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TensorMechanicsPlasticIsotropicSD Class Reference

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

#include <TensorMechanicsPlasticIsotropicSD.h>

Inheritance diagram for TensorMechanicsPlasticIsotropicSD:
[legend]

Public Member Functions

 TensorMechanicsPlasticIsotropicSD (const InputParameters &parameters)
 
virtual std::string modelName () const override
 
virtual bool useCustomReturnMap () const override
 Returns false. You will want to override this in your derived class if you write a custom returnMap function. More...
 
virtual bool useCustomCTO () const override
 Returns false. You will want to override this in your derived class if you write a custom consistent tangent operator function. More...
 
virtual bool returnMap (const RankTwoTensor &trial_stress, Real intnl_old, const RankFourTensor &E_ijkl, Real ep_plastic_tolerance, RankTwoTensor &returned_stress, Real &returned_intnl, std::vector< Real > &dpm, RankTwoTensor &delta_dp, std::vector< Real > &yf, bool &trial_stress_inadmissible) const override
 Performs a custom return-map. More...
 
virtual RankFourTensor consistentTangentOperator (const RankTwoTensor &trial_stress, Real intnl_old, const RankTwoTensor &stress, Real intnl, const RankFourTensor &E_ijkl, const std::vector< Real > &cumulative_pm) const override
 Calculates a custom consistent tangent operator. More...
 
void initialize ()
 
void execute ()
 
void finalize ()
 
virtual unsigned int numberSurfaces () const
 The number of yield surfaces for this plasticity model. More...
 
virtual void yieldFunctionV (const RankTwoTensor &stress, Real intnl, std::vector< Real > &f) const
 Calculates the yield functions. More...
 
virtual void dyieldFunction_dstressV (const RankTwoTensor &stress, Real intnl, std::vector< RankTwoTensor > &df_dstress) const
 The derivative of yield functions with respect to stress. More...
 
virtual void dyieldFunction_dintnlV (const RankTwoTensor &stress, Real intnl, std::vector< Real > &df_dintnl) const
 The derivative of yield functions with respect to the internal parameter. More...
 
virtual void flowPotentialV (const RankTwoTensor &stress, Real intnl, std::vector< RankTwoTensor > &r) const
 The flow potentials. More...
 
virtual void dflowPotential_dstressV (const RankTwoTensor &stress, Real intnl, std::vector< RankFourTensor > &dr_dstress) const
 The derivative of the flow potential with respect to stress. More...
 
virtual void dflowPotential_dintnlV (const RankTwoTensor &stress, Real intnl, std::vector< RankTwoTensor > &dr_dintnl) const
 The derivative of the flow potential with respect to the internal parameter. More...
 
virtual void hardPotentialV (const RankTwoTensor &stress, Real intnl, std::vector< Real > &h) const
 The hardening potential. More...
 
virtual void dhardPotential_dstressV (const RankTwoTensor &stress, Real intnl, std::vector< RankTwoTensor > &dh_dstress) const
 The derivative of the hardening potential with respect to stress. More...
 
virtual void dhardPotential_dintnlV (const RankTwoTensor &stress, Real intnl, std::vector< Real > &dh_dintnl) const
 The derivative of the hardening potential with respect to the internal parameter. More...
 
virtual void activeConstraints (const std::vector< Real > &f, const RankTwoTensor &stress, Real intnl, const RankFourTensor &Eijkl, std::vector< bool > &act, RankTwoTensor &returned_stress) const
 The active yield surfaces, given a vector of yield functions. More...
 
bool KuhnTuckerSingleSurface (Real yf, Real dpm, Real dpm_tol) const
 Returns true if the Kuhn-Tucker conditions for the single surface are satisfied. More...
 

Public Attributes

const Real _f_tol
 Tolerance on yield function. More...
 
const Real _ic_tol
 Tolerance on internal constraint. More...
 

Protected Member Functions

Real dphi_dj2 (const Real j2, const Real j3) const
 derivative of phi with respect to J2, phi is b*I1 + (J2^{3/2} - c*J3)^{1/3} More...
 
Real dphi_dj3 (const Real j2, const Real j3) const
 derivative of phi with respect to J3 More...
 
Real dfj2_dj2 (const Real j2, const Real j3) const
 derivative of dphi_dJ2 with respect to J2 More...
 
Real dfj2_dj3 (const Real j2, const Real j3) const
 derivative of dphi_dJ2 with respect to J3 More...
 
Real dfj3_dj2 (const Real j2, const Real j3) const
 derivative of dphi_dJ3 with respect to J2 More...
 
Real dfj3_dj3 (const Real j2, const Real j3) const
 derivative of dphi_dJ3 with respect to J3 More...
 
RankTwoTensor dI_sigma () const
 derivative of the trace with respect to sigma rank two tensor More...
 
RankTwoTensor dj2_dSkl (const RankTwoTensor &stress) const
 derivative of the second invariant with respect to the stress deviatoric tensor More...
 
Real yieldFunction (const RankTwoTensor &stress, Real intnl) const override
 Yield_function = a[b*I1 + (J2^{3/2} - c*J3)^{1/3}] - yield_strength. More...
 
RankTwoTensor dyieldFunction_dstress (const RankTwoTensor &stress, Real intnl) const override
 Tensor derivative of the yield_function with respect to the stress tensor. More...
 
RankFourTensor dflowPotential_dstress (const RankTwoTensor &stress, Real intnl) const override
 Tensor derivative of the tensor derivative of the yield_function with respect to the stress tensor. More...
 
RankTwoTensor flowPotential (const RankTwoTensor &stress, Real intnl) const override
 Receives the flag for associative or non-associative and calculates the flow potential accordingly. More...
 
Real dyieldFunction_dintnl (const RankTwoTensor &stress, Real intnl) const override
 The derivative of yield function with respect to the internal parameter. More...
 
RankTwoTensor dflowPotential_dintnl (const RankTwoTensor &stress, Real intnl) const override
 The derivative of the flow potential with respect to the internal parameter. More...
 
virtual Real yieldStrength (Real intnl) const
 YieldStrength. More...
 
virtual Real dyieldStrength (Real intnl) const
 d(yieldStrength)/d(intnl) More...
 
virtual Real hardPotential (const RankTwoTensor &stress, Real intnl) const
 The hardening potential. More...
 
virtual RankTwoTensor dhardPotential_dstress (const RankTwoTensor &stress, Real intnl) const
 The derivative of the hardening potential with respect to stress. More...
 
virtual Real dhardPotential_dintnl (const RankTwoTensor &stress, Real intnl) const
 The derivative of the hardening potential with respect to the internal parameter. More...
 

Protected Attributes

const Real _b
 A constant to model the influence of pressure. More...
 
Real _c
 A constant to model the influence of strength differential effect. More...
 
const bool _associative
 Flag for flow-rule, true if not specified. More...
 
RankFourTensor _h
 Comes from transforming the stress tensor to the deviatoric stress tensor. More...
 
Real _a
 A constant used in the constructor that depends on _b and _c. More...
 

Detailed Description

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

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

Definition at line 28 of file TensorMechanicsPlasticIsotropicSD.h.

Constructor & Destructor Documentation

TensorMechanicsPlasticIsotropicSD::TensorMechanicsPlasticIsotropicSD ( const InputParameters &  parameters)

Definition at line 23 of file TensorMechanicsPlasticIsotropicSD.C.

25  : TensorMechanicsPlasticJ2(parameters),
26  _b(getParam<Real>("b")),
27  _c(getParam<Real>("c")),
28  _associative(getParam<bool>("associative"))
29 {
30  _a = 1.0 / (_b + std::pow(1.0 / std::sqrt(27.0) - _c / 27.0, 1.0 / 3.0));
31  for (unsigned i = 0; i < 3; ++i)
32  for (unsigned j = 0; j < 3; ++j)
33  for (unsigned k = 0; k < 3; ++k)
34  for (unsigned l = 0; l < 3; ++l)
35  _h(i, j, k, l) = ((i == k) * (j == l) - 1.0 / 3.0 * (i == j) * (k == l));
36 }
Real _c
A constant to model the influence of strength differential effect.
TensorMechanicsPlasticJ2(const InputParameters &parameters)
RankFourTensor _h
Comes from transforming the stress tensor to the deviatoric stress tensor.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real _a
A constant used in the constructor that depends on _b and _c.
const Real _b
A constant to model the influence of pressure.
const bool _associative
Flag for flow-rule, true if not specified.

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

Calculates a custom consistent tangent operator.

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

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

Parameters
stress_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 from TensorMechanicsPlasticModel.

Definition at line 186 of file TensorMechanicsPlasticJ2.C.

192 {
193  if (!_use_custom_cto)
195  trial_stress, intnl_old, stress, intnl, E_ijkl, cumulative_pm);
196 
197  Real mu = E_ijkl(0, 1, 0, 1);
198 
199  Real h = 3 * mu + dyieldStrength(intnl);
200  RankTwoTensor sij = stress.deviatoric();
201  Real sII = stress.secondInvariant();
202  Real equivalent_stress = std::sqrt(3.0 * sII);
203  Real zeta = cumulative_pm[0] / (1.0 + 3.0 * mu * cumulative_pm[0] / equivalent_stress);
204 
205  return E_ijkl - 3.0 * mu * mu / sII / h * sij.outerProduct(sij) -
206  4.0 * mu * mu * zeta * dflowPotential_dstress(stress, intnl);
207 }
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.
virtual Real dyieldStrength(Real intnl) const
d(yieldStrength)/d(intnl)
const bool _use_custom_cto
Whether to use the custom consistent tangent operator calculation.
virtual RankFourTensor dflowPotential_dstress(const RankTwoTensor &stress, Real intnl) const override
The derivative of the flow potential with respect to stress.
Real TensorMechanicsPlasticIsotropicSD::dfj2_dj2 ( const Real  j2,
const Real  j3 
) const
protected

derivative of dphi_dJ2 with respect to J2

Definition at line 51 of file TensorMechanicsPlasticIsotropicSD.C.

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

52 {
53  return std::pow(j2, -1.0 / 2.0) / (4 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 2.0 / 3.0)) -
54  j2 / (2 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 5.0 / 3.0));
55 }
Real _c
A constant to model the influence of strength differential effect.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real TensorMechanicsPlasticIsotropicSD::dfj2_dj3 ( const Real  j2,
const Real  j3 
) const
protected

derivative of dphi_dJ2 with respect to J3

Definition at line 58 of file TensorMechanicsPlasticIsotropicSD.C.

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

59 {
60  return _c * std::pow(j2, 1.0 / 2.0) /
61  (3 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 5.0 / 3.0));
62 }
Real _c
A constant to model the influence of strength differential effect.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real TensorMechanicsPlasticIsotropicSD::dfj3_dj2 ( const Real  j2,
const Real  j3 
) const
protected

derivative of dphi_dJ3 with respect to J2

Definition at line 65 of file TensorMechanicsPlasticIsotropicSD.C.

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

66 {
67  return _c * std::pow(j2, 1.0 / 2.0) /
68  (3 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 5.0 / 3.0));
69 }
Real _c
A constant to model the influence of strength differential effect.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real TensorMechanicsPlasticIsotropicSD::dfj3_dj3 ( const Real  j2,
const Real  j3 
) const
protected

derivative of dphi_dJ3 with respect to J3

Definition at line 72 of file TensorMechanicsPlasticIsotropicSD.C.

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

73 {
74  return -_c * _c * 2.0 / (9 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 5.0 / 3.0));
75 }
Real _c
A constant to model the influence of strength differential effect.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
RankTwoTensor TensorMechanicsPlasticJ2::dflowPotential_dintnl ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtualinherited

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 90 of file TensorMechanicsPlasticJ2.C.

92 {
93  return RankTwoTensor();
94 }
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 TensorMechanicsPlasticIsotropicSD::dflowPotential_dstress ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

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

Reimplemented from TensorMechanicsPlasticJ2.

Reimplemented in TensorMechanicsPlasticOrthotropic.

Definition at line 116 of file TensorMechanicsPlasticIsotropicSD.C.

118 {
119  if (_associative)
120  {
121  const RankTwoTensor sDev = stress.deviatoric();
122  const RankTwoTensor dj2 = dj2_dSkl(sDev);
123  const RankTwoTensor dj3 = sDev.ddet();
124  const Real j2 = stress.secondInvariant();
125  const Real j3 = stress.thirdInvariant();
126  return _a * (dfj2_dj2(j2, j3) *
127  _h.innerProductTranspose(dj2).outerProduct(_h.innerProductTranspose(dj2)) +
128  dfj2_dj3(j2, j3) *
129  _h.innerProductTranspose(dj2).outerProduct(_h.innerProductTranspose(dj3)) +
130  dfj3_dj2(j2, j3) *
131  _h.innerProductTranspose(dj3).outerProduct(_h.innerProductTranspose(dj2)) +
132  dfj3_dj3(j2, j3) *
133  _h.innerProductTranspose(dj3).outerProduct(_h.innerProductTranspose(dj3)));
134  }
135  else
137 }
RankTwoTensor dj2_dSkl(const RankTwoTensor &stress) const
derivative of the second invariant with respect to the stress deviatoric tensor
Real dfj2_dj2(const Real j2, const Real j3) const
derivative of dphi_dJ2 with respect to J2
Real dfj3_dj2(const Real j2, const Real j3) const
derivative of dphi_dJ3 with respect to J2
RankFourTensor _h
Comes from transforming the stress tensor to the deviatoric stress tensor.
Real dfj3_dj3(const Real j2, const Real j3) const
derivative of dphi_dJ3 with respect to J3
Real _a
A constant used in the constructor that depends on _b and _c.
virtual RankFourTensor dflowPotential_dstress(const RankTwoTensor &stress, Real intnl) const override
The derivative of the flow potential with respect to stress.
Real dfj2_dj3(const Real j2, const Real j3) const
derivative of dphi_dJ2 with respect to J3
const bool _associative
Flag for flow-rule, true if not specified.
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.
RankTwoTensor TensorMechanicsPlasticIsotropicSD::dI_sigma ( ) const
protected

derivative of the trace with respect to sigma rank two tensor

Definition at line 78 of file TensorMechanicsPlasticIsotropicSD.C.

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

79 {
80  return RankTwoTensor(RankTwoTensor::initIdentity);
81 }
RankTwoTensor TensorMechanicsPlasticIsotropicSD::dj2_dSkl ( const RankTwoTensor &  stress) const
protected

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

Definition at line 84 of file TensorMechanicsPlasticIsotropicSD.C.

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

85 {
86  RankTwoTensor a;
87  const Real trace = stress.trace();
88  for (unsigned i = 0; i < 3; ++i)
89  for (unsigned j = 0; j < 3; ++j)
90  a(i, j) = (trace - stress(i, j)) * -1 * (i == j) + stress(i, j) * (i != j);
91 
92  return a;
93 }
Real TensorMechanicsPlasticIsotropicSD::dphi_dj2 ( const Real  j2,
const Real  j3 
) const
protected

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

Definition at line 39 of file TensorMechanicsPlasticIsotropicSD.C.

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

40 {
41  return std::pow(j2, 1.0 / 2.0) / (2 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 2.0 / 3.0));
42 }
Real _c
A constant to model the influence of strength differential effect.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real TensorMechanicsPlasticIsotropicSD::dphi_dj3 ( const Real  j2,
const Real  j3 
) const
protected

derivative of phi with respect to J3

Definition at line 45 of file TensorMechanicsPlasticIsotropicSD.C.

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

46 {
47  return -_c / (3 * std::pow(std::pow(j2, 3.0 / 2.0) - _c * j3, 2.0 / 3.0));
48 }
Real _c
A constant to model the influence of strength differential effect.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real TensorMechanicsPlasticJ2::dyieldFunction_dintnl ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtualinherited

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 60 of file TensorMechanicsPlasticJ2.C.

61 {
62  return -dyieldStrength(intnl);
63 }
virtual Real dyieldStrength(Real intnl) const
d(yieldStrength)/d(intnl)
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 TensorMechanicsPlasticIsotropicSD::dyieldFunction_dstress ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

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

Reimplemented from TensorMechanicsPlasticJ2.

Reimplemented in TensorMechanicsPlasticOrthotropic.

Definition at line 105 of file TensorMechanicsPlasticIsotropicSD.C.

Referenced by flowPotential().

107 {
108  const RankTwoTensor sDev = stress.deviatoric();
109  const Real j2 = stress.secondInvariant();
110  const Real j3 = stress.thirdInvariant();
111  return _a * (_b * dI_sigma() + dphi_dj2(j2, j3) * _h.innerProductTranspose(dj2_dSkl(sDev)) +
112  dphi_dj3(j2, j3) * _h.innerProductTranspose(sDev.ddet()));
113 }
RankTwoTensor dI_sigma() const
derivative of the trace with respect to sigma rank two tensor
RankTwoTensor dj2_dSkl(const RankTwoTensor &stress) const
derivative of the second invariant with respect to the stress deviatoric tensor
Real dphi_dj3(const Real j2, const Real j3) const
derivative of phi with respect to J3
RankFourTensor _h
Comes from transforming the stress tensor to the deviatoric stress tensor.
Real dphi_dj2(const Real j2, const Real j3) const
derivative of phi with respect to J2, phi is b*I1 + (J2^{3/2} - c*J3)^{1/3}
Real _a
A constant used in the constructor that depends on _b and _c.
const Real _b
A constant to model the influence of pressure.
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.
Real TensorMechanicsPlasticJ2::dyieldStrength ( Real  intnl) const
protectedvirtualinherited

d(yieldStrength)/d(intnl)

Definition at line 103 of file TensorMechanicsPlasticJ2.C.

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

104 {
105  return _strength.derivative(intnl);
106 }
virtual Real derivative(Real intnl) const
const TensorMechanicsHardeningModel & _strength
yield strength, from user input
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 TensorMechanicsPlasticIsotropicSD::flowPotential ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

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

Reimplemented from TensorMechanicsPlasticJ2.

Reimplemented in TensorMechanicsPlasticOrthotropic.

Definition at line 140 of file TensorMechanicsPlasticIsotropicSD.C.

141 {
142  if (_associative)
143  return dyieldFunction_dstress(stress, intnl);
144  else
146 }
virtual RankTwoTensor dyieldFunction_dstress(const RankTwoTensor &stress, Real intnl) const override
The derivative of yield function with respect to stress.
RankTwoTensor dyieldFunction_dstress(const RankTwoTensor &stress, Real intnl) const override
Tensor derivative of the yield_function with respect to the stress tensor.
const bool _associative
Flag for flow-rule, true if not specified.
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 TensorMechanicsPlasticJ2::modelName ( ) const
overridevirtualinherited

Implements TensorMechanicsPlasticModel.

Definition at line 109 of file TensorMechanicsPlasticJ2.C.

110 {
111  return "J2";
112 }
unsigned TensorMechanicsPlasticModel::numberSurfaces ( ) const
virtualinherited
bool TensorMechanicsPlasticJ2::returnMap ( const RankTwoTensor &  trial_stress,
Real  intnl_old,
const RankFourTensor &  E_ijkl,
Real  ep_plastic_tolerance,
RankTwoTensor &  returned_stress,
Real &  returned_intnl,
std::vector< Real > &  dpm,
RankTwoTensor &  delta_dp,
std::vector< Real > &  yf,
bool &  trial_stress_inadmissible 
) const
overridevirtualinherited

Performs a custom return-map.

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

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

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

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

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

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

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

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

Parameters
trial_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 from TensorMechanicsPlasticModel.

Definition at line 115 of file TensorMechanicsPlasticJ2.C.

125 {
126  if (!(_use_custom_returnMap))
127  return TensorMechanicsPlasticModel::returnMap(trial_stress,
128  intnl_old,
129  E_ijkl,
130  ep_plastic_tolerance,
131  returned_stress,
132  returned_intnl,
133  dpm,
134  delta_dp,
135  yf,
136  trial_stress_inadmissible);
137 
138  yf.resize(1);
139 
140  Real yf_orig = yieldFunction(trial_stress, intnl_old);
141 
142  yf[0] = yf_orig;
143 
144  if (yf_orig < _f_tol)
145  {
146  // the trial_stress is admissible
147  trial_stress_inadmissible = false;
148  return true;
149  }
150 
151  trial_stress_inadmissible = true;
152  Real mu = E_ijkl(0, 1, 0, 1);
153 
154  // Perform a Newton-Raphson to find dpm when
155  // residual = 3*mu*dpm - trial_equivalent_stress + yieldStrength(intnl_old + dpm) = 0
156  Real trial_equivalent_stress = yf_orig + yieldStrength(intnl_old);
157  Real residual;
158  Real jac;
159  dpm[0] = 0;
160  unsigned int iter = 0;
161  do
162  {
163  residual = 3.0 * mu * dpm[0] - trial_equivalent_stress + yieldStrength(intnl_old + dpm[0]);
164  jac = 3.0 * mu + dyieldStrength(intnl_old + dpm[0]);
165  dpm[0] += -residual / jac;
166  if (iter > _max_iters) // not converging
167  return false;
168  iter++;
169  } while (residual * residual > _f_tol * _f_tol);
170 
171  // set the returned values
172  yf[0] = 0;
173  returned_intnl = intnl_old + dpm[0];
174  RankTwoTensor nn = 1.5 * trial_stress.deviatoric() /
175  trial_equivalent_stress; // = dyieldFunction_dstress(trial_stress, intnl_old) =
176  // the normal to the yield surface, at the trial
177  // stress
178  returned_stress = 2.0 / 3.0 * nn * yieldStrength(returned_intnl);
179  returned_stress.addIa(1.0 / 3.0 * trial_stress.trace());
180  delta_dp = nn * dpm[0];
181 
182  return true;
183 }
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.
const unsigned _max_iters
max iters for custom return map loop
virtual Real dyieldStrength(Real intnl) const
d(yieldStrength)/d(intnl)
virtual Real yieldStrength(Real intnl) const
YieldStrength.
const bool _use_custom_returnMap
Whether to use the custom return-map algorithm.
const Real _f_tol
Tolerance on yield function.
virtual Real yieldFunction(const RankTwoTensor &stress, Real intnl) const override
The following functions are what you should override when building single-plasticity models...
bool TensorMechanicsPlasticJ2::useCustomCTO ( ) const
overridevirtualinherited

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

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 216 of file TensorMechanicsPlasticJ2.C.

217 {
218  return _use_custom_cto;
219 }
const bool _use_custom_cto
Whether to use the custom consistent tangent operator calculation.
bool TensorMechanicsPlasticJ2::useCustomReturnMap ( ) const
overridevirtualinherited

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

Reimplemented from TensorMechanicsPlasticModel.

Definition at line 210 of file TensorMechanicsPlasticJ2.C.

211 {
212  return _use_custom_returnMap;
213 }
const bool _use_custom_returnMap
Whether to use the custom return-map algorithm.
Real TensorMechanicsPlasticIsotropicSD::yieldFunction ( const RankTwoTensor &  stress,
Real  intnl 
) const
overrideprotectedvirtual

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

Reimplemented from TensorMechanicsPlasticJ2.

Reimplemented in TensorMechanicsPlasticOrthotropic.

Definition at line 96 of file TensorMechanicsPlasticIsotropicSD.C.

97 {
98  return _a * (_b * stress.trace() +
99  std::pow(std::pow(stress.secondInvariant(), 1.5) - _c * stress.thirdInvariant(),
100  1.0 / 3.0)) -
101  yieldStrength(intnl);
102 }
Real _c
A constant to model the influence of strength differential effect.
virtual Real yieldStrength(Real intnl) const
YieldStrength.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real _a
A constant used in the constructor that depends on _b and _c.
const Real _b
A constant to model the influence of pressure.
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...
Real TensorMechanicsPlasticJ2::yieldStrength ( Real  intnl) const
protectedvirtualinherited

YieldStrength.

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

Definition at line 97 of file TensorMechanicsPlasticJ2.C.

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

98 {
99  return _strength.value(intnl);
100 }
virtual Real value(Real intnl) const
const TensorMechanicsHardeningModel & _strength
yield strength, from user input

Member Data Documentation

Real TensorMechanicsPlasticIsotropicSD::_a
protected

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

Definition at line 47 of file TensorMechanicsPlasticIsotropicSD.h.

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

const bool TensorMechanicsPlasticIsotropicSD::_associative
protected
const Real TensorMechanicsPlasticIsotropicSD::_b
protected
Real TensorMechanicsPlasticIsotropicSD::_c
protected
const Real TensorMechanicsPlasticModel::_f_tol
inherited
RankFourTensor TensorMechanicsPlasticIsotropicSD::_h
protected

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

Definition at line 44 of file TensorMechanicsPlasticIsotropicSD.h.

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

const Real TensorMechanicsPlasticModel::_ic_tol
inherited

Tolerance on internal constraint.

Definition at line 174 of file TensorMechanicsPlasticModel.h.


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