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TensorMechanicsPlasticMohrCoulomb Class Reference

Mohr-Coulomb plasticity, nonassociative with hardening/softening. More...

#include <TensorMechanicsPlasticMohrCoulomb.h>

Inheritance diagram for TensorMechanicsPlasticMohrCoulomb:
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Public Member Functions

 TensorMechanicsPlasticMohrCoulomb (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 cohesion (const Real internal_param) const
 cohesion as a function of internal parameter More...
 
virtual Real dcohesion (const Real internal_param) const
 d(cohesion)/d(internal_param); More...
 
virtual Real phi (const Real internal_param) const
 friction angle as a function of internal parameter More...
 
virtual Real dphi (const Real internal_param) const
 d(phi)/d(internal_param); More...
 
virtual Real psi (const Real internal_param) const
 dilation angle as a function of internal parameter More...
 
virtual Real dpsi (const Real internal_param) const
 d(psi)/d(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_cohesion
 Hardening model for cohesion. More...
 
const TensorMechanicsHardeningModel_phi
 Hardening model for phi. More...
 
const TensorMechanicsHardeningModel_psi
 Hardening model for psi. More...
 
MooseEnum _tip_scheme
 The yield function is modified to f = s_m*sinphi + sqrt(a + s_bar^2 K^2) - C*cosphi 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 _costt
 cos(_tt) More...
 
Real _sintt
 sin(_tt) More...
 
Real _cos3tt
 cos(3*_tt) More...
 
Real _sin3tt
 sin(3*_tt) - useful for making comparisons with Lode angle More...
 
Real _cos6tt
 cos(6*_tt) More...
 
Real _sin6tt
 sin(6*_tt) More...
 
Real _lode_cutoff
 if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-loss More...
 

Private Member Functions

void abbo (const Real sin3lode, const Real sin_angle, Real &aaa, Real &bbb, Real &ccc) const
 Computes Abbo et al's A, B and C parameters. More...
 
void dabbo (const Real sin3lode, const Real sin_angle, Real &daaa, Real &dbbb, Real &dccc) const
 Computes derivatives of Abbo et al's A, B and C parameters wrt sin_angle. More...
 
RankTwoTensor df_dsig (const RankTwoTensor &stress, const Real sin_angle) const
 d(yieldFunction)/d(stress), but with the ability to put friction or dilation angle into the result More...
 

Detailed Description

Mohr-Coulomb plasticity, nonassociative with hardening/softening.

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 31 of file TensorMechanicsPlasticMohrCoulomb.h.

Constructor & Destructor Documentation

TensorMechanicsPlasticMohrCoulomb::TensorMechanicsPlasticMohrCoulomb ( const InputParameters &  parameters)

Definition at line 64 of file TensorMechanicsPlasticMohrCoulomb.C.

66  : TensorMechanicsPlasticModel(parameters),
67  _cohesion(getUserObject<TensorMechanicsHardeningModel>("cohesion")),
68  _phi(getUserObject<TensorMechanicsHardeningModel>("friction_angle")),
69  _psi(getUserObject<TensorMechanicsHardeningModel>("dilation_angle")),
70  _tip_scheme(getParam<MooseEnum>("tip_scheme")),
71  _small_smoother2(Utility::pow<2>(getParam<Real>("mc_tip_smoother"))),
72  _cap_start(getParam<Real>("cap_start")),
73  _cap_rate(getParam<Real>("cap_rate")),
74  _tt(getParam<Real>("mc_edge_smoother") * libMesh::pi / 180.0),
75  _costt(std::cos(_tt)),
76  _sintt(std::sin(_tt)),
77  _cos3tt(std::cos(3 * _tt)),
78  _sin3tt(std::sin(3 * _tt)),
79  _cos6tt(std::cos(6 * _tt)),
80  _sin6tt(std::sin(6 * _tt)),
81  _lode_cutoff(parameters.isParamValid("mc_lode_cutoff") ? getParam<Real>("mc_lode_cutoff")
82  : 1.0E-5 * Utility::pow<2>(_f_tol))
83 
84 {
85  if (_lode_cutoff < 0)
86  mooseError("mc_lode_cutoff must not be negative");
87 
88  // With arbitary UserObjects, it is impossible to check everything, and
89  // I think this is the best I can do
90  if (phi(0) < 0 || psi(0) < 0 || phi(0) > libMesh::pi / 2.0 || psi(0) > libMesh::pi / 2.0)
91  mooseError("Mohr-Coulomb friction and dilation angles must lie in [0, Pi/2]");
92  if (phi(0) < psi(0))
93  mooseError("Mohr-Coulomb friction angle must not be less than Mohr-Coulomb dilation angle");
94  if (cohesion(0) < 0)
95  mooseError("Mohr-Coulomb cohesion must not be negative");
96 
97  // check Abbo et al's convexity constraint (Eqn c.18 in their paper)
98  // With an arbitrary UserObject, it is impossible to check for all angles
99  // I think the following is the best we can do
100  Real sin_angle = std::sin(std::max(phi(0), psi(0)));
101  sin_angle = std::max(sin_angle, std::sin(std::max(phi(1E6), psi(1E6))));
102  Real rhs = std::sqrt(3) * (35 * std::sin(_tt) + 14 * std::sin(5 * _tt) - 5 * std::sin(7 * _tt)) /
103  16 / Utility::pow<5>(std::cos(_tt)) / (11 - 10 * std::cos(2 * _tt));
104  if (rhs <= sin_angle)
105  mooseError("Mohr-Coulomb edge smoothing angle is too small and a non-convex yield surface will "
106  "result. Please choose a larger value");
107 }
virtual Real psi(const Real internal_param) const
dilation angle as a function of internal parameter
const TensorMechanicsHardeningModel & _cohesion
Hardening model for cohesion.
TensorMechanicsPlasticModel(const InputParameters &parameters)
Real _cap_start
smoothing parameter dictating when the &#39;cap&#39; will start - see doco for _tip_scheme ...
const TensorMechanicsHardeningModel & _phi
Hardening model for phi.
Real _cap_rate
dictates how quickly the &#39;cap&#39; degenerates to a hemisphere - see doco for _tip_scheme ...
Real _tt
edge smoothing parameter, in radians
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
virtual Real cohesion(const Real internal_param) const
cohesion as a function of internal parameter
const Real _f_tol
Tolerance on yield function.
MooseEnum _tip_scheme
The yield function is modified to f = s_m*sinphi + sqrt(a + s_bar^2 K^2) - C*cosphi where "a" depends...
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
virtual Real phi(const Real internal_param) const
friction angle as a function of internal parameter
Real _small_smoother2
Square of tip smoothing parameter to smooth the cone at mean_stress = T.
const TensorMechanicsHardeningModel & _psi
Hardening model for psi.

Member Function Documentation

void TensorMechanicsPlasticMohrCoulomb::abbo ( const Real  sin3lode,
const Real  sin_angle,
Real &  aaa,
Real &  bbb,
Real &  ccc 
) const
private

Computes Abbo et al's A, B and C parameters.

Parameters
sin3lodesin(3*(lode angle))
sin_anglesin(friction_angle) (for yield function), or sin(dilation_angle) (for potential function)
[out]aaaAbbo's A
[out]bbbAbbo's B
[out]cccAbbo's C

Definition at line 405 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by df_dsig(), dflowPotential_dintnl(), dflowPotential_dstress(), dyieldFunction_dintnl(), and yieldFunction().

407 {
408  Real tmp1 = (sin3lode >= 0 ? _costt - sin_angle * _sintt / std::sqrt(3.0)
409  : _costt + sin_angle * _sintt / std::sqrt(3.0));
410  Real tmp2 = (sin3lode >= 0 ? _sintt + sin_angle * _costt / std::sqrt(3.0)
411  : -_sintt + sin_angle * _costt / std::sqrt(3.0));
412 
413  ccc = -_cos3tt * tmp1;
414  ccc += (sin3lode >= 0 ? -3 * _sin3tt * tmp2 : 3 * _sin3tt * tmp2);
415  ccc /= 18 * Utility::pow<3>(_cos3tt);
416 
417  bbb = (sin3lode >= 0 ? _sin6tt * tmp1 : -_sin6tt * tmp1);
418  bbb -= 6 * _cos6tt * tmp2;
419  bbb /= 18 * Utility::pow<3>(_cos3tt);
420 
421  aaa = (sin3lode >= 0 ? -sin_angle * _sintt / std::sqrt(3.0) - bbb * _sin3tt
422  : sin_angle * _sintt / std::sqrt(3.0) + bbb * _sin3tt);
423  aaa += -ccc * Utility::pow<2>(_sin3tt) + _costt;
424 }
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
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.
Real TensorMechanicsPlasticMohrCoulomb::cohesion ( const Real  internal_param) const
protectedvirtual

cohesion as a function of internal parameter

Definition at line 369 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dyieldFunction_dintnl(), TensorMechanicsPlasticMohrCoulomb(), and yieldFunction().

370 {
371  return _cohesion.value(internal_param);
372 }
const TensorMechanicsHardeningModel & _cohesion
Hardening model for cohesion.
virtual Real value(Real intnl) const
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 TensorMechanicsPlasticMohrCoulomb::d2smooth ( const RankTwoTensor &  stress) const
protectedvirtual

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

Definition at line 481 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dflowPotential_dstress().

482 {
483  Real d2smoother2 = 0;
484  if (_tip_scheme == "cap")
485  {
486  Real x = stress.trace() / 3.0 - _cap_start;
487  Real p = 0;
488  Real dp_dx = 0;
489  Real d2p_dx2 = 0;
490  if (x > 0)
491  {
492  p = x * (1 - std::exp(-_cap_rate * x));
493  dp_dx = (1 - std::exp(-_cap_rate * x)) + x * _cap_rate * std::exp(-_cap_rate * x);
494  d2p_dx2 = 2 * _cap_rate * std::exp(-_cap_rate * x) -
495  x * Utility::pow<2>(_cap_rate) * std::exp(-_cap_rate * x);
496  }
497  d2smoother2 += 2 * Utility::pow<2>(dp_dx) + 2 * p * d2p_dx2;
498  }
499  return d2smoother2;
500 }
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*sinphi + sqrt(a + s_bar^2 K^2) - C*cosphi where "a" depends...
void TensorMechanicsPlasticMohrCoulomb::dabbo ( const Real  sin3lode,
const Real  sin_angle,
Real &  daaa,
Real &  dbbb,
Real &  dccc 
) const
private

Computes derivatives of Abbo et al's A, B and C parameters wrt sin_angle.

Parameters
sin3lodesin(3*(lode angle))
sin_anglesin(friction_angle) (for yield function), or sin(dilation_angle) (for potential function)
[out]daaad(Abbo's A)/d(sin_angle)
[out]dbbbd(Abbo's B)/d(sin_angle)
[out]dcccd(Abbo's C)/d(sin_angle)

Definition at line 427 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dflowPotential_dintnl(), and dyieldFunction_dintnl().

429 {
430  Real dtmp1 = (sin3lode >= 0 ? -_sintt / std::sqrt(3.0) : _sintt / std::sqrt(3.0));
431  Real dtmp2 = _costt / std::sqrt(3.0);
432 
433  dccc = -_cos3tt * dtmp1;
434  dccc += (sin3lode >= 0 ? -3 * _sin3tt * dtmp2 : 3 * _sin3tt * dtmp2);
435  dccc /= 18 * Utility::pow<3>(_cos3tt);
436 
437  dbbb = (sin3lode >= 0 ? _sin6tt * dtmp1 : -_sin6tt * dtmp1);
438  dbbb -= 6 * _cos6tt * dtmp2;
439  dbbb /= 18 * Utility::pow<3>(_cos3tt);
440 
441  daaa = (sin3lode >= 0 ? -_sintt / std::sqrt(3.0) - dbbb * _sin3tt
442  : _sintt / std::sqrt(3.0) + dbbb * _sin3tt);
443  daaa += -dccc * Utility::pow<2>(_sin3tt);
444 }
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
Real TensorMechanicsPlasticMohrCoulomb::dcohesion ( const Real  internal_param) const
protectedvirtual

d(cohesion)/d(internal_param);

Definition at line 375 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dyieldFunction_dintnl().

376 {
377  return _cohesion.derivative(internal_param);
378 }
const TensorMechanicsHardeningModel & _cohesion
Hardening model for cohesion.
virtual Real derivative(Real intnl) const
RankTwoTensor TensorMechanicsPlasticMohrCoulomb::df_dsig ( const RankTwoTensor &  stress,
const Real  sin_angle 
) const
private

d(yieldFunction)/d(stress), but with the ability to put friction or dilation angle into the result

Parameters
stressthe stress at which to calculate
sin_angleeither sin(friction angle) or sin(dilation angle)

Definition at line 140 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dyieldFunction_dstress(), and flowPotential().

141 {
142  Real mean_stress = stress.trace() / 3.0;
143  RankTwoTensor dmean_stress = stress.dtrace() / 3.0;
144  Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
145  if (std::abs(sin3Lode) <= _sin3tt)
146  {
147  // the non-edge-smoothed version
148  std::vector<Real> eigvals;
149  std::vector<RankTwoTensor> deigvals;
150  stress.dsymmetricEigenvalues(eigvals, deigvals);
151  Real tmp = eigvals[2] - eigvals[0] + (eigvals[2] + eigvals[0] - 2 * mean_stress) * sin_angle;
152  RankTwoTensor dtmp =
153  deigvals[2] - deigvals[0] + (deigvals[2] + deigvals[0] - 2 * dmean_stress) * sin_angle;
154  Real denom = std::sqrt(smooth(stress) + 0.25 * Utility::pow<2>(tmp));
155  return dmean_stress * sin_angle +
156  (0.5 * dsmooth(stress) * dmean_stress + 0.25 * tmp * dtmp) / denom;
157  }
158  else
159  {
160  // the edge-smoothed version
161  Real aaa, bbb, ccc;
162  abbo(sin3Lode, sin_angle, aaa, bbb, ccc);
163  Real kk = aaa + bbb * sin3Lode + ccc * Utility::pow<2>(sin3Lode);
164  RankTwoTensor dkk = (bbb + 2 * ccc * sin3Lode) * stress.dsin3Lode(_lode_cutoff);
165  Real sibar2 = stress.secondInvariant();
166  RankTwoTensor dsibar2 = stress.dsecondInvariant();
167  Real denom = std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk));
168  return dmean_stress * sin_angle +
169  (0.5 * dsmooth(stress) * dmean_stress + 0.5 * dsibar2 * Utility::pow<2>(kk) +
170  sibar2 * kk * dkk) /
171  denom;
172  }
173 }
virtual Real dsmooth(const RankTwoTensor &stress) const
returns the da/dstress_mean - see doco for _tip_scheme
virtual Real smooth(const RankTwoTensor &stress) const
returns the &#39;a&#39; parameter - see doco for _tip_scheme
void abbo(const Real sin3lode, const Real sin_angle, Real &aaa, Real &bbb, Real &ccc) const
Computes Abbo et al&#39;s A, B and C parameters.
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
RankTwoTensor TensorMechanicsPlasticMohrCoulomb::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 312 of file TensorMechanicsPlasticMohrCoulomb.C.

314 {
315  Real sin_angle = std::sin(psi(intnl));
316  Real dsin_angle = std::cos(psi(intnl)) * dpsi(intnl);
317 
318  Real mean_stress = stress.trace() / 3.0;
319  RankTwoTensor dmean_stress = stress.dtrace() / 3.0;
320  Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
321 
322  if (std::abs(sin3Lode) <= _sin3tt)
323  {
324  // the non-edge-smoothed version
325  std::vector<Real> eigvals;
326  std::vector<RankTwoTensor> deigvals;
327  stress.dsymmetricEigenvalues(eigvals, deigvals);
328  Real tmp = eigvals[2] - eigvals[0] + (eigvals[2] + eigvals[0] - 2 * mean_stress) * sin_angle;
329  Real dtmp_dintnl = (eigvals[2] + eigvals[0] - 2 * mean_stress) * dsin_angle;
330  RankTwoTensor dtmp_dstress =
331  deigvals[2] - deigvals[0] + (deigvals[2] + deigvals[0] - 2 * dmean_stress) * sin_angle;
332  RankTwoTensor d2tmp_dstress_dintnl =
333  (deigvals[2] + deigvals[0] - 2 * dmean_stress) * dsin_angle;
334  Real denom = std::sqrt(smooth(stress) + 0.25 * Utility::pow<2>(tmp));
335  return dmean_stress * dsin_angle + 0.25 * dtmp_dintnl * dtmp_dstress / denom +
336  0.25 * tmp * d2tmp_dstress_dintnl / denom -
337  0.5 * (dsmooth(stress) * dmean_stress + 0.5 * tmp * dtmp_dstress) * 0.25 * tmp *
338  dtmp_dintnl / Utility::pow<3>(denom);
339  }
340  else
341  {
342  // the edge-smoothed version
343  Real aaa, bbb, ccc;
344  abbo(sin3Lode, sin_angle, aaa, bbb, ccc);
345  Real kk = aaa + bbb * sin3Lode + ccc * Utility::pow<2>(sin3Lode);
346 
347  Real daaa, dbbb, dccc;
348  dabbo(sin3Lode, sin_angle, daaa, dbbb, dccc);
349  Real dkk_dintnl = (daaa + dbbb * sin3Lode + dccc * Utility::pow<2>(sin3Lode)) * dsin_angle;
350  RankTwoTensor dkk_dstress = (bbb + 2 * ccc * sin3Lode) * stress.dsin3Lode(_lode_cutoff);
351  RankTwoTensor d2kk_dstress_dintnl =
352  (dbbb + 2 * dccc * sin3Lode) * stress.dsin3Lode(_lode_cutoff) * dsin_angle;
353 
354  Real sibar2 = stress.secondInvariant();
355  RankTwoTensor dsibar2 = stress.dsecondInvariant();
356  Real denom = std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk));
357 
358  return dmean_stress * dsin_angle +
359  (dsibar2 * kk * dkk_dintnl + sibar2 * dkk_dintnl * dkk_dstress +
360  sibar2 * kk * d2kk_dstress_dintnl) /
361  denom -
362  (0.5 * dsmooth(stress) * dmean_stress + 0.5 * dsibar2 * Utility::pow<2>(kk) +
363  sibar2 * kk * dkk_dstress) *
364  sibar2 * kk * dkk_dintnl / Utility::pow<3>(denom);
365  }
366 }
virtual Real dsmooth(const RankTwoTensor &stress) const
returns the da/dstress_mean - see doco for _tip_scheme
virtual Real psi(const Real internal_param) const
dilation angle as a function of internal parameter
virtual Real dpsi(const Real internal_param) const
d(psi)/d(internal_param);
virtual Real smooth(const RankTwoTensor &stress) const
returns the &#39;a&#39; parameter - see doco for _tip_scheme
void abbo(const Real sin3lode, const Real sin_angle, Real &aaa, Real &bbb, Real &ccc) const
Computes Abbo et al&#39;s A, B and C parameters.
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
void dabbo(const Real sin3lode, const Real sin_angle, Real &daaa, Real &dbbb, Real &dccc) const
Computes derivatives of Abbo et al&#39;s A, B and C parameters wrt sin_angle.
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 TensorMechanicsPlasticMohrCoulomb::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 229 of file TensorMechanicsPlasticMohrCoulomb.C.

231 {
232  RankFourTensor dr_dstress;
233  Real sin_angle = std::sin(psi(intnl));
234  Real mean_stress = stress.trace() / 3.0;
235  RankTwoTensor dmean_stress = stress.dtrace() / 3.0;
236  Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
237  if (std::abs(sin3Lode) <= _sin3tt)
238  {
239  // the non-edge-smoothed version
240  std::vector<Real> eigvals;
241  std::vector<RankTwoTensor> deigvals;
242  std::vector<RankFourTensor> d2eigvals;
243  stress.dsymmetricEigenvalues(eigvals, deigvals);
244  stress.d2symmetricEigenvalues(d2eigvals);
245 
246  Real tmp = eigvals[2] - eigvals[0] + (eigvals[2] + eigvals[0] - 2 * mean_stress) * sin_angle;
247  RankTwoTensor dtmp =
248  deigvals[2] - deigvals[0] + (deigvals[2] + deigvals[0] - 2 * dmean_stress) * sin_angle;
249  Real denom = std::sqrt(smooth(stress) + 0.25 * Utility::pow<2>(tmp));
250  Real denom3 = Utility::pow<3>(denom);
251  Real d2smooth_over_denom = d2smooth(stress) / denom;
252  RankTwoTensor numer = dsmooth(stress) * dmean_stress + 0.5 * tmp * dtmp;
253 
254  dr_dstress = 0.25 * tmp *
255  (d2eigvals[2] - d2eigvals[0] + (d2eigvals[2] + d2eigvals[0]) * sin_angle) / denom;
256 
257  for (unsigned i = 0; i < 3; ++i)
258  for (unsigned j = 0; j < 3; ++j)
259  for (unsigned k = 0; k < 3; ++k)
260  for (unsigned l = 0; l < 3; ++l)
261  {
262  dr_dstress(i, j, k, l) +=
263  0.5 * d2smooth_over_denom * dmean_stress(i, j) * dmean_stress(k, l);
264  dr_dstress(i, j, k, l) += 0.25 * dtmp(i, j) * dtmp(k, l) / denom;
265  dr_dstress(i, j, k, l) -= 0.25 * numer(i, j) * numer(k, l) / denom3;
266  }
267  }
268  else
269  {
270  // the edge-smoothed version
271  Real aaa, bbb, ccc;
272  abbo(sin3Lode, sin_angle, aaa, bbb, ccc);
273  RankTwoTensor dsin3Lode = stress.dsin3Lode(_lode_cutoff);
274  Real kk = aaa + bbb * sin3Lode + ccc * Utility::pow<2>(sin3Lode);
275  RankTwoTensor dkk = (bbb + 2 * ccc * sin3Lode) * dsin3Lode;
276  RankFourTensor d2kk = (bbb + 2 * ccc * sin3Lode) * stress.d2sin3Lode(_lode_cutoff);
277  for (unsigned i = 0; i < 3; ++i)
278  for (unsigned j = 0; j < 3; ++j)
279  for (unsigned k = 0; k < 3; ++k)
280  for (unsigned l = 0; l < 3; ++l)
281  d2kk(i, j, k, l) += 2 * ccc * dsin3Lode(i, j) * dsin3Lode(k, l);
282 
283  Real sibar2 = stress.secondInvariant();
284  RankTwoTensor dsibar2 = stress.dsecondInvariant();
285  RankFourTensor d2sibar2 = stress.d2secondInvariant();
286 
287  Real denom = std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk));
288  Real denom3 = Utility::pow<3>(denom);
289  Real d2smooth_over_denom = d2smooth(stress) / denom;
290  RankTwoTensor numer_full =
291  0.5 * dsmooth(stress) * dmean_stress + 0.5 * dsibar2 * kk * kk + sibar2 * kk * dkk;
292 
293  dr_dstress = (0.5 * d2sibar2 * Utility::pow<2>(kk) + sibar2 * kk * d2kk) / denom;
294  for (unsigned i = 0; i < 3; ++i)
295  for (unsigned j = 0; j < 3; ++j)
296  for (unsigned k = 0; k < 3; ++k)
297  for (unsigned l = 0; l < 3; ++l)
298  {
299  dr_dstress(i, j, k, l) +=
300  0.5 * d2smooth_over_denom * dmean_stress(i, j) * dmean_stress(k, l);
301  dr_dstress(i, j, k, l) +=
302  (dsibar2(i, j) * dkk(k, l) * kk + dkk(i, j) * dsibar2(k, l) * kk +
303  sibar2 * dkk(i, j) * dkk(k, l)) /
304  denom;
305  dr_dstress(i, j, k, l) -= numer_full(i, j) * numer_full(k, l) / denom3;
306  }
307  }
308  return dr_dstress;
309 }
virtual Real dsmooth(const RankTwoTensor &stress) const
returns the da/dstress_mean - see doco for _tip_scheme
virtual Real psi(const Real internal_param) const
dilation angle as a function of internal parameter
virtual Real smooth(const RankTwoTensor &stress) const
returns the &#39;a&#39; parameter - see doco for _tip_scheme
void abbo(const Real sin3lode, const Real sin_angle, Real &aaa, Real &bbb, Real &ccc) const
Computes Abbo et al&#39;s A, B and C parameters.
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
virtual Real d2smooth(const RankTwoTensor &stress) const
returns the d^2a/dstress_mean^2 - see doco for _tip_scheme
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 TensorMechanicsPlasticMohrCoulomb::dphi ( const Real  internal_param) const
protectedvirtual

d(phi)/d(internal_param);

Definition at line 387 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dyieldFunction_dintnl().

388 {
389  return _phi.derivative(internal_param);
390 }
virtual Real derivative(Real intnl) const
const TensorMechanicsHardeningModel & _phi
Hardening model for phi.
Real TensorMechanicsPlasticMohrCoulomb::dpsi ( const Real  internal_param) const
protectedvirtual

d(psi)/d(internal_param);

Definition at line 399 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dflowPotential_dintnl().

400 {
401  return _psi.derivative(internal_param);
402 }
virtual Real derivative(Real intnl) const
const TensorMechanicsHardeningModel & _psi
Hardening model for psi.
Real TensorMechanicsPlasticMohrCoulomb::dsmooth ( const RankTwoTensor &  stress) const
protectedvirtual

returns the da/dstress_mean - see doco for _tip_scheme

Definition at line 462 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by df_dsig(), dflowPotential_dintnl(), and dflowPotential_dstress().

463 {
464  Real dsmoother2 = 0;
465  if (_tip_scheme == "cap")
466  {
467  Real x = stress.trace() / 3.0 - _cap_start;
468  Real p = 0;
469  Real dp_dx = 0;
470  if (x > 0)
471  {
472  p = x * (1 - std::exp(-_cap_rate * x));
473  dp_dx = (1 - std::exp(-_cap_rate * x)) + x * _cap_rate * std::exp(-_cap_rate * x);
474  }
475  dsmoother2 += 2 * p * dp_dx;
476  }
477  return dsmoother2;
478 }
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*sinphi + sqrt(a + s_bar^2 K^2) - C*cosphi where "a" depends...
Real TensorMechanicsPlasticMohrCoulomb::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 184 of file TensorMechanicsPlasticMohrCoulomb.C.

186 {
187  Real sin_angle = std::sin(phi(intnl));
188  Real cos_angle = std::cos(phi(intnl));
189  Real dsin_angle = cos_angle * dphi(intnl);
190  Real dcos_angle = -sin_angle * dphi(intnl);
191 
192  Real mean_stress = stress.trace() / 3.0;
193  Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
194  if (std::abs(sin3Lode) <= _sin3tt)
195  {
196  // the non-edge-smoothed version
197  std::vector<Real> eigvals;
198  stress.symmetricEigenvalues(eigvals);
199  Real tmp = eigvals[2] - eigvals[0] + (eigvals[2] + eigvals[0] - 2 * mean_stress) * sin_angle;
200  Real dtmp = (eigvals[2] + eigvals[0] - 2 * mean_stress) * dsin_angle;
201  Real denom = std::sqrt(smooth(stress) + 0.25 * Utility::pow<2>(tmp));
202  return mean_stress * dsin_angle + 0.25 * tmp * dtmp / denom - dcohesion(intnl) * cos_angle -
203  cohesion(intnl) * dcos_angle;
204  }
205  else
206  {
207  // the edge-smoothed version
208  Real aaa, bbb, ccc;
209  abbo(sin3Lode, sin_angle, aaa, bbb, ccc);
210  Real daaa, dbbb, dccc;
211  dabbo(sin3Lode, sin_angle, daaa, dbbb, dccc);
212  Real kk = aaa + bbb * sin3Lode + ccc * Utility::pow<2>(sin3Lode);
213  Real dkk = (daaa + dbbb * sin3Lode + dccc * Utility::pow<2>(sin3Lode)) * dsin_angle;
214  Real sibar2 = stress.secondInvariant();
215  Real denom = std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk));
216  return mean_stress * dsin_angle + sibar2 * kk * dkk / denom - dcohesion(intnl) * cos_angle -
217  cohesion(intnl) * dcos_angle;
218  }
219 }
virtual Real smooth(const RankTwoTensor &stress) const
returns the &#39;a&#39; parameter - see doco for _tip_scheme
virtual Real dcohesion(const Real internal_param) const
d(cohesion)/d(internal_param);
void abbo(const Real sin3lode, const Real sin_angle, Real &aaa, Real &bbb, Real &ccc) const
Computes Abbo et al&#39;s A, B and C parameters.
virtual Real dphi(const Real internal_param) const
d(phi)/d(internal_param);
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
virtual Real cohesion(const Real internal_param) const
cohesion as a function of internal parameter
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
virtual Real phi(const Real internal_param) const
friction angle as a function of internal parameter
void dabbo(const Real sin3lode, const Real sin_angle, Real &daaa, Real &dbbb, Real &dccc) const
Computes derivatives of Abbo et al&#39;s A, B and C parameters wrt sin_angle.
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 TensorMechanicsPlasticMohrCoulomb::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 176 of file TensorMechanicsPlasticMohrCoulomb.C.

178 {
179  Real sinphi = std::sin(phi(intnl));
180  return df_dsig(stress, sinphi);
181 }
RankTwoTensor df_dsig(const RankTwoTensor &stress, const Real sin_angle) const
d(yieldFunction)/d(stress), but with the ability to put friction or dilation angle into the result ...
virtual Real phi(const Real internal_param) const
friction angle as a function of internal parameter
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 TensorMechanicsPlasticMohrCoulomb::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 222 of file TensorMechanicsPlasticMohrCoulomb.C.

223 {
224  Real sinpsi = std::sin(psi(intnl));
225  return df_dsig(stress, sinpsi);
226 }
virtual Real psi(const Real internal_param) const
dilation angle as a function of internal parameter
RankTwoTensor df_dsig(const RankTwoTensor &stress, const Real sin_angle) const
d(yieldFunction)/d(stress), but with the ability to put friction or dilation angle into the result ...
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 TensorMechanicsPlasticMohrCoulomb::modelName ( ) const
overridevirtual

Implements TensorMechanicsPlasticModel.

Definition at line 503 of file TensorMechanicsPlasticMohrCoulomb.C.

504 {
505  return "MohrCoulomb";
506 }
unsigned TensorMechanicsPlasticModel::numberSurfaces ( ) const
virtualinherited
Real TensorMechanicsPlasticMohrCoulomb::phi ( const Real  internal_param) const
protectedvirtual

friction angle as a function of internal parameter

Definition at line 381 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dyieldFunction_dintnl(), dyieldFunction_dstress(), TensorMechanicsPlasticMohrCoulomb(), and yieldFunction().

382 {
383  return _phi.value(internal_param);
384 }
const TensorMechanicsHardeningModel & _phi
Hardening model for phi.
virtual Real value(Real intnl) const
Real TensorMechanicsPlasticMohrCoulomb::psi ( const Real  internal_param) const
protectedvirtual

dilation angle as a function of internal parameter

Definition at line 393 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by dflowPotential_dintnl(), dflowPotential_dstress(), flowPotential(), and TensorMechanicsPlasticMohrCoulomb().

394 {
395  return _psi.value(internal_param);
396 }
virtual Real value(Real intnl) const
const TensorMechanicsHardeningModel & _psi
Hardening model for psi.
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 TensorMechanicsPlasticMohrCoulomb::smooth ( const RankTwoTensor &  stress) const
protectedvirtual

returns the 'a' parameter - see doco for _tip_scheme

Definition at line 447 of file TensorMechanicsPlasticMohrCoulomb.C.

Referenced by df_dsig(), dflowPotential_dintnl(), dflowPotential_dstress(), dyieldFunction_dintnl(), and yieldFunction().

448 {
449  Real smoother2 = _small_smoother2;
450  if (_tip_scheme == "cap")
451  {
452  Real x = stress.trace() / 3.0 - _cap_start;
453  Real p = 0;
454  if (x > 0)
455  p = x * (1 - std::exp(-_cap_rate * x));
456  smoother2 += Utility::pow<2>(p);
457  }
458  return smoother2;
459 }
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*sinphi + sqrt(a + s_bar^2 K^2) - C*cosphi where "a" depends...
Real _small_smoother2
Square of tip smoothing parameter to smooth the cone at mean_stress = T.
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 TensorMechanicsPlasticMohrCoulomb::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 110 of file TensorMechanicsPlasticMohrCoulomb.C.

111 {
112  Real mean_stress = stress.trace() / 3.0;
113  Real sinphi = std::sin(phi(intnl));
114  Real cosphi = std::cos(phi(intnl));
115  Real sin3Lode = stress.sin3Lode(_lode_cutoff, 0);
116  if (std::abs(sin3Lode) <= _sin3tt)
117  {
118  // the non-edge-smoothed version
119  std::vector<Real> eigvals;
120  stress.symmetricEigenvalues(eigvals);
121  return mean_stress * sinphi +
122  std::sqrt(smooth(stress) +
123  0.25 * Utility::pow<2>(eigvals[2] - eigvals[0] +
124  (eigvals[2] + eigvals[0] - 2 * mean_stress) * sinphi)) -
125  cohesion(intnl) * cosphi;
126  }
127  else
128  {
129  // the edge-smoothed version
130  Real aaa, bbb, ccc;
131  abbo(sin3Lode, sinphi, aaa, bbb, ccc);
132  Real kk = aaa + bbb * sin3Lode + ccc * Utility::pow<2>(sin3Lode);
133  Real sibar2 = stress.secondInvariant();
134  return mean_stress * sinphi + std::sqrt(smooth(stress) + sibar2 * Utility::pow<2>(kk)) -
135  cohesion(intnl) * cosphi;
136  }
137 }
virtual Real smooth(const RankTwoTensor &stress) const
returns the &#39;a&#39; parameter - see doco for _tip_scheme
void abbo(const Real sin3lode, const Real sin_angle, Real &aaa, Real &bbb, Real &ccc) const
Computes Abbo et al&#39;s A, B and C parameters.
Real _lode_cutoff
if secondInvariant < _lode_cutoff then set Lode angle to zero. This is to guard against precision-los...
virtual Real cohesion(const Real internal_param) const
cohesion as a function of internal parameter
Real _sin3tt
sin(3*_tt) - useful for making comparisons with Lode angle
virtual Real phi(const Real internal_param) const
friction angle as a function of internal parameter
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 TensorMechanicsPlasticMohrCoulomb::_cap_rate
protected

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

Definition at line 77 of file TensorMechanicsPlasticMohrCoulomb.h.

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

Real TensorMechanicsPlasticMohrCoulomb::_cap_start
protected

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

Definition at line 74 of file TensorMechanicsPlasticMohrCoulomb.h.

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

const TensorMechanicsHardeningModel& TensorMechanicsPlasticMohrCoulomb::_cohesion
protected

Hardening model for cohesion.

Definition at line 52 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by cohesion(), and dcohesion().

Real TensorMechanicsPlasticMohrCoulomb::_cos3tt
protected

cos(3*_tt)

Definition at line 89 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by abbo(), and dabbo().

Real TensorMechanicsPlasticMohrCoulomb::_cos6tt
protected

cos(6*_tt)

Definition at line 95 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by abbo(), and dabbo().

Real TensorMechanicsPlasticMohrCoulomb::_costt
protected

cos(_tt)

Definition at line 83 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by abbo(), and dabbo().

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 TensorMechanicsPlasticMohrCoulomb::_lode_cutoff
protected

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

Definition at line 101 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by df_dsig(), dflowPotential_dintnl(), dflowPotential_dstress(), dyieldFunction_dintnl(), TensorMechanicsPlasticMohrCoulomb(), and yieldFunction().

const TensorMechanicsHardeningModel& TensorMechanicsPlasticMohrCoulomb::_phi
protected

Hardening model for phi.

Definition at line 55 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by dphi(), and phi().

const TensorMechanicsHardeningModel& TensorMechanicsPlasticMohrCoulomb::_psi
protected

Hardening model for psi.

Definition at line 58 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by dpsi(), and psi().

Real TensorMechanicsPlasticMohrCoulomb::_sin3tt
protected

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

Definition at line 92 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by abbo(), dabbo(), df_dsig(), dflowPotential_dintnl(), dflowPotential_dstress(), dyieldFunction_dintnl(), and yieldFunction().

Real TensorMechanicsPlasticMohrCoulomb::_sin6tt
protected

sin(6*_tt)

Definition at line 98 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by abbo(), and dabbo().

Real TensorMechanicsPlasticMohrCoulomb::_sintt
protected

sin(_tt)

Definition at line 86 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by abbo(), and dabbo().

Real TensorMechanicsPlasticMohrCoulomb::_small_smoother2
protected

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

Definition at line 71 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by smooth().

MooseEnum TensorMechanicsPlasticMohrCoulomb::_tip_scheme
protected

The yield function is modified to f = s_m*sinphi + sqrt(a + s_bar^2 K^2) - C*cosphi 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 68 of file TensorMechanicsPlasticMohrCoulomb.h.

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

Real TensorMechanicsPlasticMohrCoulomb::_tt
protected

edge smoothing parameter, in radians

Definition at line 80 of file TensorMechanicsPlasticMohrCoulomb.h.

Referenced by TensorMechanicsPlasticMohrCoulomb().


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