MaterialTensorCalculatorTools Namespace Reference

Functions
Real	component (const SymmTensor &symm_tensor, unsigned int index)
Real	component (const SymmTensor &symm_tensor, unsigned int index, RealVectorValue &direction)
Real	vonMisesStress (const SymmTensor &symm_stress)
Real	effectiveStrain (const SymmTensor &symm_strain)
Real	hydrostatic (const SymmTensor &symm_tensor)
Real	volumetricStrain (const SymmTensor &symm_strain)
Real	firstInvariant (const SymmTensor &symm_tensor)
Real	secondInvariant (const SymmTensor &symm_tensor)
Real	thirdInvariant (const SymmTensor &symm_tensor)
Real	maxPrincipal (const SymmTensor &symm_tensor, RealVectorValue &direction)
Real	maxPrinciple (const SymmTensor &symm_tensor, RealVectorValue &direction)
Real	midPrincipal (const SymmTensor &symm_tensor, RealVectorValue &direction)
Real	midPrinciple (const SymmTensor &symm_tensor, RealVectorValue &direction)
Real	minPrincipal (const SymmTensor &symm_tensor, RealVectorValue &direction)
Real	minPrinciple (const SymmTensor &symm_tensor, RealVectorValue &direction)
Real	calcPrincipalValues (const SymmTensor &symm_tensor, unsigned int index, RealVectorValue &direction)
Real	axialStress (const SymmTensor &symm_stress, const Point &point1, const Point &point2, RealVectorValue &direction)
Real	hoopStress (const SymmTensor &symm_stress, const Point &point1, const Point &point2, const Point &curr_point, RealVectorValue &direction)
Real	radialStress (const SymmTensor &symm_stress, const Point &point1, const Point &point2, const Point &curr_point, RealVectorValue &direction)
void	normalPositionVector (const Point &point1, const Point &point2, const Point &curr_point, Point &normalPosition)
Real	directionValueTensor (const SymmTensor &symm_tensor, const RealVectorValue &input_direction)
Real	triaxialityStress (const SymmTensor &symm_stress)

Function Documentation

axialStress()

Real MaterialTensorCalculatorTools::axialStress	(	const SymmTensor &	symm_stress,
		const Point &	point1,
		const Point &	point2,
		RealVectorValue &	direction
	)

Definition at line 180 of file MaterialTensorCalculatorTools.C.

{
  Point axis = point2 - point1;
  axis /= axis.norm();
 
  // Calculate the stress in the direction of the axis specifed by the user
  Real axial_stress = 0.0;
  for (unsigned int i = 0; i < 3; ++i)
  {
    for (unsigned int j = 0; j < 3; ++j)
      axial_stress += axis(j) * symm_stress(j, i) * axis(i);
  }
  direction = axis;
  return axial_stress;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

calcPrincipalValues()

Real MaterialTensorCalculatorTools::calcPrincipalValues	(	const SymmTensor &	symm_tensor,
		unsigned int	index,
		RealVectorValue &	direction
	)

Definition at line 167 of file MaterialTensorCalculatorTools.C.

{
  ColumnMajorMatrix eval(3, 1);
  ColumnMajorMatrix evec(3, 3);
  symm_tensor.columnMajorMatrix().eigen(eval, evec);
  // Eigen computes low to high.  We want high first.
  direction(0) = evec(0, index);
  direction(1) = evec(1, index);
  direction(2) = evec(2, index);
  return eval(index);
}

Referenced by maxPrincipal(), maxPrinciple(), midPrincipal(), midPrinciple(), minPrincipal(), and minPrinciple().

component() [1/2]

Real MaterialTensorCalculatorTools::component	(	const SymmTensor &	symm_tensor,
		unsigned int	index
	)

Definition at line 16 of file MaterialTensorCalculatorTools.C.

{
  return symm_tensor.component(index);
}

Referenced by AddNavierStokesKernelsAction::act(), AddNavierStokesBCsAction::act(), AddNavierStokesBCsAction::addNoPenetrationBC(), AddNavierStokesKernelsAction::addNSMomentumInviscidFlux(), AddNavierStokesBCsAction::addNSMomentumInviscidSpecifiedPressureBC(), AddNavierStokesBCsAction::addNSMomentumWeakStagnationBC(), AddNavierStokesKernelsAction::addNSSUPGMomentum(), AddNavierStokesKernelsAction::addNSVelocityAux(), StressDivergenceRZTensors::computeAverageGradientPhi(), StressDivergenceTensors::computeAverageGradientPhi(), ADComputeIncrementalShellStrain< compute_stage >::computeBMatrix(), ADComputeFiniteShellStrain< compute_stage >::computeBNLMatrix(), FiniteStrainMechanicsNOSPD::computeDinvFTDU(), GeneralizedPlaneStrainOffDiagNOSPD::computeDispFullOffDiagJacobianScalar(), GeneralizedPlaneStrainOffDiagOSPD::computeDispFullOffDiagJacobianScalar(), GeneralizedPlaneStrainOffDiag::computeDispOffDiagJacobianScalar(), GeneralizedPlaneStrainOffDiagNOSPD::computeDispPartialOffDiagJacobianScalar(), GeneralizedPlaneStrainOffDiagOSPD::computeDispPartialOffDiagJacobianScalar(), FiniteStrainMechanicsNOSPD::computeDJDU(), MechanicsBaseNOSPD::computeDSDU(), FiniteStrainMechanicsNOSPD::computeDSDU(), StressDivergenceBeam::computeGlobalResidual(), ADComputeIncrementalShellStrain< compute_stage >::computeGMatrix(), StressDivergence::computeJacobian(), StressDivergenceRZ::computeJacobian(), StressDivergence::computeOffDiagJacobian(), StressDivergenceRZ::computeOffDiagJacobian(), DashpotBC::computeQpOffDiagJacobian(), BrineFluidProperties::getComponent(), MechanicalContactConstraint::getConnectedDofIndices(), MechanicalContactConstraint::getCoupledVarComponent(), PETScDMDAMesh::getMaxInDimension(), PETScDMDAMesh::getMinInDimension(), MaterialTensorCalculator::getTensorQuantity(), PetscProjectSolutionOntoBounds::lineSearch(), ADComputeFiniteShellStrain< compute_stage >::updatedxyz(), ADComputeFiniteShellStrain< compute_stage >::updateGVectors(), validParams< AEFVBC >(), validParams< AEFVKernel >(), validParams< DarcyFluxComponent >(), validParams< GrainAdvectionAux >(), validParams< NormalNodalMechanicalContact >(), validParams< PorousFlowDarcyVelocityComponent >(), validParams< RANFSNormalMechanicalContact >(), and validParams< RANFSTieNode >().

component() [2/2]

Real MaterialTensorCalculatorTools::component	(	const SymmTensor &	symm_tensor,
		unsigned int	index,
		RealVectorValue &	direction
	)

Definition at line 22 of file MaterialTensorCalculatorTools.C.

{
  direction.zero();
  if (index < 3)
    direction(index) = 1.0;
 
  else if (index == 3) // xy
  {
    direction(0) = std::sqrt(0.5);
    direction(1) = direction(0);
  }
  else if (index == 4) // yz
  {
    direction(1) = std::sqrt(0.5);
    direction(2) = direction(1);
  }
  else if (index == 5) // zx
  {
    direction(0) = std::sqrt(0.5);
    direction(2) = direction(0);
  }
  return symm_tensor.component(index);
}

directionValueTensor()

Real MaterialTensorCalculatorTools::directionValueTensor	(	const SymmTensor &	symm_tensor,
		const RealVectorValue &	input_direction
	)

Definition at line 269 of file MaterialTensorCalculatorTools.C.

{
  Real tensor_value_in_direction = 0.0;
  for (unsigned int i = 0; i < 3; ++i)
  {
    for (unsigned int j = 0; j < 3; ++j)
      tensor_value_in_direction += input_direction(j) * symm_tensor(j, i) * input_direction(i);
  }
  return tensor_value_in_direction;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

effectiveStrain()

Real MaterialTensorCalculatorTools::effectiveStrain

(

const SymmTensor &

symm_strain

)

Definition at line 58 of file MaterialTensorCalculatorTools.C.

{
  return std::sqrt(2.0 / 3.0 * symm_strain.doubleContraction(symm_strain));
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

firstInvariant()

Real MaterialTensorCalculatorTools::firstInvariant

(

const SymmTensor &

symm_tensor

)

Definition at line 92 of file MaterialTensorCalculatorTools.C.

{
  return symm_tensor.trace();
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

hoopStress()

Real MaterialTensorCalculatorTools::hoopStress	(	const SymmTensor &	symm_stress,
		const Point &	point1,
		const Point &	point2,
		const Point &	curr_point,
		RealVectorValue &	direction
	)

Definition at line 200 of file MaterialTensorCalculatorTools.C.

{
  // Calculate the cross of the normal to the axis of rotation from the current
  // location and the axis of rotation
  Point xp;
  normalPositionVector(point1, point2, curr_point, xp);
 
  Point axis_rotation = point2 - point1;
  Point yp = axis_rotation / axis_rotation.norm();
  Point zp = xp.cross(yp);
 
  // Calculate the scalar value of the hoop stress
  Real hoop_stress = 0.0;
  for (unsigned int i = 0; i < 3; ++i)
  {
    for (unsigned int j = 0; j < 3; ++j)
      hoop_stress += zp(j) * symm_stress(j, i) * zp(i);
  }
  direction = zp;
  return hoop_stress;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

hydrostatic()

Real MaterialTensorCalculatorTools::hydrostatic

(

const SymmTensor &

symm_tensor

)

Definition at line 64 of file MaterialTensorCalculatorTools.C.

{
  return symm_tensor.trace() / 3.0;
}

Referenced by MaterialTensorCalculator::getTensorQuantity(), and triaxialityStress().

maxPrincipal()

Real MaterialTensorCalculatorTools::maxPrincipal	(	const SymmTensor &	symm_tensor,
		RealVectorValue &	direction
	)

Definition at line 122 of file MaterialTensorCalculatorTools.C.

{
  Real val = calcPrincipalValues(symm_tensor, (LIBMESH_DIM - 1), direction);
  return val;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

maxPrinciple()

Real MaterialTensorCalculatorTools::maxPrinciple	(	const SymmTensor &	symm_tensor,
		RealVectorValue &	direction
	)

Definition at line 146 of file MaterialTensorCalculatorTools.C.

{
  Real val = calcPrincipalValues(symm_tensor, (LIBMESH_DIM - 1), direction);
  return val;
}

midPrincipal()

Real MaterialTensorCalculatorTools::midPrincipal	(	const SymmTensor &	symm_tensor,
		RealVectorValue &	direction
	)

Definition at line 129 of file MaterialTensorCalculatorTools.C.

{
  Real val = calcPrincipalValues(symm_tensor, 1, direction);
  return val;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

midPrinciple()

Real MaterialTensorCalculatorTools::midPrinciple	(	const SymmTensor &	symm_tensor,
		RealVectorValue &	direction
	)

Definition at line 153 of file MaterialTensorCalculatorTools.C.

{
  Real val = calcPrincipalValues(symm_tensor, 1, direction);
  return val;
}

minPrincipal()

Real MaterialTensorCalculatorTools::minPrincipal	(	const SymmTensor &	symm_tensor,
		RealVectorValue &	direction
	)

Definition at line 136 of file MaterialTensorCalculatorTools.C.

{
  Real val = calcPrincipalValues(symm_tensor, 0, direction);
  return val;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

minPrinciple()

Real MaterialTensorCalculatorTools::minPrinciple	(	const SymmTensor &	symm_tensor,
		RealVectorValue &	direction
	)

Definition at line 160 of file MaterialTensorCalculatorTools.C.

{
  Real val = calcPrincipalValues(symm_tensor, 0, direction);
  return val;
}

normalPositionVector()

void MaterialTensorCalculatorTools::normalPositionVector	(	const Point &	point1,
		const Point &	point2,
		const Point &	curr_point,
		Point &	normalPosition
	)

Definition at line 249 of file MaterialTensorCalculatorTools.C.

{
  // Find the nearest point on the axis of rotation (defined by point2 - point1)
  // to the current position, e.g. the normal to the axis of rotation at the
  // current position
  Point axis_rotation = point2 - point1;
  Point positionWRTpoint1 = point1 - curr_point;
  Real projection = (axis_rotation * positionWRTpoint1) / axis_rotation.norm_sq();
  Point normal = point1 - projection * axis_rotation;
 
  // Calculate the direction normal to the plane formed by the axis of rotation
  // and the normal to the axis of rotation from the current position.
  normalPosition = curr_point - normal;
  normalPosition /= normalPosition.norm();
}

Referenced by hoopStress(), and radialStress().

radialStress()

Real MaterialTensorCalculatorTools::radialStress	(	const SymmTensor &	symm_stress,
		const Point &	point1,
		const Point &	point2,
		const Point &	curr_point,
		RealVectorValue &	direction
	)

Definition at line 227 of file MaterialTensorCalculatorTools.C.

{
  Point radial_norm;
  normalPositionVector(point1, point2, curr_point, radial_norm);
 
  // Compute the scalar stress component in the direciton of the normal vector from the
  // user-defined axis of rotation.
  Real radial_stress = 0.0;
  for (unsigned int i = 0; i < 3; ++i)
  {
    for (unsigned int j = 0; j < 3; ++j)
      radial_stress += radial_norm(j) * symm_stress(j, i) * radial_norm(i);
  }
  direction = radial_norm;
  return radial_stress;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

secondInvariant()

Real MaterialTensorCalculatorTools::secondInvariant

(

const SymmTensor &

symm_tensor

)

Definition at line 98 of file MaterialTensorCalculatorTools.C.

{
  Real value = symm_tensor.xx() * symm_tensor.yy() + symm_tensor.yy() * symm_tensor.zz() +
               symm_tensor.zz() * symm_tensor.xx() - symm_tensor.xy() * symm_tensor.xy() -
               symm_tensor.yz() * symm_tensor.yz() - symm_tensor.zx() * symm_tensor.zx();
 
  return value;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

thirdInvariant()

Real MaterialTensorCalculatorTools::thirdInvariant

(

const SymmTensor &

symm_tensor

)

Definition at line 108 of file MaterialTensorCalculatorTools.C.

{
  Real val = 0.0;
  val = symm_tensor.xx() * symm_tensor.yy() * symm_tensor.zz() -
        symm_tensor.xx() * symm_tensor.yz() * symm_tensor.yz() +
        symm_tensor.xy() * symm_tensor.yz() * symm_tensor.zx() -
        symm_tensor.xy() * symm_tensor.xy() * symm_tensor.zz() +
        symm_tensor.zx() * symm_tensor.xy() * symm_tensor.yz() -
        symm_tensor.zx() * symm_tensor.yy() * symm_tensor.zx();
 
  return val;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

triaxialityStress()

Real MaterialTensorCalculatorTools::triaxialityStress

(

const SymmTensor &

symm_stress

)

Definition at line 281 of file MaterialTensorCalculatorTools.C.

{
  Real val = hydrostatic(symm_stress) / vonMisesStress(symm_stress);
  return val;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

volumetricStrain()

Real MaterialTensorCalculatorTools::volumetricStrain

(

const SymmTensor &

symm_strain

)

Definition at line 70 of file MaterialTensorCalculatorTools.C.

{
  // Since the strains are logarithmic strains, which are by definition log(L/L0),
  // exp(log_strain) = L/L0
  // The ratio of the volume change of a strained cube to the original volume
  // (delta V / V) is thus:
  // exp(log_strain_11) * exp(log_strain_22) * exp(log_strain_33) - 1
  //
  // Since eng_strain = exp(log_strain) - 1, the equivalent calculation using
  // engineering strains would be:
  // (1 + eng_strain_11) * (1 + eng_strain_22) + (1 + eng_strain_33) - 1
  // If strains are small, the resulting terms that involve squared and cubed
  // strains are negligible, resulting in the following approximate form:
  // strain_11 + strain_22 + strain_33
  // There is not currently an option to compute this small-strain form of the
  // volumetric strain, but at small strains, it is approximately equal to the
  // finite strain form that is computed.
 
  return std::exp(symm_strain.xx()) * std::exp(symm_strain.yy()) * std::exp(symm_strain.zz()) - 1.0;
}

Referenced by MaterialTensorCalculator::getTensorQuantity().

vonMisesStress()

Real MaterialTensorCalculatorTools::vonMisesStress

(

const SymmTensor &

symm_stress

)

Definition at line 47 of file MaterialTensorCalculatorTools.C.

{
  Real value = std::pow(symm_stress.xx() - symm_stress.yy(), 2) +
               std::pow(symm_stress.yy() - symm_stress.zz(), 2) +
               std::pow(symm_stress.zz() - symm_stress.xx(), 2) +
               6 * (std::pow(symm_stress.xy(), 2) + std::pow(symm_stress.yz(), 2) +
                    std::pow(symm_stress.zx(), 2));
  return std::sqrt(value / 2.0);
}

Referenced by MaterialTensorCalculator::getTensorQuantity(), and triaxialityStress().