OpPlasticTools Namespace Reference

Classes
struct	BubbleTauPolynomialBase
struct	CommonData
	[Common data] More...
struct	OpCalculateConstraintLhs_dEP
struct	OpCalculateConstraintLhs_dTAU
struct	OpCalculateConstraintLhs_dU
struct	OpCalculateConstraintRhs
struct	OpCalculatePlasticFlowLhs_dEP
struct	OpCalculatePlasticFlowLhs_dTAU
struct	OpCalculatePlasticFlowLhs_dU
struct	OpCalculatePlasticFlowRhs
struct	OpCalculatePlasticInternalForceLhs_dEP
struct	OpCalculatePlasticInternalForceLhs_dTAU
struct	OpCalculatePlasticSurfaceAndFlow
struct	OpGetGaussPtsPlasticState
struct	OpPlasticStress
struct	OpPostProcPlastic

Functions
auto	diff_tensor ()
	[Operators definitions] More...
auto	symm_L_tensor ()
auto	diff_symmetrize ()
template<typename T1 >
auto	deviator (Tensor2_symmetric< T1, 3 > &t_stress)
auto	diff_deviator (Ddg< double, 3, 3 > &&t_diff_stress)
template<typename T >
auto	get_effective_stress (Tensor2_symmetric< T, 3 > &t_stress, Tensor2_symmetric< T, 3 > &t_plastic_strain)
auto	hardening (long double tau)
auto	hardening_dtau (long double tau)
auto	plastic_surface (Tensor2_symmetric< double, 3 > &&t_stress_deviator)
auto	plastic_flow (long double f, Tensor2_symmetric< double, 3 > &&t_dev_stress, Ddg< double, 3, 3 > &t_diff_deviator)
template<typename T >
auto	diff_plastic_flow_dstress (long double f, Tensor2_symmetric< T, 3 > &t_flow, Ddg< double, 3, 3 > &t_diff_deviator)
template<typename T >
auto	diff_plastic_flow_dstrain (Ddg< T, 3, 3 > &t_D, Ddg< double, 3, 3 > &&t_diff_plastic_flow_dstress)
template<typename T >
auto	diff_plastic_flow_kin_hard_dstrain (Ddg< T, 3, 3 > &t_D, Ddg< double, 3, 3 > &&t_diff_plastic_flow_dstress)
double	constrain_abs (long double x)
double	constraint_sign (long double x)
double	w (long double tau_dot, long double f, long double hardening)
double	constraint (long double tau_dot, long double f, long double hardening)
double	diff_constrain_dtau_dot (long double tau_dot, long double f, long double hardening)
auto	diff_constrain_df (long double tau_dot, long double f, long double hardening)
auto	diff_constrain_dsigma_y (long double tau_dot, long double f, long double hardening)
template<typename T >
auto	diff_constrain_dstress (long double &&diff_constrain_df, Tensor2_symmetric< T, 3 > &t_plastic_flow)
template<typename T1 , typename T2 >
auto	diff_constrain_dstrain (Ddg< T1, 3, 3 > &t_D, Tensor2_symmetric< T2, 3 > &&t_diff_constrain_dstress)
template<typename T1 , typename T2 >
auto	diff_constrain_kin_hard_dstrain (Ddg< T1, 3, 3 > &t_D, Tensor2_symmetric< T2, 3 > &&t_diff_constrain_dstress)

Variables
constexpr double	sqrt2by3 = 0.816496580927726

Function Documentation

constrain_abs()

double OpPlasticTools::constrain_abs ( long double  x )

inline

Definition at line 397 of file PlasticOperators.hpp.

{ return std::abs(x); };

constraint()

double OpPlasticTools::constraint ( long double  tau_dot, long double  f, long double  hardening  )

inline

Definition at line 414 of file PlasticOperators.hpp.

                                                {
  auto &cn = (*cache).cn_pl;
  auto &visH = (*cache).visH;
  auto &sigmaY = (*cache).sigmaY;
  return visH * tau_dot +
         (sigmaY / 2) * ((cn * tau_dot - (f - hardening) / sigmaY) -
                         constrain_abs(w(tau_dot, f, hardening)));
};

constraint_sign()

double OpPlasticTools::constraint_sign ( long double  x )

inline

Definition at line 399 of file PlasticOperators.hpp.

                                             {
  if (x > 0)
    return 1;
  else if (x < 0)
    return -1;
  else
    return 0;
};

deviator()

template<typename T1 >

auto OpPlasticTools::deviator ( Tensor2_symmetric< T1, 3 > &  t_stress )

inline

Definition at line 259 of file PlasticOperators.hpp.

                                                         {
  Tensor2_symmetric<double, 3> t_dev;
  t_dev(I, J) = 0;
  constexpr double third = boost::math::constants::third<double>();
  const double trace = t_stress(i, i);
 
  t_dev(i, j) = t_stress(i, j);
  t_dev(0, 0) -= trace * third;
  t_dev(1, 1) -= trace * third;
  t_dev(2, 2) -= trace * third;
  return t_dev;
};

diff_constrain_df()

auto OpPlasticTools::diff_constrain_df ( long double  tau_dot, long double  f, long double  hardening  )

inline

Definition at line 433 of file PlasticOperators.hpp.

                                                     {
  return (-1 - constraint_sign(w(tau_dot, f, hardening))) / 2;
};

diff_constrain_dsigma_y()

auto OpPlasticTools::diff_constrain_dsigma_y ( long double  tau_dot, long double  f, long double  hardening  )

inline

Definition at line 438 of file PlasticOperators.hpp.

                                                           {
  return (1 + constraint_sign(w(tau_dot, f, hardening))) / 2;
}

diff_constrain_dstrain()

template<typename T1 , typename T2 >

auto OpPlasticTools::diff_constrain_dstrain ( Ddg< T1, 3, 3 > &  t_D, Tensor2_symmetric< T2, 3 > &&  t_diff_constrain_dstress  )

inline

Definition at line 453 of file PlasticOperators.hpp.

                                                                            {
  Tensor2_symmetric<double, 3> t_diff_constrain_dstrain;
  t_diff_constrain_dstrain(k, l) =
      t_diff_constrain_dstress(i, j) * t_D(i, j, k, l);
  return t_diff_constrain_dstrain;
};

diff_constrain_dstress()

template<typename T >

auto OpPlasticTools::diff_constrain_dstress ( long double &&  diff_constrain_df, Tensor2_symmetric< T, 3 > &  t_plastic_flow  )

inline

Definition at line 444 of file PlasticOperators.hpp.

                                                                            {
  Tensor2_symmetric<double, 3> t_diff_constrain_dstress;
  t_diff_constrain_dstress(i, j) = diff_constrain_df * t_plastic_flow(i, j);
  return t_diff_constrain_dstress;
};

diff_constrain_dtau_dot()

double OpPlasticTools::diff_constrain_dtau_dot ( long double  tau_dot, long double  f, long double  hardening  )

inline

Definition at line 424 of file PlasticOperators.hpp.

                                                             {
  auto &cn = (*cache).cn_pl;
  auto &visH = (*cache).visH;
  auto &sigmaY = (*cache).sigmaY;
  return visH +
         (sigmaY / 2) * (cn - cn * constraint_sign(w(tau_dot, f, hardening)));
};

diff_constrain_kin_hard_dstrain()

template<typename T1 , typename T2 >

auto OpPlasticTools::diff_constrain_kin_hard_dstrain ( Ddg< T1, 3, 3 > &  t_D, Tensor2_symmetric< T2, 3 > &&  t_diff_constrain_dstress  )

inline

Definition at line 462 of file PlasticOperators.hpp.

                                                                             {
  Tensor2_symmetric<double, 3> t_diff_constrain_kin_hard_dstrain;
  t_diff_constrain_kin_hard_dstrain(k, l) =
      t_diff_constrain_dstress(i, j) * t_D(i, j, k, l) +
      1.5 * (*cache).C1_k * t_diff_constrain_dstress(k, l);
  return t_diff_constrain_kin_hard_dstrain;
};

diff_deviator()

auto OpPlasticTools::diff_deviator ( Ddg< double, 3, 3 > &&  t_diff_stress )

inline

Definition at line 272 of file PlasticOperators.hpp.

                                                             {
  Ddg<double, 3, 3> t_diff_deviator;
  t_diff_deviator(I, J, K, L) = 0;
  for (int ii = 0; ii != 3; ++ii)
    for (int jj = ii; jj != 3; ++jj)
      for (int kk = 0; kk != 3; ++kk)
        for (int ll = kk; ll != 3; ++ll)
          t_diff_deviator(ii, jj, kk, ll) = t_diff_stress(ii, jj, kk, ll);
 
  constexpr double third = boost::math::constants::third<double>();
 
  t_diff_deviator(0, 0, 0, 0) = 1. - third;
  t_diff_deviator(0, 0, 1, 1) = -third;
  t_diff_deviator(0, 0, 2, 2) = -third;
 
  t_diff_deviator(1, 1, 0, 0) = -third;
  t_diff_deviator(1, 1, 1, 1) = 1. - third;
  t_diff_deviator(1, 1, 2, 2) = -third;
 
  t_diff_deviator(2, 2, 0, 0) = -third;
  t_diff_deviator(2, 2, 1, 1) = -third;
  t_diff_deviator(2, 2, 2, 2) = 1. - third;
 
  return t_diff_deviator;
};

diff_plastic_flow_dstrain()

template<typename T >

auto OpPlasticTools::diff_plastic_flow_dstrain ( Ddg< T, 3, 3 > &  t_D, Ddg< double, 3, 3 > &&  t_diff_plastic_flow_dstress  )

inline

Definition at line 377 of file PlasticOperators.hpp.

                                                                           {
  Ddg<double, 3, 3> t_diff_flow;
  t_diff_flow(i, j, k, l) =
      t_diff_plastic_flow_dstress(i, j, m, n) * t_D(m, n, k, l);
 
  return t_diff_flow;
};

diff_plastic_flow_dstress()

template<typename T >

auto OpPlasticTools::diff_plastic_flow_dstress ( long double  f, Tensor2_symmetric< T, 3 > &  t_flow, Ddg< double, 3, 3 > &  t_diff_deviator  )

inline

Definition at line 363 of file PlasticOperators.hpp.

                                                                          {
  Ddg<double, 3, 3> t_diff_flow;
  t_diff_flow(i, j, k, l) =
      ((1.5) * (t_diff_deviator(M, N, i, j) * t_diff_deviator(M, N, k, l) -
                2. / 3. * t_flow(i, j) * t_flow(k, l))) /
      f;
 
  return t_diff_flow;
};

diff_plastic_flow_kin_hard_dstrain()

template<typename T >

auto OpPlasticTools::diff_plastic_flow_kin_hard_dstrain ( Ddg< T, 3, 3 > &  t_D, Ddg< double, 3, 3 > &&  t_diff_plastic_flow_dstress  )

inline

Definition at line 387 of file PlasticOperators.hpp.

                                                                        {
  Ddg<double, 3, 3> t_diff_flow_kin_hard;
  t_diff_flow_kin_hard(i, j, k, l) =
      t_diff_plastic_flow_dstress(i, j, m, n) * t_D(m, n, k, l) +
      1.5 * (*cache).C1_k * t_diff_plastic_flow_dstress(i, j, k, l);
 
  return t_diff_flow_kin_hard;
};

diff_symmetrize()

auto OpPlasticTools::diff_symmetrize ( )

inline

Definition at line 256 of file PlasticOperators.hpp.

{ return (*cache).Is; };

diff_tensor()

auto OpPlasticTools::diff_tensor ( )

inline

[Operators definitions]

[Lambda functions]

Definition at line 220 of file PlasticOperators.hpp.

                          {
  Ddg<double, 3, 3> t_diff;
  constexpr auto t_kd = Kronecker_Delta_symmetric<int>();
  t_diff(i, j, k, l) = (t_kd(i, k) ^ t_kd(j, l)) / 4.;
  return t_diff;
};

get_effective_stress()

template<typename T >

auto OpPlasticTools::get_effective_stress ( Tensor2_symmetric< T, 3 > &  t_stress, Tensor2_symmetric< T, 3 > &  t_plastic_strain  )

inline

Definition at line 299 of file PlasticOperators.hpp.

                                                                            {
 
  Tensor2_symmetric<double, 3> stress_tmp;
 
  stress_tmp(i, j) =
      t_stress(i, j) - 1.5 * (*cache).C1_k * t_plastic_strain(i, j);
 
  return stress_tmp;
};

hardening()

auto OpPlasticTools::hardening ( long double  tau )

inline

Definition at line 311 of file PlasticOperators.hpp.

                                       {
  return (*cache).H * tau + (*cache).Q_inf * (1. - exp(-(*cache).b_iso * tau)) +
         (*cache).sigmaY;
}

hardening_dtau()

auto OpPlasticTools::hardening_dtau ( long double  tau )

inline

Definition at line 316 of file PlasticOperators.hpp.

                                            {
  return (*cache).H +
         (*cache).Q_inf * (*cache).b_iso * exp(-(*cache).b_iso * tau);
}

plastic_flow()

auto OpPlasticTools::plastic_flow ( long double  f, Tensor2_symmetric< double, 3 > &&  t_dev_stress, Ddg< double, 3, 3 > &  t_diff_deviator  )

inline

Definition at line 349 of file PlasticOperators.hpp.

                                                             {
  Tensor2_symmetric<double, 3> t_diff_f;
  t_diff_f(k, l) =
      ((1.5) * (t_dev_stress(I, J)) * t_diff_deviator(I, J, k, l)) / f;
 
  return t_diff_f;
};

plastic_surface()

auto OpPlasticTools::plastic_surface ( Tensor2_symmetric< double, 3 > &&  t_stress_deviator )

inline

\[ \begin{split} f&=\sqrt{s_{ij}s_{ij}}\\ A_{ij}&=\frac{\partial f}{\partial \sigma_{ij}}= \frac{1}{f} s_{kl} \frac{\partial s_{kl}}{\partial \sigma_{ij}}\\ \frac{\partial A_{ij}}{\partial \sigma_{kl}}&= \frac{\partial^2 f}{\partial \sigma_{ij}\partial\sigma_{mn}}= \frac{1}{f} \left( \frac{\partial s_{kl}}{\partial \sigma_{mn}}\frac{\partial s_{kl}}{\partial \sigma_{ij}} -A_{mn}A_{ij} \right)\\ \frac{\partial f}{\partial \varepsilon_{ij}}&=A_{mn}D_{mnij} \\ \frac{\partial A_{ij}}{\partial \varepsilon_{kl}}&= \frac{\partial A_{ij}}{\partial \sigma_{mn}} \frac{\partial \sigma_{mn}}{\partial \varepsilon_{kl}}= \frac{\partial A_{ij}}{\partial \sigma_{mn}} D_{mnkl} \end{split} \]

Definition at line 344 of file PlasticOperators.hpp.

                                                                              {
  return std::sqrt(1.5 * t_stress_deviator(I, J) * t_stress_deviator(I, J)) +
         std::numeric_limits<double>::epsilon();
};

symm_L_tensor()

auto OpPlasticTools::symm_L_tensor ( )

inline

Definition at line 227 of file PlasticOperators.hpp.

                            {
  Dg<double, 3, 6> L;
  Index<'L', 6> Li;
  // dg(T 000, T 001, T 002, T 010, T 011, T 012, T 020, T 021, T 022,
  //    T 110, T 111, T 112, T 120, T 121, T 122, T 220, T 221, T 222);
 
  // Tensor2_symmetric_constructor(T data[(3 * 4) / 2], T d00, T d01, T d02, T
  // d11,
  //                               T d12, T d22);
  // Tensor2<double, 3, 3> test_tensor{1., 2., 3., 2., 5., 6., 3., 6., 9.};
  // Tensor1<double, 6> test_vec;
 
  L(i, j, Li) = 0;
  L(0, 0, 0) = 1;
  L(0, 1, 1) = 1;
  L(0, 2, 2) = 1;
  L(1, 0, 1) = 1;
  L(1, 1, 3) = 1;
  L(1, 2, 4) = 1;
  L(2, 0, 2) = 1;
  L(2, 1, 4) = 1;
  L(2, 2, 5) = 1;
 
  // test_vec(Li) = test_tensor(i, j) * L(i, j, Li);
 
  //  (00,  01,  02,  11,  12,  22)
  return L;
}

w()

double OpPlasticTools::w ( long double  tau_dot, long double  f, long double  hardening  )

inline

Definition at line 408 of file PlasticOperators.hpp.

                                                                           {
  auto &cn = (*cache).cn_pl;
  auto &sigmaY = (*cache).sigmaY;
  return (f - hardening) / sigmaY + cn * tau_dot;
};

Variable Documentation

sqrt2by3

constexpr double OpPlasticTools::sqrt2by3 = 0.816496580927726

constexpr

Definition at line 310 of file PlasticOperators.hpp.