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TensorMechanicsPlasticTensile Class Reference

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

#include <TensorMechanicsPlasticTensile.h>

Inheritance diagram for TensorMechanicsPlasticTensile:
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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...
 

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 30 of file TensorMechanicsPlasticTensile.h.

Constructor & Destructor Documentation

TensorMechanicsPlasticTensile::TensorMechanicsPlasticTensile ( const InputParameters &  parameters)

Definition at line 55 of file TensorMechanicsPlasticTensile.C.

56  : TensorMechanicsPlasticModel(parameters),
57  _strength(getUserObject<TensorMechanicsHardeningModel>("tensile_strength")),
58  _tip_scheme(getParam<MooseEnum>("tip_scheme")),
59  _small_smoother2(Utility::pow<2>(getParam<Real>("tensile_tip_smoother"))),
60  _cap_start(getParam<Real>("cap_start")),
61  _cap_rate(getParam<Real>("cap_rate")),
62  _tt(getParam<Real>("tensile_edge_smoother") * libMesh::pi / 180.0),
63  _sin3tt(std::sin(3.0 * _tt)),
64  _lode_cutoff(parameters.isParamValid("tensile_lode_cutoff")
65  ? getParam<Real>("tensile_lode_cutoff")
66  : 1.0e-5 * Utility::pow<2>(_f_tol))
67 
68 {
69  if (_lode_cutoff < 0)
70  mooseError("tensile_lode_cutoff must not be negative");
71  _ccc = (-std::cos(3.0 * _tt) * (std::cos(_tt) - std::sin(_tt) / std::sqrt(3.0)) -
72  3.0 * _sin3tt * (std::sin(_tt) + std::cos(_tt) / std::sqrt(3.0))) /
73  (18.0 * Utility::pow<3>(std::cos(3.0 * _tt)));
74  _bbb = (std::sin(6.0 * _tt) * (std::cos(_tt) - std::sin(_tt) / std::sqrt(3.0)) -
75  6.0 * std::cos(6.0 * _tt) * (std::sin(_tt) + std::cos(_tt) / std::sqrt(3.0))) /
76  (18.0 * Utility::pow<3>(std::cos(3.0 * _tt)));
77  _aaa = -std::sin(_tt) / std::sqrt(3.0) - _bbb * _sin3tt - _ccc * Utility::pow<2>(_sin3tt) +
78  std::cos(_tt);
79 }
Real _bbb
Abbo et al&#39;s B parameter.
TensorMechanicsPlasticModel(const InputParameters &parameters)
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
Real _ccc
Abbo et al&#39;s C parameter.
Real _tt
edge smoothing parameter, in radians
Real _small_smoother2
Square of tip smoothing parameter to smooth the cone at mean_stress = T.
Real _cap_start
smoothing parameter dictating when the &#39;cap&#39; will start - see doco for _tip_scheme ...
const Real _f_tol
Tolerance on yield function.
Real _aaa
Abbo et al&#39;s A parameter.
Real _cap_rate
dictates how quickly the &#39;cap&#39; degenerates to a hemisphere - see doco for _tip_scheme ...
MooseEnum _tip_scheme
The yield function is modified to f = s_m + sqrt(a + s_bar^2 K^2) - tensile_strength where "a" depend...
const TensorMechanicsHardeningModel & _strength
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...

Member Function Documentation

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
fvalues of the yield functions
stressstress tensor
intnlinternal parameter
Eijklelasticity tensor (stress = Eijkl*strain)
[out]actact[i] = true if the i_th yield function is active
[out]returned_stressApproximate value of the returned stress

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

Definition at line 183 of file TensorMechanicsPlasticModel.C.

189 {
190  mooseAssert(f.size() == numberSurfaces(),
191  "f incorrectly sized at " << f.size() << " in activeConstraints");
192  act.resize(numberSurfaces());
193  for (unsigned surface = 0; surface < numberSurfaces(); ++surface)
194  act[surface] = (f[surface] > _f_tol);
195 }
virtual unsigned int numberSurfaces() const
The number of yield surfaces for this plasticity model.
const Real _f_tol
Tolerance on yield function.
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_oldtrial stress before returning
intnl_oldinternal parameter before returning
stresscurrent returned stress state
intnlinternal parameter
E_ijklelasticity tensor
cumulative_pmthe cumulative plastic multipliers
Returns
the consistent tangent operator: E_ijkl if not over-ridden

Reimplemented in TensorMechanicsPlasticTensileMulti, TensorMechanicsPlasticDruckerPragerHyperbolic, TensorMechanicsPlasticMeanCapTC, and TensorMechanicsPlasticJ2.

Definition at line 249 of file TensorMechanicsPlasticModel.C.

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

256 {
257  return E_ijkl;
258 }
Real TensorMechanicsPlasticTensile::d2smooth ( const RankTwoTensor &  stress) const
protectedvirtual

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

Definition at line 283 of file TensorMechanicsPlasticTensile.C.

Referenced by dflowPotential_dstress().

284 {
285  Real d2smoother2 = 0;
286  if (_tip_scheme == "cap")
287  {
288  Real x = stress.trace() / 3.0 - _cap_start;
289  Real p = 0;
290  Real dp_dx = 0;
291  Real d2p_dx2 = 0;
292  if (x > 0)
293  {
294  p = x * (1 - std::exp(-_cap_rate * x));
295  dp_dx = (1 - std::exp(-_cap_rate * x)) + x * _cap_rate * std::exp(-_cap_rate * x);
296  d2p_dx2 = 2.0 * _cap_rate * std::exp(-_cap_rate * x) -
297  x * Utility::pow<2>(_cap_rate) * std::exp(-_cap_rate * x);
298  }
299  d2smoother2 += 2.0 * Utility::pow<2>(dp_dx) + 2.0 * p * d2p_dx2;
300  }
301  return d2smoother2;
302 }
Real _cap_start
smoothing parameter dictating when the &#39;cap&#39; will start - see doco for _tip_scheme ...
Real _cap_rate
dictates how quickly the &#39;cap&#39; degenerates to a hemisphere - see doco for _tip_scheme ...
MooseEnum _tip_scheme
The yield function is modified to f = s_m + sqrt(a + s_bar^2 K^2) - tensile_strength where "a" depend...
RankTwoTensor TensorMechanicsPlasticTensile::dflowPotential_dintnl ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

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

Parameters
stressthe stress at which to calculate the flow potential
intnlinternal parameter
Returns
dr_dintnl(i, j) = dr(i, j)/dintnl

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 230 of file TensorMechanicsPlasticTensile.C.

232 {
233  return RankTwoTensor();
234 }
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
stressthe stress at which to calculate the flow potential
intnlinternal parameter
[out]dr_dintnldr_dintnl[alpha](i, j) = dr[alpha](i, j)/dintnl

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 134 of file TensorMechanicsPlasticModel.C.

137 {
138  return dr_dintnl.assign(1, dflowPotential_dintnl(stress, intnl));
139 }
virtual RankTwoTensor dflowPotential_dintnl(const RankTwoTensor &stress, Real intnl) const
The derivative of the flow potential with respect to the internal parameter.
RankFourTensor TensorMechanicsPlasticTensile::dflowPotential_dstress ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

The derivative of the flow potential with respect to stress.

Parameters
stressthe stress at which to calculate the flow potential
intnlinternal parameter
Returns
dr_dstress(i, j, k, l) = dr(i, j)/dstress(k, l)

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 153 of file TensorMechanicsPlasticTensile.C.

155 {
156  Real mean_stress = stress.trace() / 3.0;
157  RankTwoTensor dmean_stress = stress.dtrace() / 3.0;
158  Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
159  if (sin3Lode <= _sin3tt)
160  {
161  // the non-edge-smoothed version
162  std::vector<Real> eigvals;
163  std::vector<RankTwoTensor> deigvals;
164  std::vector<RankFourTensor> d2eigvals;
165  stress.dsymmetricEigenvalues(eigvals, deigvals);
166  stress.d2symmetricEigenvalues(d2eigvals);
167 
168  Real denom = std::sqrt(smooth(stress) + Utility::pow<2>(eigvals[2] - mean_stress));
169  Real denom3 = Utility::pow<3>(denom);
170  RankTwoTensor numer_part = deigvals[2] - dmean_stress;
171  RankTwoTensor numer_full =
172  0.5 * dsmooth(stress) * dmean_stress + (eigvals[2] - mean_stress) * numer_part;
173  Real d2smooth_over_denom = d2smooth(stress) / denom;
174 
175  RankFourTensor dr_dstress = (eigvals[2] - mean_stress) * d2eigvals[2] / denom;
176  for (unsigned i = 0; i < 3; ++i)
177  for (unsigned j = 0; j < 3; ++j)
178  for (unsigned k = 0; k < 3; ++k)
179  for (unsigned l = 0; l < 3; ++l)
180  {
181  dr_dstress(i, j, k, l) +=
182  0.5 * d2smooth_over_denom * dmean_stress(i, j) * dmean_stress(k, l);
183  dr_dstress(i, j, k, l) += numer_part(i, j) * numer_part(k, l) / denom;
184  dr_dstress(i, j, k, l) -= numer_full(i, j) * numer_full(k, l) / denom3;
185  }
186  return dr_dstress;
187  }
188  else
189  {
190  // the edge-smoothed version
191  RankTwoTensor dsin3Lode = stress.dsin3Lode(_lode_cutoff);
192  Real kk = _aaa + _bbb * sin3Lode + _ccc * Utility::pow<2>(sin3Lode);
193  RankTwoTensor dkk = (_bbb + 2.0 * _ccc * sin3Lode) * dsin3Lode;
194  RankFourTensor d2kk = (_bbb + 2.0 * _ccc * sin3Lode) * stress.d2sin3Lode(_lode_cutoff);
195  for (unsigned i = 0; i < 3; ++i)
196  for (unsigned j = 0; j < 3; ++j)
197  for (unsigned k = 0; k < 3; ++k)
198  for (unsigned l = 0; l < 3; ++l)
199  d2kk(i, j, k, l) += 2.0 * _ccc * dsin3Lode(i, j) * dsin3Lode(k, l);
200 
201  Real sibar2 = stress.secondInvariant();
202  RankTwoTensor dsibar2 = stress.dsecondInvariant();
203  RankFourTensor d2sibar2 = stress.d2secondInvariant();
204 
205  Real denom = std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk));
206  Real denom3 = Utility::pow<3>(denom);
207  Real d2smooth_over_denom = d2smooth(stress) / denom;
208  RankTwoTensor numer_full =
209  0.5 * dsmooth(stress) * dmean_stress + 0.5 * dsibar2 * kk * kk + sibar2 * kk * dkk;
210 
211  RankFourTensor dr_dstress = (0.5 * d2sibar2 * Utility::pow<2>(kk) + sibar2 * kk * d2kk) / denom;
212  for (unsigned i = 0; i < 3; ++i)
213  for (unsigned j = 0; j < 3; ++j)
214  for (unsigned k = 0; k < 3; ++k)
215  for (unsigned l = 0; l < 3; ++l)
216  {
217  dr_dstress(i, j, k, l) +=
218  0.5 * d2smooth_over_denom * dmean_stress(i, j) * dmean_stress(k, l);
219  dr_dstress(i, j, k, l) +=
220  (dsibar2(i, j) * dkk(k, l) * kk + dkk(i, j) * dsibar2(k, l) * kk +
221  sibar2 * dkk(i, j) * dkk(k, l)) /
222  denom;
223  dr_dstress(i, j, k, l) -= numer_full(i, j) * numer_full(k, l) / denom3;
224  }
225  return dr_dstress;
226  }
227 }
virtual Real d2smooth(const RankTwoTensor &stress) const
returns the d^2a/dstress_mean^2 - see doco for _tip_scheme
Real _bbb
Abbo et al&#39;s B parameter.
virtual Real dsmooth(const RankTwoTensor &stress) const
returns the da/dstress_mean - see doco for _tip_scheme
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
Real _ccc
Abbo et al&#39;s C parameter.
Real _aaa
Abbo et al&#39;s A parameter.
virtual Real smooth(const RankTwoTensor &stress) const
returns the &#39;a&#39; parameter - see doco for _tip_scheme
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
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
stressthe stress at which to calculate the flow potential
intnlinternal parameter
[out]dr_dstressdr_dstress[alpha](i, j, k, l) = dr[alpha](i, j)/dstress(k, l)

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 120 of file TensorMechanicsPlasticModel.C.

123 {
124  return dr_dstress.assign(1, dflowPotential_dstress(stress, intnl));
125 }
virtual RankFourTensor dflowPotential_dstress(const RankTwoTensor &stress, Real intnl) const
The derivative of the flow potential with respect to stress.
Real TensorMechanicsPlasticModel::dhardPotential_dintnl ( const RankTwoTensor &  stress,
Real  intnl 
) const
protectedvirtualinherited

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

Parameters
stressthe stress at which to calculate the hardening potentials
intnlinternal parameter
Returns
the derivative

Reimplemented in TensorMechanicsPlasticMeanCapTC.

Definition at line 169 of file TensorMechanicsPlasticModel.C.

Referenced by TensorMechanicsPlasticModel::dhardPotential_dintnlV().

171 {
172  return 0.0;
173 }
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
stressthe stress at which to calculate the hardening potentials
intnlinternal parameter
[out]dh_dintnldh_dintnl[alpha] = dh[alpha]/dintnl

Definition at line 175 of file TensorMechanicsPlasticModel.C.

178 {
179  dh_dintnl.resize(numberSurfaces(), dhardPotential_dintnl(stress, intnl));
180 }
virtual unsigned int numberSurfaces() const
The number of yield surfaces for this plasticity model.
virtual Real dhardPotential_dintnl(const RankTwoTensor &stress, Real intnl) const
The derivative of the hardening potential with respect to the internal parameter. ...
RankTwoTensor TensorMechanicsPlasticModel::dhardPotential_dstress ( const RankTwoTensor &  stress,
Real  intnl 
) const
protectedvirtualinherited

The derivative of the hardening potential with respect to stress.

Parameters
stressthe stress at which to calculate the hardening potentials
intnlinternal parameter
Returns
dh_dstress(i, j) = dh/dstress(i, j)

Reimplemented in TensorMechanicsPlasticMeanCapTC.

Definition at line 155 of file TensorMechanicsPlasticModel.C.

Referenced by TensorMechanicsPlasticModel::dhardPotential_dstressV().

157 {
158  return RankTwoTensor();
159 }
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
stressthe stress at which to calculate the hardening potentials
intnlinternal parameter
[out]dh_dstressdh_dstress[alpha](i, j) = dh[alpha]/dstress(i, j)

Definition at line 161 of file TensorMechanicsPlasticModel.C.

164 {
165  dh_dstress.assign(numberSurfaces(), dhardPotential_dstress(stress, intnl));
166 }
virtual unsigned int numberSurfaces() const
The number of yield surfaces for this plasticity model.
virtual RankTwoTensor dhardPotential_dstress(const RankTwoTensor &stress, Real intnl) const
The derivative of the hardening potential with respect to stress.
Real TensorMechanicsPlasticTensile::dsmooth ( const RankTwoTensor &  stress) const
protectedvirtual

returns the da/dstress_mean - see doco for _tip_scheme

Definition at line 264 of file TensorMechanicsPlasticTensile.C.

Referenced by dflowPotential_dstress(), and dyieldFunction_dstress().

265 {
266  Real dsmoother2 = 0;
267  if (_tip_scheme == "cap")
268  {
269  Real x = stress.trace() / 3.0 - _cap_start;
270  Real p = 0;
271  Real dp_dx = 0;
272  if (x > 0)
273  {
274  p = x * (1 - std::exp(-_cap_rate * x));
275  dp_dx = (1 - std::exp(-_cap_rate * x)) + x * _cap_rate * std::exp(-_cap_rate * x);
276  }
277  dsmoother2 += 2.0 * p * dp_dx;
278  }
279  return dsmoother2;
280 }
Real _cap_start
smoothing parameter dictating when the &#39;cap&#39; will start - see doco for _tip_scheme ...
Real _cap_rate
dictates how quickly the &#39;cap&#39; degenerates to a hemisphere - see doco for _tip_scheme ...
MooseEnum _tip_scheme
The yield function is modified to f = s_m + sqrt(a + s_bar^2 K^2) - tensile_strength where "a" depend...
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 243 of file TensorMechanicsPlasticTensile.C.

Referenced by dyieldFunction_dintnl().

244 {
245  return _strength.derivative(internal_param);
246 }
virtual Real derivative(Real intnl) const
const TensorMechanicsHardeningModel & _strength
Real TensorMechanicsPlasticTensile::dyieldFunction_dintnl ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

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

Parameters
stressthe stress at which to calculate the yield function
intnlinternal parameter
Returns
the derivative

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 139 of file TensorMechanicsPlasticTensile.C.

141 {
142  return -dtensile_strength(intnl);
143 }
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 ...
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
stressthe stress at which to calculate the yield function
intnlinternal parameter
[out]df_dintnldf_dintnl[alpha] = df[alpha]/dintnl

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 93 of file TensorMechanicsPlasticModel.C.

96 {
97  return df_dintnl.assign(1, dyieldFunction_dintnl(stress, intnl));
98 }
virtual Real dyieldFunction_dintnl(const RankTwoTensor &stress, Real intnl) const
The derivative of yield function with respect to the internal parameter.
RankTwoTensor TensorMechanicsPlasticTensile::dyieldFunction_dstress ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

The derivative of yield function with respect to stress.

Parameters
stressthe stress at which to calculate the yield function
intnlinternal parameter
Returns
df_dstress(i, j) = dyieldFunction/dstress(i, j)

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 105 of file TensorMechanicsPlasticTensile.C.

Referenced by flowPotential().

107 {
108  Real mean_stress = stress.trace() / 3.0;
109  RankTwoTensor dmean_stress = stress.dtrace() / 3.0;
110  Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
111  if (sin3Lode <= _sin3tt)
112  {
113  // the non-edge-smoothed version
114  std::vector<Real> eigvals;
115  std::vector<RankTwoTensor> deigvals;
116  stress.dsymmetricEigenvalues(eigvals, deigvals);
117  Real denom = std::sqrt(smooth(stress) + Utility::pow<2>(eigvals[2] - mean_stress));
118  return dmean_stress +
119  (0.5 * dsmooth(stress) * dmean_stress +
120  (eigvals[2] - mean_stress) * (deigvals[2] - dmean_stress)) /
121  denom;
122  }
123  else
124  {
125  // the edge-smoothed version
126  Real kk = _aaa + _bbb * sin3Lode + _ccc * Utility::pow<2>(sin3Lode);
127  RankTwoTensor dkk = (_bbb + 2.0 * _ccc * sin3Lode) * stress.dsin3Lode(_lode_cutoff);
128  Real sibar2 = stress.secondInvariant();
129  RankTwoTensor dsibar2 = stress.dsecondInvariant();
130  Real denom = std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk));
131  return dmean_stress +
132  (0.5 * dsmooth(stress) * dmean_stress + 0.5 * dsibar2 * Utility::pow<2>(kk) +
133  sibar2 * kk * dkk) /
134  denom;
135  }
136 }
Real _bbb
Abbo et al&#39;s B parameter.
virtual Real dsmooth(const RankTwoTensor &stress) const
returns the da/dstress_mean - see doco for _tip_scheme
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
Real _ccc
Abbo et al&#39;s C parameter.
Real _aaa
Abbo et al&#39;s A parameter.
virtual Real smooth(const RankTwoTensor &stress) const
returns the &#39;a&#39; parameter - see doco for _tip_scheme
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
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
stressthe stress at which to calculate the yield function
intnlinternal parameter
[out]df_dstressdf_dstress[alpha](i, j) = dyieldFunction[alpha]/dstress(i, j)

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 79 of file TensorMechanicsPlasticModel.C.

82 {
83  df_dstress.assign(1, dyieldFunction_dstress(stress, intnl));
84 }
virtual RankTwoTensor dyieldFunction_dstress(const RankTwoTensor &stress, Real intnl) const
The derivative of yield function with respect to stress.
void TensorMechanicsPlasticModel::execute ( )
inherited

Definition at line 42 of file TensorMechanicsPlasticModel.C.

43 {
44 }
void TensorMechanicsPlasticModel::finalize ( )
inherited

Definition at line 47 of file TensorMechanicsPlasticModel.C.

48 {
49 }
RankTwoTensor TensorMechanicsPlasticTensile::flowPotential ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

The flow potential.

Parameters
stressthe stress at which to calculate the flow potential
intnlinternal parameter
Returns
the flow potential

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 146 of file TensorMechanicsPlasticTensile.C.

147 {
148  // This plasticity is associative so
149  return dyieldFunction_dstress(stress, intnl);
150 }
RankTwoTensor dyieldFunction_dstress(const RankTwoTensor &stress, Real intnl) const override
The derivative of yield function with respect to stress.
void TensorMechanicsPlasticModel::flowPotentialV ( const RankTwoTensor &  stress,
Real  intnl,
std::vector< RankTwoTensor > &  r 
) const
virtualinherited

The flow potentials.

Parameters
stressthe stress at which to calculate the flow potential
intnlinternal parameter
[out]rr[alpha] is the flow potential for the "alpha" yield function

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 106 of file TensorMechanicsPlasticModel.C.

109 {
110  return r.assign(1, flowPotential(stress, intnl));
111 }
virtual RankTwoTensor flowPotential(const RankTwoTensor &stress, Real intnl) const
The flow potential.
Real TensorMechanicsPlasticModel::hardPotential ( const RankTwoTensor &  stress,
Real  intnl 
) const
protectedvirtualinherited

The hardening potential.

Parameters
stressthe stress at which to calculate the hardening potential
intnlinternal parameter
Returns
the hardening potential

Reimplemented in TensorMechanicsPlasticMeanCapTC.

Definition at line 142 of file TensorMechanicsPlasticModel.C.

Referenced by TensorMechanicsPlasticModel::hardPotentialV().

143 {
144  return -1.0;
145 }
void TensorMechanicsPlasticModel::hardPotentialV ( const RankTwoTensor &  stress,
Real  intnl,
std::vector< Real > &  h 
) const
virtualinherited

The hardening potential.

Parameters
stressthe stress at which to calculate the hardening potential
intnlinternal parameter
[out]hh[alpha] is the hardening potential for the "alpha" yield function

Definition at line 147 of file TensorMechanicsPlasticModel.C.

150 {
151  h.assign(numberSurfaces(), hardPotential(stress, intnl));
152 }
virtual Real hardPotential(const RankTwoTensor &stress, Real intnl) const
The hardening potential.
virtual unsigned int numberSurfaces() const
The number of yield surfaces for this plasticity model.
void TensorMechanicsPlasticModel::initialize ( )
inherited

Definition at line 37 of file TensorMechanicsPlasticModel.C.

38 {
39 }
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
yfYield function value
dpmplastic multiplier
dpm_toltolerance on plastic multiplier: viz dpm>-dpm_tol means "dpm is non-negative"

Definition at line 243 of file TensorMechanicsPlasticModel.C.

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

244 {
245  return (dpm == 0 && yf <= _f_tol) || (dpm > -dpm_tol && yf <= _f_tol && yf >= -_f_tol);
246 }
const Real _f_tol
Tolerance on yield function.
std::string TensorMechanicsPlasticTensile::modelName ( ) const
overridevirtual

Implements TensorMechanicsPlasticModel.

Definition at line 305 of file TensorMechanicsPlasticTensile.C.

306 {
307  return "Tensile";
308 }
unsigned TensorMechanicsPlasticModel::numberSurfaces ( ) const
virtualinherited
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_stressThe trial stress
intnl_oldValue of the internal parameter
E_ijklElasticity tensor
ep_plastic_toleranceTolerance defined by the user for the plastic strain
[out]returned_stressIn case (C): lies on the yield surface after returning and produces the correct plastic strain (normality condition). Otherwise: not defined
[out]returned_intnlIn case (C): the value of the internal parameter after returning. Otherwise: not defined
[out]dpmIn case (C): the plastic multipliers needed to bring about the return. Otherwise: not defined
[out]delta_dpIn case (C): The change in plastic strain induced by the return process. Otherwise: not defined
[out]yfIn case (C): the yield function at (returned_stress, returned_intnl). Otherwise: the yield function at (trial_stress, intnl_old)
[out]trial_stress_inadmissibleShould 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 216 of file TensorMechanicsPlasticModel.C.

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

226 {
227  trial_stress_inadmissible = false;
228  yieldFunctionV(trial_stress, intnl_old, yf);
229 
230  for (unsigned sf = 0; sf < numberSurfaces(); ++sf)
231  if (yf[sf] > _f_tol)
232  trial_stress_inadmissible = true;
233 
234  // example of checking Kuhn-Tucker
235  std::vector<Real> dpm(numberSurfaces(), 0);
236  for (unsigned sf = 0; sf < numberSurfaces(); ++sf)
237  if (!KuhnTuckerSingleSurface(yf[sf], dpm[sf], 0))
238  return false;
239  return true;
240 }
virtual unsigned int numberSurfaces() const
The number of yield surfaces for this plasticity model.
bool KuhnTuckerSingleSurface(Real yf, Real dpm, Real dpm_tol) const
Returns true if the Kuhn-Tucker conditions for the single surface are satisfied.
const Real _f_tol
Tolerance on yield function.
virtual void yieldFunctionV(const RankTwoTensor &stress, Real intnl, std::vector< Real > &f) const
Calculates the yield functions.
Real TensorMechanicsPlasticTensile::smooth ( const RankTwoTensor &  stress) const
protectedvirtual

returns the 'a' parameter - see doco for _tip_scheme

Definition at line 249 of file TensorMechanicsPlasticTensile.C.

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

250 {
251  Real smoother2 = _small_smoother2;
252  if (_tip_scheme == "cap")
253  {
254  Real x = stress.trace() / 3.0 - _cap_start;
255  Real p = 0;
256  if (x > 0)
257  p = x * (1 - std::exp(-_cap_rate * x));
258  smoother2 += Utility::pow<2>(p);
259  }
260  return smoother2;
261 }
Real _small_smoother2
Square of tip smoothing parameter to smooth the cone at mean_stress = T.
Real _cap_start
smoothing parameter dictating when the &#39;cap&#39; will start - see doco for _tip_scheme ...
Real _cap_rate
dictates how quickly the &#39;cap&#39; degenerates to a hemisphere - see doco for _tip_scheme ...
MooseEnum _tip_scheme
The yield function is modified to f = s_m + sqrt(a + s_bar^2 K^2) - tensile_strength where "a" depend...
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 237 of file TensorMechanicsPlasticTensile.C.

Referenced by yieldFunction().

238 {
239  return _strength.value(internal_param);
240 }
virtual Real value(Real intnl) const
const TensorMechanicsHardeningModel & _strength
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 210 of file TensorMechanicsPlasticModel.C.

211 {
212  return false;
213 }
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 204 of file TensorMechanicsPlasticModel.C.

205 {
206  return false;
207 }
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
stressthe stress at which to calculate the yield function
intnlinternal parameter
Returns
the yield function

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 82 of file TensorMechanicsPlasticTensile.C.

83 {
84  Real mean_stress = stress.trace() / 3.0;
85  Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
86  if (sin3Lode <= _sin3tt)
87  {
88  // the non-edge-smoothed version
89  std::vector<Real> eigvals;
90  stress.symmetricEigenvalues(eigvals);
91  return mean_stress + std::sqrt(smooth(stress) + Utility::pow<2>(eigvals[2] - mean_stress)) -
92  tensile_strength(intnl);
93  }
94  else
95  {
96  // the edge-smoothed version
97  Real kk = _aaa + _bbb * sin3Lode + _ccc * Utility::pow<2>(sin3Lode);
98  Real sibar2 = stress.secondInvariant();
99  return mean_stress + std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk)) -
100  tensile_strength(intnl);
101  }
102 }
Real _bbb
Abbo et al&#39;s B parameter.
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
Real _ccc
Abbo et al&#39;s C parameter.
virtual Real tensile_strength(const Real internal_param) const
tensile strength as a function of residual value, rate, and internal_param
Real _aaa
Abbo et al&#39;s A parameter.
virtual Real smooth(const RankTwoTensor &stress) const
returns the &#39;a&#39; parameter - see doco for _tip_scheme
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
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
stressthe stress at which to calculate the yield function
intnlinternal parameter
[out]fthe yield functions

Reimplemented in TensorMechanicsPlasticMohrCoulombMulti, and TensorMechanicsPlasticTensileMulti.

Definition at line 64 of file TensorMechanicsPlasticModel.C.

Referenced by TensorMechanicsPlasticModel::returnMap().

67 {
68  f.assign(1, yieldFunction(stress, intnl));
69 }
virtual Real yieldFunction(const RankTwoTensor &stress, Real intnl) const
The following functions are what you should override when building single-plasticity models...

Member Data Documentation

Real TensorMechanicsPlasticTensile::_aaa
protected
Real TensorMechanicsPlasticTensile::_bbb
protected
Real TensorMechanicsPlasticTensile::_cap_rate
protected

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

Definition at line 69 of file TensorMechanicsPlasticTensile.h.

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

Real TensorMechanicsPlasticTensile::_cap_start
protected

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

Definition at line 66 of file TensorMechanicsPlasticTensile.h.

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

Real TensorMechanicsPlasticTensile::_ccc
protected
const Real TensorMechanicsPlasticModel::_f_tol
inherited
const Real TensorMechanicsPlasticModel::_ic_tol
inherited

Tolerance on internal constraint.

Definition at line 174 of file TensorMechanicsPlasticModel.h.

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 78 of file TensorMechanicsPlasticTensile.h.

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

Real TensorMechanicsPlasticTensile::_sin3tt
protected

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

Definition at line 75 of file TensorMechanicsPlasticTensile.h.

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

Real TensorMechanicsPlasticTensile::_small_smoother2
protected

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

Definition at line 63 of file TensorMechanicsPlasticTensile.h.

Referenced by smooth().

const TensorMechanicsHardeningModel& TensorMechanicsPlasticTensile::_strength
protected

Definition at line 50 of file TensorMechanicsPlasticTensile.h.

Referenced by dtensile_strength(), and tensile_strength().

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 60 of file TensorMechanicsPlasticTensile.h.

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

Real TensorMechanicsPlasticTensile::_tt
protected

edge smoothing parameter, in radians

Definition at line 72 of file TensorMechanicsPlasticTensile.h.

Referenced by TensorMechanicsPlasticTensile().


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