix tmp1 = dq * stress_cf;
  Real term1 = aux_du.doubleContraction(tmp1);

  // Term2 = aux stress * x1-derivative of disp * dq
  ColumnMajorMatrix tmp2 = dq * _aux_stress[_qp];
  Real term2 = grad_disp_cf(0,0)*tmp2(0,0)+grad_disp_cf(1,0)*tmp2(0,1)+grad_disp_cf(2,0)*tmp2(0,2);

  // Term3 = aux stress * strain * dq_x   (= stress * aux strain * dq_x)
  Real term3 = dq(0,0) * _aux_stress[_qp].doubleContraction(strain_cf);

  Real q_avg_seg = 1.0;
  if (!_crack_front_definition->treatAs2D())
  {
    q_avg_seg = (_crack_front_definition->getCrackFrontForwardSegmentLength(_crack_front_point_index) +
                 _crack_front_definition->getCrackFrontBackwardSegmentLength(_crack_front_point_index)) / 2.0;
  }

  Real eq = term1 + term2 - term3;

  if (_has_symmetry_plane)
    eq *= 2.0;

  return eq/q_avg_seg;
}