FiniteStrainTensile implements rate-independent associative tensile failure with hardening/softening in the finite-strain framework. More...

#include <TensorMechanicsPlasticTensile.h>

Inheritance diagram for TensorMechanicsPlasticTensile:

[legend]

Public Member Functions
	TensorMechanicsPlasticTensile (const InputParameters &parameters)

virtual std::string	modelName () const override

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...

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

virtual bool	useCustomCTO () const
	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
	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
	Calculates a custom consistent tangent operator. 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	yieldFunction (const RankTwoTensor &stress, Real intnl) const override
	The following functions are what you should override when building single-plasticity models. More...

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

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

RankTwoTensor	flowPotential (const RankTwoTensor &stress, Real intnl) const override
	The flow potential. More...

RankFourTensor	dflowPotential_dstress (const RankTwoTensor &stress, Real intnl) const override
	The derivative of the flow potential with respect to stress. 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	smooth (const RankTwoTensor &stress) const
	returns the 'a' parameter - see doco for _tip_scheme More...

virtual Real	dsmooth (const RankTwoTensor &stress) const
	returns the da/dstress_mean - see doco for _tip_scheme More...

virtual Real	d2smooth (const RankTwoTensor &stress) const
	returns the d^2a/dstress_mean^2 - see doco for _tip_scheme More...

virtual Real	tensile_strength (const Real internal_param) const
	tensile strength as a function of residual value, rate, and internal_param More...

virtual Real	dtensile_strength (const Real internal_param) const
	d(tensile strength)/d(internal_param) as a function of residual value, rate, and internal_param 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 TensorMechanicsHardeningModel &	_strength

MooseEnum	_tip_scheme
	The yield function is modified to f = s_m + sqrt(a + s_bar^2 K^2) - tensile_strength where "a" depends on the tip_scheme. More...

Real	_small_smoother2
	Square of tip smoothing parameter to smooth the cone at mean_stress = T. More...

Real	_cap_start
	smoothing parameter dictating when the 'cap' will start - see doco for _tip_scheme More...

Real	_cap_rate
	dictates how quickly the 'cap' degenerates to a hemisphere - see doco for _tip_scheme More...

Real	_tt
	edge smoothing parameter, in radians More...

Real	_sin3tt
	sin(3*_tt) - useful for making comparisons with Lode angle More...

Real	_lode_cutoff
	if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-loss More...

Real	_ccc
	Abbo et al's C parameter. More...

Real	_bbb
	Abbo et al's B parameter. More...

Real	_aaa
	Abbo et al's A parameter. More...

Detailed Description

FiniteStrainTensile implements rate-independent associative tensile failure with hardening/softening in the finite-strain framework.

For 'hyperbolic' smoothing, the smoothing of the tip of the yield-surface cone is described in Zienkiewicz and Prande "Some useful forms of isotropic yield surfaces for soil and rock mechanics" (1977) In G Gudehus (editor) "Finite Elements in Geomechanics" Wile, Chichester, pp 179-190. For 'cap' smoothing, additional smoothing is performed. The smoothing of the edges of the cone is described in AJ Abbo, AV Lyamin, SW Sloan, JP Hambleton "A C2 continuous approximation to the Mohr-Coulomb yield surface" International Journal of Solids and Structures 48 (2011) 3001-3010

Definition at line 32 of file TensorMechanicsPlasticTensile.h.

Constructor & Destructor Documentation

◆ TensorMechanicsPlasticTensile()

TensorMechanicsPlasticTensile::TensorMechanicsPlasticTensile ( const InputParameters & parameters )

Definition at line 62 of file TensorMechanicsPlasticTensile.C.

   : TensorMechanicsPlasticModel(parameters),
     _strength(getUserObject<TensorMechanicsHardeningModel>("tensile_strength")),
     _tip_scheme(getParam<MooseEnum>("tip_scheme")),
     _small_smoother2(Utility::pow<2>(getParam<Real>("tensile_tip_smoother"))),
     _cap_start(getParam<Real>("cap_start")),
     _cap_rate(getParam<Real>("cap_rate")),
     _tt(getParam<Real>("tensile_edge_smoother") * libMesh::pi / 180.0),
     _sin3tt(std::sin(3.0 * _tt)),
     _lode_cutoff(parameters.isParamValid("tensile_lode_cutoff")
                      ? getParam<Real>("tensile_lode_cutoff")
                      : 1.0e-5 * Utility::pow<2>(_f_tol))
  
 {
   if (_lode_cutoff < 0)
     mooseError("tensile_lode_cutoff must not be negative");
   _ccc = (-std::cos(3.0 * _tt) * (std::cos(_tt) - std::sin(_tt) / std::sqrt(3.0)) -
           3.0 * _sin3tt * (std::sin(_tt) + std::cos(_tt) / std::sqrt(3.0))) /
          (18.0 * Utility::pow<3>(std::cos(3.0 * _tt)));
   _bbb = (std::sin(6.0 * _tt) * (std::cos(_tt) - std::sin(_tt) / std::sqrt(3.0)) -
           6.0 * std::cos(6.0 * _tt) * (std::sin(_tt) + std::cos(_tt) / std::sqrt(3.0))) /
          (18.0 * Utility::pow<3>(std::cos(3.0 * _tt)));
   _aaa = -std::sin(_tt) / std::sqrt(3.0) - _bbb * _sin3tt - _ccc * Utility::pow<2>(_sin3tt) +
          std::cos(_tt);
 }

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

virtualinherited

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 in TensorMechanicsPlasticTensileMulti, TensorMechanicsPlasticDruckerPragerHyperbolic, TensorMechanicsPlasticMeanCapTC, and TensorMechanicsPlasticJ2.

Definition at line 254 of file TensorMechanicsPlasticModel.C.

 {
   return E_ijkl;
 }

Referenced by TensorMechanicsPlasticJ2::consistentTangentOperator(), TensorMechanicsPlasticDruckerPragerHyperbolic::consistentTangentOperator(), TensorMechanicsPlasticMeanCapTC::consistentTangentOperator(), and TensorMechanicsPlasticTensileMulti::consistentTangentOperator().

◆ d2smooth()

Real TensorMechanicsPlasticTensile::d2smooth ( const RankTwoTensor & stress ) const

protectedvirtual

returns the d^2a/dstress_mean^2 - see doco for _tip_scheme

Definition at line 288 of file TensorMechanicsPlasticTensile.C.

 {
   Real d2smoother2 = 0;
   if (_tip_scheme == "cap")
   {
     Real x = stress.trace() / 3.0 - _cap_start;
     Real p = 0;
     Real dp_dx = 0;
     Real d2p_dx2 = 0;
     if (x > 0)
     {
       p = x * (1 - std::exp(-_cap_rate * x));
       dp_dx = (1 - std::exp(-_cap_rate * x)) + x * _cap_rate * std::exp(-_cap_rate * x);
       d2p_dx2 = 2.0 * _cap_rate * std::exp(-_cap_rate * x) -
                 x * Utility::pow<2>(_cap_rate) * std::exp(-_cap_rate * x);
     }
     d2smoother2 += 2.0 * Utility::pow<2>(dp_dx) + 2.0 * p * d2p_dx2;
   }
   return d2smoother2;
 }

Referenced by dflowPotential_dstress().

◆ dflowPotential_dintnl()

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

overrideprotectedvirtual

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 235 of file TensorMechanicsPlasticTensile.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 TensorMechanicsPlasticTensile::dflowPotential_dstress	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtual

The derivative of the flow potential with respect to stress.

Parameters

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

Returns: dr_dstress(i, j, k, l) = dr(i, j)/dstress(k, l)

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 158 of file TensorMechanicsPlasticTensile.C.

 {
   Real mean_stress = stress.trace() / 3.0;
   RankTwoTensor dmean_stress = stress.dtrace() / 3.0;
   Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
   if (sin3Lode <= _sin3tt)
   {
     // the non-edge-smoothed version
     std::vector<Real> eigvals;
     std::vector<RankTwoTensor> deigvals;
     std::vector<RankFourTensor> d2eigvals;
     stress.dsymmetricEigenvalues(eigvals, deigvals);
     stress.d2symmetricEigenvalues(d2eigvals);
  
     Real denom = std::sqrt(smooth(stress) + Utility::pow<2>(eigvals[2] - mean_stress));
     Real denom3 = Utility::pow<3>(denom);
     RankTwoTensor numer_part = deigvals[2] - dmean_stress;
     RankTwoTensor numer_full =
         0.5 * dsmooth(stress) * dmean_stress + (eigvals[2] - mean_stress) * numer_part;
     Real d2smooth_over_denom = d2smooth(stress) / denom;
  
     RankFourTensor dr_dstress = (eigvals[2] - mean_stress) * d2eigvals[2] / denom;
     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)
           {
             dr_dstress(i, j, k, l) +=
                 0.5 * d2smooth_over_denom * dmean_stress(i, j) * dmean_stress(k, l);
             dr_dstress(i, j, k, l) += numer_part(i, j) * numer_part(k, l) / denom;
             dr_dstress(i, j, k, l) -= numer_full(i, j) * numer_full(k, l) / denom3;
           }
     return dr_dstress;
   }
   else
   {
     // the edge-smoothed version
     RankTwoTensor dsin3Lode = stress.dsin3Lode(_lode_cutoff);
     Real kk = _aaa + _bbb * sin3Lode + _ccc * Utility::pow<2>(sin3Lode);
     RankTwoTensor dkk = (_bbb + 2.0 * _ccc * sin3Lode) * dsin3Lode;
     RankFourTensor d2kk = (_bbb + 2.0 * _ccc * sin3Lode) * stress.d2sin3Lode(_lode_cutoff);
     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)
             d2kk(i, j, k, l) += 2.0 * _ccc * dsin3Lode(i, j) * dsin3Lode(k, l);
  
     Real sibar2 = stress.secondInvariant();
     RankTwoTensor dsibar2 = stress.dsecondInvariant();
     RankFourTensor d2sibar2 = stress.d2secondInvariant();
  
     Real denom = std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk));
     Real denom3 = Utility::pow<3>(denom);
     Real d2smooth_over_denom = d2smooth(stress) / denom;
     RankTwoTensor numer_full =
         0.5 * dsmooth(stress) * dmean_stress + 0.5 * dsibar2 * kk * kk + sibar2 * kk * dkk;
  
     RankFourTensor dr_dstress = (0.5 * d2sibar2 * Utility::pow<2>(kk) + sibar2 * kk * d2kk) / denom;
     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)
           {
             dr_dstress(i, j, k, l) +=
                 0.5 * d2smooth_over_denom * dmean_stress(i, j) * dmean_stress(k, l);
             dr_dstress(i, j, k, l) +=
                 (dsibar2(i, j) * dkk(k, l) * kk + dkk(i, j) * dsibar2(k, l) * kk +
                  sibar2 * dkk(i, j) * dkk(k, l)) /
                 denom;
             dr_dstress(i, j, k, l) -= numer_full(i, j) * numer_full(k, l) / denom3;
           }
     return dr_dstress;
   }
 }

◆ 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));
 }

◆ dsmooth()

Real TensorMechanicsPlasticTensile::dsmooth ( const RankTwoTensor & stress ) const

protectedvirtual

returns the da/dstress_mean - see doco for _tip_scheme

Definition at line 269 of file TensorMechanicsPlasticTensile.C.

 {
   Real dsmoother2 = 0;
   if (_tip_scheme == "cap")
   {
     Real x = stress.trace() / 3.0 - _cap_start;
     Real p = 0;
     Real dp_dx = 0;
     if (x > 0)
     {
       p = x * (1 - std::exp(-_cap_rate * x));
       dp_dx = (1 - std::exp(-_cap_rate * x)) + x * _cap_rate * std::exp(-_cap_rate * x);
     }
     dsmoother2 += 2.0 * p * dp_dx;
   }
   return dsmoother2;
 }

Referenced by dflowPotential_dstress(), and dyieldFunction_dstress().

◆ dtensile_strength()

Real TensorMechanicsPlasticTensile::dtensile_strength ( const Real internal_param ) const

protectedvirtual

d(tensile strength)/d(internal_param) as a function of residual value, rate, and internal_param

Definition at line 248 of file TensorMechanicsPlasticTensile.C.

 {
   return _strength.derivative(internal_param);
 }

Referenced by dyieldFunction_dintnl().

◆ dyieldFunction_dintnl()

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

overrideprotectedvirtual

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 144 of file TensorMechanicsPlasticTensile.C.

 {
   return -dtensile_strength(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 TensorMechanicsPlasticTensile::dyieldFunction_dstress	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtual

The derivative of yield function with respect to stress.

Parameters

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

Returns: df_dstress(i, j) = dyieldFunction/dstress(i, j)

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 112 of file TensorMechanicsPlasticTensile.C.

 {
   Real mean_stress = stress.trace() / 3.0;
   RankTwoTensor dmean_stress = stress.dtrace() / 3.0;
   Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
   if (sin3Lode <= _sin3tt)
   {
     // the non-edge-smoothed version
     std::vector<Real> eigvals;
     std::vector<RankTwoTensor> deigvals;
     stress.dsymmetricEigenvalues(eigvals, deigvals);
     Real denom = std::sqrt(smooth(stress) + Utility::pow<2>(eigvals[2] - mean_stress));
     return dmean_stress + (0.5 * dsmooth(stress) * dmean_stress +
                            (eigvals[2] - mean_stress) * (deigvals[2] - dmean_stress)) /
                               denom;
   }
   else
   {
     // the edge-smoothed version
     Real kk = _aaa + _bbb * sin3Lode + _ccc * Utility::pow<2>(sin3Lode);
     RankTwoTensor dkk = (_bbb + 2.0 * _ccc * sin3Lode) * stress.dsin3Lode(_lode_cutoff);
     Real sibar2 = stress.secondInvariant();
     RankTwoTensor dsibar2 = stress.dsecondInvariant();
     Real denom = std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk));
     return dmean_stress + (0.5 * dsmooth(stress) * dmean_stress +
                            0.5 * dsibar2 * Utility::pow<2>(kk) + sibar2 * kk * dkk) /
                               denom;
   }
 }

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));
 }

◆ 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 TensorMechanicsPlasticTensile::flowPotential	(	const RankTwoTensor &	stress,
		Real	intnl
	)		const

overrideprotectedvirtual

The flow potential.

Parameters

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

Returns: the flow potential

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 151 of file TensorMechanicsPlasticTensile.C.

 {
   // This plasticity is associative so
   return 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 TensorMechanicsPlasticTensile::modelName ( ) const

overridevirtual

Implements TensorMechanicsPlasticModel.

Definition at line 310 of file TensorMechanicsPlasticTensile.C.

 {
   return "Tensile";
 }

◆ 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 TensorMechanicsPlasticModel::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

virtualinherited

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 in TensorMechanicsPlasticTensileMulti, TensorMechanicsPlasticMohrCoulombMulti, TensorMechanicsPlasticDruckerPragerHyperbolic, TensorMechanicsPlasticMeanCapTC, and TensorMechanicsPlasticJ2.

Definition at line 221 of file TensorMechanicsPlasticModel.C.

 {
   trial_stress_inadmissible = false;
   yieldFunctionV(trial_stress, intnl_old, yf);
  
   for (unsigned sf = 0; sf < numberSurfaces(); ++sf)
     if (yf[sf] > _f_tol)
       trial_stress_inadmissible = true;
  
   // example of checking Kuhn-Tucker
   std::vector<Real> dpm(numberSurfaces(), 0);
   for (unsigned sf = 0; sf < numberSurfaces(); ++sf)
     if (!KuhnTuckerSingleSurface(yf[sf], dpm[sf], 0))
       return false;
   return true;
 }

Referenced by TensorMechanicsPlasticJ2::returnMap(), TensorMechanicsPlasticDruckerPragerHyperbolic::returnMap(), TensorMechanicsPlasticMeanCapTC::returnMap(), TensorMechanicsPlasticMohrCoulombMulti::returnMap(), and TensorMechanicsPlasticTensileMulti::returnMap().

◆ smooth()

Real TensorMechanicsPlasticTensile::smooth ( const RankTwoTensor & stress ) const

protectedvirtual

returns the 'a' parameter - see doco for _tip_scheme

Definition at line 254 of file TensorMechanicsPlasticTensile.C.

 {
   Real smoother2 = _small_smoother2;
   if (_tip_scheme == "cap")
   {
     Real x = stress.trace() / 3.0 - _cap_start;
     Real p = 0;
     if (x > 0)
       p = x * (1 - std::exp(-_cap_rate * x));
     smoother2 += Utility::pow<2>(p);
   }
   return smoother2;
 }

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

◆ tensile_strength()

Real TensorMechanicsPlasticTensile::tensile_strength ( const Real internal_param ) const

protectedvirtual

tensile strength as a function of residual value, rate, and internal_param

Definition at line 242 of file TensorMechanicsPlasticTensile.C.

 {
   return _strength.value(internal_param);
 }

Referenced by yieldFunction().

◆ useCustomCTO()

bool TensorMechanicsPlasticModel::useCustomCTO ( ) const

virtualinherited

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

Reimplemented in TensorMechanicsPlasticTensileMulti, TensorMechanicsPlasticMeanCapTC, TensorMechanicsPlasticDruckerPragerHyperbolic, and TensorMechanicsPlasticJ2.

Definition at line 215 of file TensorMechanicsPlasticModel.C.

 {
   return false;
 }

◆ useCustomReturnMap()

bool TensorMechanicsPlasticModel::useCustomReturnMap ( ) const

virtualinherited

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

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, TensorMechanicsPlasticTensileMulti, TensorMechanicsPlasticMeanCapTC, TensorMechanicsPlasticDruckerPragerHyperbolic, and TensorMechanicsPlasticJ2.

Definition at line 209 of file TensorMechanicsPlasticModel.C.

 {
   return false;
 }

◆ validParams()

InputParameters TensorMechanicsPlasticTensile::validParams ( )

static

Definition at line 19 of file TensorMechanicsPlasticTensile.C.

 {
   InputParameters params = TensorMechanicsPlasticModel::validParams();
   params.addRequiredParam<UserObjectName>(
       "tensile_strength",
       "A TensorMechanicsHardening UserObject that defines hardening of the tensile strength");
   params.addRangeCheckedParam<Real>(
       "tensile_edge_smoother",
       25.0,
       "tensile_edge_smoother>=0 & tensile_edge_smoother<=30",
       "Smoothing parameter: the edges of the cone are smoothed by the given amount.");
   MooseEnum tip_scheme("hyperbolic cap", "hyperbolic");
   params.addParam<MooseEnum>(
       "tip_scheme", tip_scheme, "Scheme by which the pyramid's tip will be smoothed.");
   params.addRequiredRangeCheckedParam<Real>("tensile_tip_smoother",
                                             "tensile_tip_smoother>=0",
                                             "For the 'hyperbolic' tip_scheme, the pyramid vertex "
                                             "will be smoothed by the given amount.  For the 'cap' "
                                             "tip_scheme, additional smoothing will occur.  Typical "
                                             "value is 0.1*tensile_strength");
   params.addParam<Real>(
       "cap_start",
       0.0,
       "For the 'cap' tip_scheme, smoothing is performed in the stress_mean > cap_start region");
   params.addRangeCheckedParam<Real>("cap_rate",
                                     0.0,
                                     "cap_rate>=0",
                                     "For the 'cap' tip_scheme, this controls how quickly the cap "
                                     "degenerates to a hemisphere: small values mean a slow "
                                     "degeneration to a hemisphere (and zero means the 'cap' will "
                                     "be totally inactive).  Typical value is 1/tensile_strength");
   params.addParam<Real>("tensile_lode_cutoff",
                         "If the second invariant of stress is less than "
                         "this amount, the Lode angle is assumed to be zero. "
                         "This is to guard against precision-loss problems, "
                         "and this parameter should be set small.  Default = "
                         "0.00001*((yield_Function_tolerance)^2)");
   params.addClassDescription(
       "Associative tensile plasticity with hardening/softening, and tensile_strength = 1");
  
   return params;
 }

◆ yieldFunction()

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

overrideprotectedvirtual

The following functions are what you should override when building single-plasticity models.

The yield function

Parameters

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

Returns: the yield function

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 89 of file TensorMechanicsPlasticTensile.C.

 {
   Real mean_stress = stress.trace() / 3.0;
   Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
   if (sin3Lode <= _sin3tt)
   {
     // the non-edge-smoothed version
     std::vector<Real> eigvals;
     stress.symmetricEigenvalues(eigvals);
     return mean_stress + std::sqrt(smooth(stress) + Utility::pow<2>(eigvals[2] - mean_stress)) -
            tensile_strength(intnl);
   }
   else
   {
     // the edge-smoothed version
     Real kk = _aaa + _bbb * sin3Lode + _ccc * Utility::pow<2>(sin3Lode);
     Real sibar2 = stress.secondInvariant();
     return mean_stress + std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk)) -
            tensile_strength(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().

Member Data Documentation

◆ _aaa

Real TensorMechanicsPlasticTensile::_aaa

protected

Abbo et al's A parameter.

Definition at line 91 of file TensorMechanicsPlasticTensile.h.

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

◆ _bbb

Real TensorMechanicsPlasticTensile::_bbb

protected

Abbo et al's B parameter.

Definition at line 88 of file TensorMechanicsPlasticTensile.h.

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

◆ _cap_rate

Real TensorMechanicsPlasticTensile::_cap_rate

protected

dictates how quickly the 'cap' degenerates to a hemisphere - see doco for _tip_scheme

Definition at line 73 of file TensorMechanicsPlasticTensile.h.

Referenced by d2smooth(), dsmooth(), and smooth().

◆ _cap_start

Real TensorMechanicsPlasticTensile::_cap_start

protected

smoothing parameter dictating when the 'cap' will start - see doco for _tip_scheme

Definition at line 70 of file TensorMechanicsPlasticTensile.h.

Referenced by d2smooth(), dsmooth(), and smooth().

◆ _ccc

Real TensorMechanicsPlasticTensile::_ccc

protected

Abbo et al's C parameter.

Definition at line 85 of file TensorMechanicsPlasticTensile.h.

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

◆ _f_tol

const Real TensorMechanicsPlasticModel::_f_tol

inherited

Tolerance on yield function.

Definition at line 175 of file TensorMechanicsPlasticModel.h.

◆ _ic_tol

const Real TensorMechanicsPlasticModel::_ic_tol

inherited

Tolerance on internal constraint.

Definition at line 178 of file TensorMechanicsPlasticModel.h.

◆ _lode_cutoff

Real TensorMechanicsPlasticTensile::_lode_cutoff

protected

if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-loss

Definition at line 82 of file TensorMechanicsPlasticTensile.h.

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

◆ _sin3tt

Real TensorMechanicsPlasticTensile::_sin3tt

protected

sin(3*_tt) - useful for making comparisons with Lode angle

Definition at line 79 of file TensorMechanicsPlasticTensile.h.

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

◆ _small_smoother2

Real TensorMechanicsPlasticTensile::_small_smoother2

protected

Square of tip smoothing parameter to smooth the cone at mean_stress = T.

Definition at line 67 of file TensorMechanicsPlasticTensile.h.

Referenced by smooth().

◆ _strength

const TensorMechanicsHardeningModel& TensorMechanicsPlasticTensile::_strength

protected

Definition at line 54 of file TensorMechanicsPlasticTensile.h.

Referenced by dtensile_strength(), and tensile_strength().

◆ _tip_scheme

MooseEnum TensorMechanicsPlasticTensile::_tip_scheme

protected

The yield function is modified to f = s_m + sqrt(a + s_bar^2 K^2) - tensile_strength where "a" depends on the tip_scheme.

Currently _tip_scheme is 'hyperbolic', where a = _small_smoother2 'cap' where a = _small_smoother2 + (p(stress_mean - _cap_start))^2 with the function p(x)=x(1-exp(-_cap_rate*x)) for x>0, and p=0 otherwise

Definition at line 64 of file TensorMechanicsPlasticTensile.h.

Referenced by d2smooth(), dsmooth(), and smooth().

◆ _tt

Real TensorMechanicsPlasticTensile::_tt

protected

edge smoothing parameter, in radians

Definition at line 76 of file TensorMechanicsPlasticTensile.h.

Referenced by TensorMechanicsPlasticTensile().

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

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

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ TensorMechanicsPlasticTensile()

Member Function Documentation

◆ activeConstraints()

◆ consistentTangentOperator()

◆ d2smooth()

◆ dflowPotential_dintnl()

◆ dflowPotential_dintnlV()

◆ dflowPotential_dstress()

◆ dflowPotential_dstressV()

◆ dhardPotential_dintnl()

◆ dhardPotential_dintnlV()

◆ dhardPotential_dstress()

◆ dhardPotential_dstressV()

◆ dsmooth()

◆ dtensile_strength()

◆ dyieldFunction_dintnl()

◆ dyieldFunction_dintnlV()

◆ dyieldFunction_dstress()

◆ dyieldFunction_dstressV()

◆ execute()

◆ finalize()

◆ flowPotential()

◆ flowPotentialV()

◆ hardPotential()

◆ hardPotentialV()

◆ initialize()

◆ KuhnTuckerSingleSurface()

◆ modelName()

◆ numberSurfaces()

◆ returnMap()

◆ smooth()

◆ tensile_strength()

◆ useCustomCTO()

◆ useCustomReturnMap()

◆ validParams()

◆ yieldFunction()

◆ yieldFunctionV()

Member Data Documentation

◆ _aaa

◆ _bbb

◆ _cap_rate

◆ _cap_start

◆ _ccc

◆ _f_tol

◆ _ic_tol

◆ _lode_cutoff

◆ _sin3tt

◆ _small_smoother2

◆ _strength

◆ _tip_scheme

◆ _tt