IsotropicSD plasticity model from Yoon (2013) the name of the paper is "Asymmetric yield function based on the stress invariants for pressure sensitive metals" published 4th December 2013. More...

#include <TensorMechanicsPlasticIsotropicSD.h>

Inheritance diagram for TensorMechanicsPlasticIsotropicSD:

[legend]

Public Member Functions
	TensorMechanicsPlasticIsotropicSD (const InputParameters &parameters)

virtual std::string	modelName () const override

virtual bool	useCustomReturnMap () const override
	Returns false. You will want to override this in your derived class if you write a custom returnMap function. More...

virtual bool	useCustomCTO () const override
	Returns false. You will want to override this in your derived class if you write a custom consistent tangent operator function. More...

virtual bool	returnMap (const RankTwoTensor &trial_stress, Real intnl_old, const RankFourTensor &E_ijkl, Real ep_plastic_tolerance, RankTwoTensor &returned_stress, Real &returned_intnl, std::vector< Real > &dpm, RankTwoTensor &delta_dp, std::vector< Real > &yf, bool &trial_stress_inadmissible) const override
	Performs a custom return-map. More...

virtual RankFourTensor	consistentTangentOperator (const RankTwoTensor &trial_stress, Real intnl_old, const RankTwoTensor &stress, Real intnl, const RankFourTensor &E_ijkl, const std::vector< Real > &cumulative_pm) const override
	Calculates a custom consistent tangent operator. More...

void	initialize ()

void	execute ()

void	finalize ()

virtual unsigned int	numberSurfaces () const
	The number of yield surfaces for this plasticity model. More...

virtual void	yieldFunctionV (const RankTwoTensor &stress, Real intnl, std::vector< Real > &f) const
	Calculates the yield functions. More...

virtual void	dyieldFunction_dstressV (const RankTwoTensor &stress, Real intnl, std::vector< RankTwoTensor > &df_dstress) const
	The derivative of yield functions with respect to stress. More...

virtual void	dyieldFunction_dintnlV (const RankTwoTensor &stress, Real intnl, std::vector< Real > &df_dintnl) const
	The derivative of yield functions with respect to the internal parameter. More...

virtual void	flowPotentialV (const RankTwoTensor &stress, Real intnl, std::vector< RankTwoTensor > &r) const
	The flow potentials. More...

virtual void	dflowPotential_dstressV (const RankTwoTensor &stress, Real intnl, std::vector< RankFourTensor > &dr_dstress) const
	The derivative of the flow potential with respect to stress. More...

virtual void	dflowPotential_dintnlV (const RankTwoTensor &stress, Real intnl, std::vector< RankTwoTensor > &dr_dintnl) const
	The derivative of the flow potential with respect to the internal parameter. More...

virtual void	hardPotentialV (const RankTwoTensor &stress, Real intnl, std::vector< Real > &h) const
	The hardening potential. More...

virtual void	dhardPotential_dstressV (const RankTwoTensor &stress, Real intnl, std::vector< RankTwoTensor > &dh_dstress) const
	The derivative of the hardening potential with respect to stress. More...

virtual void	dhardPotential_dintnlV (const RankTwoTensor &stress, Real intnl, std::vector< Real > &dh_dintnl) const
	The derivative of the hardening potential with respect to the internal parameter. More...

virtual void	activeConstraints (const std::vector< Real > &f, const RankTwoTensor &stress, Real intnl, const RankFourTensor &Eijkl, std::vector< bool > &act, RankTwoTensor &returned_stress) const
	The active yield surfaces, given a vector of yield functions. More...

bool	KuhnTuckerSingleSurface (Real yf, Real dpm, Real dpm_tol) const
	Returns true if the Kuhn-Tucker conditions for the single surface are satisfied. More...

Static Public Member Functions
static InputParameters	validParams ()

Public Attributes
const Real	_f_tol
	Tolerance on yield function. More...

const Real	_ic_tol
	Tolerance on internal constraint. More...

Protected Member Functions
Real	dphi_dj2 (const Real j2, const Real j3) const
	derivative of phi with respect to J2, phi is bI1 + (J2^{3/2} - cJ3)^{1/3} More...

Real	dphi_dj3 (const Real j2, const Real j3) const
	derivative of phi with respect to J3 More...

Real	dfj2_dj2 (const Real j2, const Real j3) const
	derivative of dphi_dJ2 with respect to J2 More...

Real	dfj2_dj3 (const Real j2, const Real j3) const
	derivative of dphi_dJ2 with respect to J3 More...

Real	dfj3_dj2 (const Real j2, const Real j3) const
	derivative of dphi_dJ3 with respect to J2 More...

Real	dfj3_dj3 (const Real j2, const Real j3) const
	derivative of dphi_dJ3 with respect to J3 More...

RankTwoTensor	dI_sigma () const
	derivative of the trace with respect to sigma rank two tensor More...

RankTwoTensor	dj2_dSkl (const RankTwoTensor &stress) const
	derivative of the second invariant with respect to the stress deviatoric tensor More...

Real	yieldFunction (const RankTwoTensor &stress, Real intnl) const override
	Yield_function = a[bI1 + (J2^{3/2} - cJ3)^{1/3}] - yield_strength. More...

RankTwoTensor	dyieldFunction_dstress (const RankTwoTensor &stress, Real intnl) const override
	Tensor derivative of the yield_function with respect to the stress tensor. More...

RankFourTensor	dflowPotential_dstress (const RankTwoTensor &stress, Real intnl) const override
	Tensor derivative of the tensor derivative of the yield_function with respect to the stress tensor. More...

RankTwoTensor	flowPotential (const RankTwoTensor &stress, Real intnl) const override
	Receives the flag for associative or non-associative and calculates the flow potential accordingly. More...

Real	dyieldFunction_dintnl (const RankTwoTensor &stress, Real intnl) const override
	The derivative of yield function with respect to the internal parameter. More...

RankTwoTensor	dflowPotential_dintnl (const RankTwoTensor &stress, Real intnl) const override
	The derivative of the flow potential with respect to the internal parameter. More...

virtual Real	yieldStrength (Real intnl) const
	YieldStrength. More...

virtual Real	dyieldStrength (Real intnl) const
	d(yieldStrength)/d(intnl) More...

virtual Real	hardPotential (const RankTwoTensor &stress, Real intnl) const
	The hardening potential. More...

virtual RankTwoTensor	dhardPotential_dstress (const RankTwoTensor &stress, Real intnl) const
	The derivative of the hardening potential with respect to stress. More...

virtual Real	dhardPotential_dintnl (const RankTwoTensor &stress, Real intnl) const
	The derivative of the hardening potential with respect to the internal parameter. More...

Protected Attributes
const Real	_b
	A constant to model the influence of pressure. More...

Real	_c
	A constant to model the influence of strength differential effect. More...

const bool	_associative
	Flag for flow-rule, true if not specified. More...

RankFourTensor	_h
	Comes from transforming the stress tensor to the deviatoric stress tensor. More...

Real	_a
	A constant used in the constructor that depends on _b and _c. More...

Private Attributes
const TensorMechanicsHardeningModel &	_strength
	yield strength, from user input More...

const unsigned	_max_iters
	max iters for custom return map loop More...

const bool	_use_custom_returnMap
	Whether to use the custom return-map algorithm. More...

const bool	_use_custom_cto
	Whether to use the custom consistent tangent operator calculation. More...

Detailed Description

IsotropicSD plasticity model from Yoon (2013) the name of the paper is "Asymmetric yield function based on the stress invariants for pressure sensitive metals" published 4th December 2013.

This model accounts for sensitivity in pressure and for the strength differential effect Yield_function = \( a[b*I_{1} + (J2^{3/2} - c*J3)^{1/3}]\) - yield_strength The last three functions are the main functions that call all other functions in this module for the Newton-Raphson method.

Definition at line 31 of file TensorMechanicsPlasticIsotropicSD.h.

Constructor & Destructor Documentation

◆ TensorMechanicsPlasticIsotropicSD()

TensorMechanicsPlasticIsotropicSD::TensorMechanicsPlasticIsotropicSD ( const InputParameters & parameters )

Definition at line 29 of file TensorMechanicsPlasticIsotropicSD.C.

   : TensorMechanicsPlasticJ2(parameters),
     _b(getParam<Real>("b")),
     _c(getParam<Real>("c")),
     _associative(getParam<bool>("associative"))
 {
   _a = 1.0 / (_b + std::pow(1.0 / std::sqrt(27.0) - _c / 27.0, 1.0 / 3.0));
   for (unsigned i = 0; i < 3; ++i)
     for (unsigned j = 0; j < 3; ++j)
       for (unsigned k = 0; k < 3; ++k)
         for (unsigned l = 0; l < 3; ++l)
           _h(i, j, k, l) = ((i == k) * (j == l) - 1.0 / 3.0 * (i == j) * (k == l));
 }

Member Function Documentation

◆ activeConstraints()

void TensorMechanicsPlasticModel::activeConstraints	(	const std::vector< Real > &	f,
		const RankTwoTensor &	stress,
		Real	intnl,
		const RankFourTensor &	Eijkl,
		std::vector< bool > &	act,
		RankTwoTensor &	returned_stress
	)		const

virtualinherited

The active yield surfaces, given a vector of yield functions.

This is used by FiniteStrainMultiPlasticity to determine the initial set of active constraints at the trial (stress, intnl) configuration. It is up to you (the coder) to determine how accurate you want the returned_stress to be. Currently it is only used by FiniteStrainMultiPlasticity to estimate a good starting value for the Newton-Rahson procedure, so currently it may not need to be super perfect.

Parameters

	f	values of the yield functions
	stress	stress tensor
	intnl	internal parameter
	Eijkl	elasticity tensor (stress = Eijkl*strain)
[out]	act	act[i] = true if the i_th yield function is active
[out]	returned_stress	Approximate value of the returned stress

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, TensorMechanicsPlasticTensileMulti, TensorMechanicsPlasticMeanCapTC, TensorMechanicsPlasticWeakPlaneShear, and TensorMechanicsPlasticWeakPlaneTensile.

Definition at line 188 of file TensorMechanicsPlasticModel.C.

 {
   mooseAssert(f.size() == numberSurfaces(),
               "f incorrectly sized at " << f.size() << " in activeConstraints");
   act.resize(numberSurfaces());
   for (unsigned surface = 0; surface < numberSurfaces(); ++surface)
     act[surface] = (f[surface] > _f_tol);
 }

◆ consistentTangentOperator()

RankFourTensor TensorMechanicsPlasticJ2::consistentTangentOperator	(	const RankTwoTensor &	trial_stress,
		Real	intnl_old,
		const RankTwoTensor &	stress,
		Real	intnl,
		const RankFourTensor &	E_ijkl,
		const std::vector< Real > &	cumulative_pm
	)		const

overridevirtualinherited

Calculates a custom consistent tangent operator.

You may choose to over-ride this in your derived TensorMechanicsPlasticXXXX class.

(Note, if you over-ride returnMap, you will probably want to override consistentTangentOpertor too, otherwise it will default to E_ijkl.)

Parameters

stress_old	trial stress before returning
intnl_old	internal parameter before returning
stress	current returned stress state
intnl	internal parameter
E_ijkl	elasticity tensor
cumulative_pm	the cumulative plastic multipliers

Returns: the consistent tangent operator: E_ijkl if not over-ridden

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 193 of file TensorMechanicsPlasticJ2.C.

 {
   if (!_use_custom_cto)
     return TensorMechanicsPlasticModel::consistentTangentOperator(
         trial_stress, intnl_old, stress, intnl, E_ijkl, cumulative_pm);
  
   Real mu = E_ijkl(0, 1, 0, 1);
  
   Real h = 3 * mu + dyieldStrength(intnl);
   RankTwoTensor sij = stress.deviatoric();
   Real sII = stress.secondInvariant();
   Real equivalent_stress = std::sqrt(3.0 * sII);
   Real zeta = cumulative_pm[0] / (1.0 + 3.0 * mu * cumulative_pm[0] / equivalent_stress);
  
   return E_ijkl - 3.0 * mu * mu / sII / h * sij.outerProduct(sij) -
          4.0 * mu * mu * zeta * dflowPotential_dstress(stress, intnl);
 }

◆ dfj2_dj2()

Real TensorMechanicsPlasticIsotropicSD::dfj2_dj2	(	const Real	j2,
		const Real	j3
	)		const

protected

derivative of dphi_dJ2 with respect to J2

Definition at line 57 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   return std::pow(j2, -1.0 / 2.0) / (4 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 2.0 / 3.0)) -
          j2 / (2 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 5.0 / 3.0));
 }

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), and dflowPotential_dstress().

◆ dfj2_dj3()

Real TensorMechanicsPlasticIsotropicSD::dfj2_dj3	(	const Real	j2,
		const Real	j3
	)		const

protected

derivative of dphi_dJ2 with respect to J3

Definition at line 64 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   return _c * std::pow(j2, 1.0 / 2.0) /
          (3 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 5.0 / 3.0));
 }

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), and dflowPotential_dstress().

◆ dfj3_dj2()

Real TensorMechanicsPlasticIsotropicSD::dfj3_dj2	(	const Real	j2,
		const Real	j3
	)		const

protected

derivative of dphi_dJ3 with respect to J2

Definition at line 71 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   return _c * std::pow(j2, 1.0 / 2.0) /
          (3 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 5.0 / 3.0));
 }

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), and dflowPotential_dstress().

◆ dfj3_dj3()

Real TensorMechanicsPlasticIsotropicSD::dfj3_dj3	(	const Real	j2,
		const Real	j3
	)		const

protected

derivative of dphi_dJ3 with respect to J3

Definition at line 78 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   return -_c * _c * 2.0 / (9 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 5.0 / 3.0));
 }

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), and dflowPotential_dstress().

◆ dflowPotential_dintnl()

RankTwoTensor TensorMechanicsPlasticJ2::dflowPotential_dintnl	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtualinherited

The derivative of the flow potential with respect to the internal parameter.

Parameters

stress	the stress at which to calculate the flow potential
intnl	internal parameter

Returns: dr_dintnl(i, j) = dr(i, j)/dintnl

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 97 of file TensorMechanicsPlasticJ2.C.

 {
   return RankTwoTensor();
 }

◆ dflowPotential_dintnlV()

void TensorMechanicsPlasticModel::dflowPotential_dintnlV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< RankTwoTensor > &	dr_dintnl
	)		const

virtualinherited

The derivative of the flow potential with respect to the internal parameter.

Parameters

	stress	the stress at which to calculate the flow potential
	intnl	internal parameter
[out]	dr_dintnl	dr_dintnl[alpha](i, j) = dr[alpha](i, j)/dintnl

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 139 of file TensorMechanicsPlasticModel.C.

 {
   return dr_dintnl.assign(1, dflowPotential_dintnl(stress, intnl));
 }

◆ dflowPotential_dstress()

RankFourTensor TensorMechanicsPlasticIsotropicSD::dflowPotential_dstress	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtual

Tensor derivative of the tensor derivative of the yield_function with respect to the stress tensor.

Reimplemented from TensorMechanicsPlasticJ2.

Reimplemented in TensorMechanicsPlasticOrthotropic.

Definition at line 122 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   if (_associative)
   {
     const RankTwoTensor sDev = stress.deviatoric();
     const RankTwoTensor dj2 = dj2_dSkl(sDev);
     const RankTwoTensor dj3 = sDev.ddet();
     const Real j2 = stress.secondInvariant();
     const Real j3 = stress.thirdInvariant();
     return _a * (dfj2_dj2(j2, j3) *
                      _h.innerProductTranspose(dj2).outerProduct(_h.innerProductTranspose(dj2)) +
                  dfj2_dj3(j2, j3) *
                      _h.innerProductTranspose(dj2).outerProduct(_h.innerProductTranspose(dj3)) +
                  dfj3_dj2(j2, j3) *
                      _h.innerProductTranspose(dj3).outerProduct(_h.innerProductTranspose(dj2)) +
                  dfj3_dj3(j2, j3) *
                      _h.innerProductTranspose(dj3).outerProduct(_h.innerProductTranspose(dj3)));
   }
   else
     return TensorMechanicsPlasticJ2::dflowPotential_dstress(stress, 0);
 }

◆ dflowPotential_dstressV()

void TensorMechanicsPlasticModel::dflowPotential_dstressV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< RankFourTensor > &	dr_dstress
	)		const

virtualinherited

The derivative of the flow potential with respect to stress.

Parameters

	stress	the stress at which to calculate the flow potential
	intnl	internal parameter
[out]	dr_dstress	dr_dstress[alpha](i, j, k, l) = dr[alpha](i, j)/dstress(k, l)

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 125 of file TensorMechanicsPlasticModel.C.

 {
   return dr_dstress.assign(1, dflowPotential_dstress(stress, intnl));
 }

◆ dhardPotential_dintnl()

Real TensorMechanicsPlasticModel::dhardPotential_dintnl	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

protectedvirtualinherited

The derivative of the hardening potential with respect to the internal parameter.

Parameters

stress	the stress at which to calculate the hardening potentials
intnl	internal parameter

Returns: the derivative

Reimplemented in TensorMechanicsPlasticMeanCapTC.

Definition at line 174 of file TensorMechanicsPlasticModel.C.

 {
   return 0.0;
 }

Referenced by TensorMechanicsPlasticModel::dhardPotential_dintnlV().

◆ dhardPotential_dintnlV()

void TensorMechanicsPlasticModel::dhardPotential_dintnlV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< Real > &	dh_dintnl
	)		const

virtualinherited

The derivative of the hardening potential with respect to the internal parameter.

Parameters

	stress	the stress at which to calculate the hardening potentials
	intnl	internal parameter
[out]	dh_dintnl	dh_dintnl[alpha] = dh[alpha]/dintnl

Definition at line 180 of file TensorMechanicsPlasticModel.C.

 {
   dh_dintnl.resize(numberSurfaces(), dhardPotential_dintnl(stress, intnl));
 }

◆ dhardPotential_dstress()

RankTwoTensor TensorMechanicsPlasticModel::dhardPotential_dstress	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

protectedvirtualinherited

The derivative of the hardening potential with respect to stress.

Parameters

stress	the stress at which to calculate the hardening potentials
intnl	internal parameter

Returns: dh_dstress(i, j) = dh/dstress(i, j)

Reimplemented in TensorMechanicsPlasticMeanCapTC.

Definition at line 160 of file TensorMechanicsPlasticModel.C.

 {
   return RankTwoTensor();
 }

Referenced by TensorMechanicsPlasticModel::dhardPotential_dstressV().

◆ dhardPotential_dstressV()

void TensorMechanicsPlasticModel::dhardPotential_dstressV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< RankTwoTensor > &	dh_dstress
	)		const

virtualinherited

The derivative of the hardening potential with respect to stress.

Parameters

	stress	the stress at which to calculate the hardening potentials
	intnl	internal parameter
[out]	dh_dstress	dh_dstress[alpha](i, j) = dh[alpha]/dstress(i, j)

Definition at line 166 of file TensorMechanicsPlasticModel.C.

 {
   dh_dstress.assign(numberSurfaces(), dhardPotential_dstress(stress, intnl));
 }

◆ dI_sigma()

RankTwoTensor TensorMechanicsPlasticIsotropicSD::dI_sigma ( ) const

protected

derivative of the trace with respect to sigma rank two tensor

Definition at line 84 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   return RankTwoTensor(RankTwoTensor::initIdentity);
 }

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), TensorMechanicsPlasticOrthotropic::dyieldFunction_dstress(), and dyieldFunction_dstress().

◆ dj2_dSkl()

RankTwoTensor TensorMechanicsPlasticIsotropicSD::dj2_dSkl ( const RankTwoTensor & stress ) const

protected

derivative of the second invariant with respect to the stress deviatoric tensor

Definition at line 90 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   RankTwoTensor a;
   const Real trace = stress.trace();
   for (unsigned i = 0; i < 3; ++i)
     for (unsigned j = 0; j < 3; ++j)
       a(i, j) = (trace - stress(i, j)) * -1 * (i == j) + stress(i, j) * (i != j);
  
   return a;
 }

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), dflowPotential_dstress(), TensorMechanicsPlasticOrthotropic::dyieldFunction_dstress(), and dyieldFunction_dstress().

◆ dphi_dj2()

Real TensorMechanicsPlasticIsotropicSD::dphi_dj2	(	const Real	j2,
		const Real	j3
	)		const

protected

derivative of phi with respect to J2, phi is b*I1 + (J2^{3/2} - c*J3)^{1/3}

Definition at line 45 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   return std::pow(j2, 1.0 / 2.0) / (2 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 2.0 / 3.0));
 }

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), TensorMechanicsPlasticOrthotropic::dyieldFunction_dstress(), and dyieldFunction_dstress().

◆ dphi_dj3()

Real TensorMechanicsPlasticIsotropicSD::dphi_dj3	(	const Real	j2,
		const Real	j3
	)		const

protected

derivative of phi with respect to J3

Definition at line 51 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   return -_c / (3 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 2.0 / 3.0));
 }

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), TensorMechanicsPlasticOrthotropic::dyieldFunction_dstress(), and dyieldFunction_dstress().

◆ dyieldFunction_dintnl()

Real TensorMechanicsPlasticJ2::dyieldFunction_dintnl	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtualinherited

The derivative of yield function with respect to the internal parameter.

Parameters

stress	the stress at which to calculate the yield function
intnl	internal parameter

Returns: the derivative

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 67 of file TensorMechanicsPlasticJ2.C.

 {
   return -dyieldStrength(intnl);
 }

◆ dyieldFunction_dintnlV()

void TensorMechanicsPlasticModel::dyieldFunction_dintnlV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< Real > &	df_dintnl
	)		const

virtualinherited

The derivative of yield functions with respect to the internal parameter.

Parameters

	stress	the stress at which to calculate the yield function
	intnl	internal parameter
[out]	df_dintnl	df_dintnl[alpha] = df[alpha]/dintnl

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 98 of file TensorMechanicsPlasticModel.C.

 {
   return df_dintnl.assign(1, dyieldFunction_dintnl(stress, intnl));
 }

◆ dyieldFunction_dstress()

RankTwoTensor TensorMechanicsPlasticIsotropicSD::dyieldFunction_dstress	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtual

Tensor derivative of the yield_function with respect to the stress tensor.

Reimplemented from TensorMechanicsPlasticJ2.

Reimplemented in TensorMechanicsPlasticOrthotropic.

Definition at line 111 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   const RankTwoTensor sDev = stress.deviatoric();
   const Real j2 = stress.secondInvariant();
   const Real j3 = stress.thirdInvariant();
   return _a * (_b * dI_sigma() + dphi_dj2(j2, j3) * _h.innerProductTranspose(dj2_dSkl(sDev)) +
                dphi_dj3(j2, j3) * _h.innerProductTranspose(sDev.ddet()));
 }

Referenced by flowPotential().

◆ dyieldFunction_dstressV()

void TensorMechanicsPlasticModel::dyieldFunction_dstressV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< RankTwoTensor > &	df_dstress
	)		const

virtualinherited

The derivative of yield functions with respect to stress.

Parameters

	stress	the stress at which to calculate the yield function
	intnl	internal parameter
[out]	df_dstress	df_dstress[alpha](i, j) = dyieldFunction[alpha]/dstress(i, j)

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 84 of file TensorMechanicsPlasticModel.C.

 {
   df_dstress.assign(1, dyieldFunction_dstress(stress, intnl));
 }

◆ dyieldStrength()

Real TensorMechanicsPlasticJ2::dyieldStrength ( Real intnl ) const

protectedvirtualinherited

d(yieldStrength)/d(intnl)

Definition at line 110 of file TensorMechanicsPlasticJ2.C.

 {
   return _strength.derivative(intnl);
 }

Referenced by TensorMechanicsPlasticJ2::consistentTangentOperator(), TensorMechanicsPlasticJ2::dyieldFunction_dintnl(), and TensorMechanicsPlasticJ2::returnMap().

◆ execute()

void TensorMechanicsPlasticModel::execute ( )

inherited

Definition at line 47 of file TensorMechanicsPlasticModel.C.

48 {

49 }

◆ finalize()

void TensorMechanicsPlasticModel::finalize ( )

inherited

Definition at line 52 of file TensorMechanicsPlasticModel.C.

53 {

54 }

◆ flowPotential()

RankTwoTensor TensorMechanicsPlasticIsotropicSD::flowPotential	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtual

Receives the flag for associative or non-associative and calculates the flow potential accordingly.

Reimplemented from TensorMechanicsPlasticJ2.

Reimplemented in TensorMechanicsPlasticOrthotropic.

Definition at line 146 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   if (_associative)
     return dyieldFunction_dstress(stress, intnl);
   else
     return TensorMechanicsPlasticJ2::dyieldFunction_dstress(stress, intnl);
 }

◆ flowPotentialV()

void TensorMechanicsPlasticModel::flowPotentialV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< RankTwoTensor > &	r
	)		const

virtualinherited

The flow potentials.

Parameters

	stress	the stress at which to calculate the flow potential
	intnl	internal parameter
[out]	r	r[alpha] is the flow potential for the "alpha" yield function

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 111 of file TensorMechanicsPlasticModel.C.

 {
   return r.assign(1, flowPotential(stress, intnl));
 }

◆ hardPotential()

Real TensorMechanicsPlasticModel::hardPotential	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

protectedvirtualinherited

The hardening potential.

Parameters

stress	the stress at which to calculate the hardening potential
intnl	internal parameter

Returns: the hardening potential

Reimplemented in TensorMechanicsPlasticMeanCapTC.

Definition at line 147 of file TensorMechanicsPlasticModel.C.

 {
   return -1.0;
 }

Referenced by TensorMechanicsPlasticModel::hardPotentialV().

◆ hardPotentialV()

void TensorMechanicsPlasticModel::hardPotentialV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< Real > &	h
	)		const

virtualinherited

The hardening potential.

Parameters

	stress	the stress at which to calculate the hardening potential
	intnl	internal parameter
[out]	h	h[alpha] is the hardening potential for the "alpha" yield function

Definition at line 152 of file TensorMechanicsPlasticModel.C.

 {
   h.assign(numberSurfaces(), hardPotential(stress, intnl));
 }

◆ initialize()

void TensorMechanicsPlasticModel::initialize ( )

inherited

Definition at line 42 of file TensorMechanicsPlasticModel.C.

43 {

44 }

◆ KuhnTuckerSingleSurface()

bool TensorMechanicsPlasticModel::KuhnTuckerSingleSurface	(	Real	yf,
		Real	dpm,
		Real	dpm_tol
	)		const

inherited

Returns true if the Kuhn-Tucker conditions for the single surface are satisfied.

Parameters

yf	Yield function value
dpm	plastic multiplier
dpm_tol	tolerance on plastic multiplier: viz dpm>-dpm_tol means "dpm is non-negative"

Definition at line 248 of file TensorMechanicsPlasticModel.C.

 {
   return (dpm == 0 && yf <= _f_tol) || (dpm > -dpm_tol && yf <= _f_tol && yf >= -_f_tol);
 }

Referenced by TensorMechanicsPlasticMohrCoulombMulti::KuhnTuckerOK(), TensorMechanicsPlasticTensileMulti::KuhnTuckerOK(), and TensorMechanicsPlasticModel::returnMap().

◆ modelName()

std::string TensorMechanicsPlasticJ2::modelName ( ) const

overridevirtualinherited

Implements TensorMechanicsPlasticModel.

Definition at line 116 of file TensorMechanicsPlasticJ2.C.

 {
   return "J2";
 }

◆ numberSurfaces()

unsigned TensorMechanicsPlasticModel::numberSurfaces ( ) const

virtualinherited

The number of yield surfaces for this plasticity model.

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 57 of file TensorMechanicsPlasticModel.C.

 {
   return 1;
 }

Referenced by TensorMechanicsPlasticModel::activeConstraints(), TensorMechanicsPlasticModel::dhardPotential_dintnlV(), TensorMechanicsPlasticModel::dhardPotential_dstressV(), TensorMechanicsPlasticModel::hardPotentialV(), and TensorMechanicsPlasticModel::returnMap().

◆ returnMap()

bool TensorMechanicsPlasticJ2::returnMap	(	const RankTwoTensor &	trial_stress,
		Real	intnl_old,
		const RankFourTensor &	E_ijkl,
		Real	ep_plastic_tolerance,
		RankTwoTensor &	returned_stress,
		Real &	returned_intnl,
		std::vector< Real > &	dpm,
		RankTwoTensor &	delta_dp,
		std::vector< Real > &	yf,
		bool &	trial_stress_inadmissible
	)		const

overridevirtualinherited

Performs a custom return-map.

You may choose to over-ride this in your derived TensorMechanicsPlasticXXXX class, and you may implement the return-map algorithm in any way that suits you. Eg, using a Newton-Raphson approach, or a radial-return, etc. This may also be used as a quick way of ascertaining whether (trial_stress, intnl_old) is in fact admissible.

For over-riding this function, please note the following.

(1) Denoting the return value of the function by "successful_return", the only possible output values should be: (A) trial_stress_inadmissible=false, successful_return=true. That is, (trial_stress, intnl_old) is in fact admissible (in the elastic domain). (B) trial_stress_inadmissible=true, successful_return=false. That is (trial_stress, intnl_old) is inadmissible (outside the yield surface), and you didn't return to the yield surface. (C) trial_stress_inadmissible=true, successful_return=true. That is (trial_stress, intnl_old) is inadmissible (outside the yield surface), but you did return to the yield surface. The default implementation only handles case (A) and (B): it does not attempt to do a return-map algorithm.

(2) you must correctly signal "successful_return" using the return value of this function. Don't assume the calling function will do Kuhn-Tucker checking and so forth!

(3) In cases (A) and (B) you needn't set returned_stress, returned_intnl, delta_dp, or dpm. This is for computational efficiency.

(4) In cases (A) and (B), you MUST place the yield function values at (trial_stress, intnl_old) into yf so the calling function can use this information optimally. You will have already calculated these yield function values, which can be quite expensive, and it's not very optimal for the calling function to have to re-calculate them.

(5) In case (C), you need to set: returned_stress (the returned value of stress) returned_intnl (the returned value of the internal variable) delta_dp (the change in plastic strain) dpm (the plastic multipliers needed to bring about the return) yf (yield function values at the returned configuration)

(Note, if you over-ride returnMap, you will probably want to override consistentTangentOpertor too, otherwise it will default to E_ijkl.)

Parameters

	trial_stress	The trial stress
	intnl_old	Value of the internal parameter
	E_ijkl	Elasticity tensor
	ep_plastic_tolerance	Tolerance defined by the user for the plastic strain
[out]	returned_stress	In case (C): lies on the yield surface after returning and produces the correct plastic strain (normality condition). Otherwise: not defined
[out]	returned_intnl	In case (C): the value of the internal parameter after returning. Otherwise: not defined
[out]	dpm	In case (C): the plastic multipliers needed to bring about the return. Otherwise: not defined
[out]	delta_dp	In case (C): The change in plastic strain induced by the return process. Otherwise: not defined
[out]	yf	In case (C): the yield function at (returned_stress, returned_intnl). Otherwise: the yield function at (trial_stress, intnl_old)
[out]	trial_stress_inadmissible	Should be set to false if the trial_stress is admissible, and true if the trial_stress is inadmissible. This can be used by the calling prorgram

Returns: true if a successful return (or a return-map not needed), false if the trial_stress is inadmissible but the return process failed

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 122 of file TensorMechanicsPlasticJ2.C.

 {
   if (!(_use_custom_returnMap))
     return TensorMechanicsPlasticModel::returnMap(trial_stress,
                                                   intnl_old,
                                                   E_ijkl,
                                                   ep_plastic_tolerance,
                                                   returned_stress,
                                                   returned_intnl,
                                                   dpm,
                                                   delta_dp,
                                                   yf,
                                                   trial_stress_inadmissible);
  
   yf.resize(1);
  
   Real yf_orig = yieldFunction(trial_stress, intnl_old);
  
   yf[0] = yf_orig;
  
   if (yf_orig < _f_tol)
   {
     // the trial_stress is admissible
     trial_stress_inadmissible = false;
     return true;
   }
  
   trial_stress_inadmissible = true;
   Real mu = E_ijkl(0, 1, 0, 1);
  
   // Perform a Newton-Raphson to find dpm when
   // residual = 3*mu*dpm - trial_equivalent_stress + yieldStrength(intnl_old + dpm) = 0
   Real trial_equivalent_stress = yf_orig + yieldStrength(intnl_old);
   Real residual;
   Real jac;
   dpm[0] = 0;
   unsigned int iter = 0;
   do
   {
     residual = 3.0 * mu * dpm[0] - trial_equivalent_stress + yieldStrength(intnl_old + dpm[0]);
     jac = 3.0 * mu + dyieldStrength(intnl_old + dpm[0]);
     dpm[0] += -residual / jac;
     if (iter > _max_iters) // not converging
       return false;
     iter++;
   } while (residual * residual > _f_tol * _f_tol);
  
   // set the returned values
   yf[0] = 0;
   returned_intnl = intnl_old + dpm[0];
   RankTwoTensor nn = 1.5 * trial_stress.deviatoric() /
                      trial_equivalent_stress; // = dyieldFunction_dstress(trial_stress, intnl_old) =
                                               // the normal to the yield surface, at the trial
                                               // stress
   returned_stress = 2.0 / 3.0 * nn * yieldStrength(returned_intnl);
   returned_stress.addIa(1.0 / 3.0 * trial_stress.trace());
   delta_dp = nn * dpm[0];
  
   return true;
 }

◆ useCustomCTO()

bool TensorMechanicsPlasticJ2::useCustomCTO ( ) const

overridevirtualinherited

Returns false. You will want to override this in your derived class if you write a custom consistent tangent operator function.

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 223 of file TensorMechanicsPlasticJ2.C.

 {
   return _use_custom_cto;
 }

◆ useCustomReturnMap()

bool TensorMechanicsPlasticJ2::useCustomReturnMap ( ) const

overridevirtualinherited

Returns false. You will want to override this in your derived class if you write a custom returnMap function.

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 217 of file TensorMechanicsPlasticJ2.C.

 {
   return _use_custom_returnMap;
 }

◆ validParams()

InputParameters TensorMechanicsPlasticIsotropicSD::validParams ( )

static

Definition at line 17 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   InputParameters params = TensorMechanicsPlasticJ2::validParams();
   params.addRequiredParam<Real>("b", "A constant to model the influence of pressure");
   params.addParam<Real>(
       "c", 0.0, "A constant to model the influence of strength differential effect");
   params.addParam<bool>("associative", true, "Flag for flow-rule, true if not specified");
   params.addClassDescription("IsotropicSD plasticity for pressure sensitive materials and also "
                              "models the strength differential effect");
   return params;
 }

Referenced by TensorMechanicsPlasticOrthotropic::validParams().

◆ yieldFunction()

Real TensorMechanicsPlasticIsotropicSD::yieldFunction	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtual

Yield_function = a[b*I1 + (J2^{3/2} - c*J3)^{1/3}] - yield_strength.

Reimplemented from TensorMechanicsPlasticJ2.

Reimplemented in TensorMechanicsPlasticOrthotropic.

Definition at line 102 of file TensorMechanicsPlasticIsotropicSD.C.

 {
   return _a * (_b * stress.trace() +
                std::pow(std::pow(stress.secondInvariant(), 1.5) - _c * stress.thirdInvariant(),
                         1.0 / 3.0)) -
          yieldStrength(intnl);
 }

◆ yieldFunctionV()

void TensorMechanicsPlasticModel::yieldFunctionV	(	const RankTwoTensor &	stress,
		Real	intnl,
		std::vector< Real > &	f
	)		const

virtualinherited

Calculates the yield functions.

Note that for single-surface plasticity you don't want to override this - override the private yieldFunction below

Parameters

	stress	the stress at which to calculate the yield function
	intnl	internal parameter
[out]	f	the yield functions

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 69 of file TensorMechanicsPlasticModel.C.

 {
   f.assign(1, yieldFunction(stress, intnl));
 }

Referenced by TensorMechanicsPlasticModel::returnMap().

◆ yieldStrength()

Real TensorMechanicsPlasticJ2::yieldStrength ( Real intnl ) const

protectedvirtualinherited

YieldStrength.

The yield function is sqrt(3*J2) - yieldStrength. In this class yieldStrength = 1, but this may be over-ridden by derived classes with nontrivial hardning

Definition at line 104 of file TensorMechanicsPlasticJ2.C.

 {
   return _strength.value(intnl);
 }

Referenced by TensorMechanicsPlasticJ2::returnMap(), TensorMechanicsPlasticOrthotropic::yieldFunction(), TensorMechanicsPlasticJ2::yieldFunction(), and yieldFunction().

Member Data Documentation

◆ _a

Real TensorMechanicsPlasticIsotropicSD::_a

protected

A constant used in the constructor that depends on _b and _c.

Definition at line 52 of file TensorMechanicsPlasticIsotropicSD.h.

Referenced by dflowPotential_dstress(), dyieldFunction_dstress(), TensorMechanicsPlasticIsotropicSD(), and yieldFunction().

◆ _associative

const bool TensorMechanicsPlasticIsotropicSD::_associative

protected

Flag for flow-rule, true if not specified.

Definition at line 46 of file TensorMechanicsPlasticIsotropicSD.h.

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), dflowPotential_dstress(), TensorMechanicsPlasticOrthotropic::flowPotential(), and flowPotential().

◆ _b

const Real TensorMechanicsPlasticIsotropicSD::_b

protected

A constant to model the influence of pressure.

Definition at line 40 of file TensorMechanicsPlasticIsotropicSD.h.

Referenced by TensorMechanicsPlasticOrthotropic::dflowPotential_dstress(), TensorMechanicsPlasticOrthotropic::dyieldFunction_dstress(), dyieldFunction_dstress(), TensorMechanicsPlasticIsotropicSD(), TensorMechanicsPlasticOrthotropic::yieldFunction(), and yieldFunction().

◆ _c

Real TensorMechanicsPlasticIsotropicSD::_c

protected

A constant to model the influence of strength differential effect.

Definition at line 43 of file TensorMechanicsPlasticIsotropicSD.h.

Referenced by dfj2_dj2(), dfj2_dj3(), dfj3_dj2(), dfj3_dj3(), dphi_dj2(), dphi_dj3(), TensorMechanicsPlasticIsotropicSD(), TensorMechanicsPlasticOrthotropic::TensorMechanicsPlasticOrthotropic(), and yieldFunction().

◆ _f_tol

const Real TensorMechanicsPlasticModel::_f_tol

inherited

Tolerance on yield function.

Definition at line 175 of file TensorMechanicsPlasticModel.h.

◆ _h

RankFourTensor TensorMechanicsPlasticIsotropicSD::_h

protected

Comes from transforming the stress tensor to the deviatoric stress tensor.

Definition at line 49 of file TensorMechanicsPlasticIsotropicSD.h.

Referenced by dflowPotential_dstress(), dyieldFunction_dstress(), and TensorMechanicsPlasticIsotropicSD().

◆ _ic_tol

const Real TensorMechanicsPlasticModel::_ic_tol

inherited

Tolerance on internal constraint.

Definition at line 178 of file TensorMechanicsPlasticModel.h.

◆ _max_iters

const unsigned TensorMechanicsPlasticJ2::_max_iters

privateinherited

max iters for custom return map loop

Definition at line 86 of file TensorMechanicsPlasticJ2.h.

Referenced by TensorMechanicsPlasticJ2::returnMap().

◆ _strength

const TensorMechanicsHardeningModel& TensorMechanicsPlasticJ2::_strength

privateinherited

yield strength, from user input

Definition at line 83 of file TensorMechanicsPlasticJ2.h.

Referenced by TensorMechanicsPlasticJ2::dyieldStrength(), and TensorMechanicsPlasticJ2::yieldStrength().

◆ _use_custom_cto

const bool TensorMechanicsPlasticJ2::_use_custom_cto

privateinherited

Whether to use the custom consistent tangent operator calculation.

Definition at line 92 of file TensorMechanicsPlasticJ2.h.

Referenced by TensorMechanicsPlasticJ2::consistentTangentOperator(), and TensorMechanicsPlasticJ2::useCustomCTO().

◆ _use_custom_returnMap

const bool TensorMechanicsPlasticJ2::_use_custom_returnMap

privateinherited

Whether to use the custom return-map algorithm.

Definition at line 89 of file TensorMechanicsPlasticJ2.h.

Referenced by TensorMechanicsPlasticJ2::returnMap(), and TensorMechanicsPlasticJ2::useCustomReturnMap().

The documentation for this class was generated from the following files:

tensor_mechanics/include/userobjects/TensorMechanicsPlasticIsotropicSD.h
tensor_mechanics/src/userobjects/TensorMechanicsPlasticIsotropicSD.C

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ TensorMechanicsPlasticIsotropicSD()

Member Function Documentation

◆ activeConstraints()

◆ consistentTangentOperator()

◆ dfj2_dj2()

◆ dfj2_dj3()

◆ dfj3_dj2()

◆ dfj3_dj3()

◆ dflowPotential_dintnl()

◆ dflowPotential_dintnlV()

◆ dflowPotential_dstress()

◆ dflowPotential_dstressV()

◆ dhardPotential_dintnl()

◆ dhardPotential_dintnlV()

◆ dhardPotential_dstress()

◆ dhardPotential_dstressV()

◆ dI_sigma()

◆ dj2_dSkl()

◆ dphi_dj2()

◆ dphi_dj3()

◆ dyieldFunction_dintnl()

◆ dyieldFunction_dintnlV()

◆ dyieldFunction_dstress()

◆ dyieldFunction_dstressV()

◆ dyieldStrength()

◆ execute()

◆ finalize()

◆ flowPotential()

◆ flowPotentialV()

◆ hardPotential()

◆ hardPotentialV()

◆ initialize()

◆ KuhnTuckerSingleSurface()

◆ modelName()

◆ numberSurfaces()

◆ returnMap()

◆ useCustomCTO()

◆ useCustomReturnMap()

◆ validParams()

◆ yieldFunction()

◆ yieldFunctionV()

◆ yieldStrength()

Member Data Documentation

◆ _a

◆ _associative

◆ _b

◆ _c

◆ _f_tol

◆ _h

◆ _ic_tol

◆ _max_iters

◆ _strength

◆ _use_custom_cto

◆ _use_custom_returnMap