void
InteractionIntegral::computeTFields(RankTwoTensor & aux_stress, RankTwoTensor & grad_disp)
{
Real t = _theta;
Real st = std::sin(t);
Real ct = std::cos(t);
Real stsq = Utility::pow<2>(st);
Real ctsq = Utility::pow<2>(ct);
Real ctcu = Utility::pow<3>(ct);
Real oneOverPiR = 1.0 / (libMesh::pi * _r);
aux_stress.zero();
aux_stress(0, 0) = -oneOverPiR * ctcu;
aux_stress(0, 1) = -oneOverPiR * st * ctsq;
aux_stress(1, 0) = -oneOverPiR * st * ctsq;
aux_stress(1, 1) = -oneOverPiR * ct * stsq;
aux_stress(2, 2) = -oneOverPiR * _poissons_ratio * (ctcu + ct * stsq);
grad_disp.zero();
grad_disp(0, 0) = oneOverPiR / (4.0 * _youngs_modulus) *
(ct * (4.0 * Utility::pow<2>(_poissons_ratio) - 3.0 + _poissons_ratio) -
std::cos(3.0 * t) * (1.0 + _poissons_ratio));
grad_disp(0, 1) = -oneOverPiR / (4.0 * _youngs_modulus) *
(st * (4.0 * Utility::pow<2>(_poissons_ratio) - 3.0 + _poissons_ratio) +
std::sin(3.0 * t) * (1.0 + _poissons_ratio));
}
bool
stznewHEVPFlowRatePowerLawJ2::computeDirection(unsigned int qp, RankTwoTensor & val) const
{
RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
// Real s_xx = _tensor[qp](0,0);
// Real s_yy = _tensor[qp](1,1);
// Real tau_xy= _tensor[qp](0,1);
// Real s_mean = 1.0/3.0*(s_xx+s_yy);
// Real PI = 3.1415926;
// Real tau_max = std::pow((s_xx-s_yy)/2*(s_xx-s_yy)/2+tau_xy*tau_xy,0.5);
// Real eqv_stress = tau_max;
// RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
Real eqv_stress = computeEqvStress(pk2_dev, _ce[qp]);
RankTwoTensor dirnew ;
Real anglec;
Real angles;
Real PI= 3.1415926;
Real theta= 0.25*PI+0.5*(_phiangle/180.0*PI);
anglec = std::cos(theta);
angles = std::sin(theta);
dirnew.zero();
dirnew(0,0)=2.0*anglec*angles;
dirnew(1,1)=-2.0*anglec*angles;
val.zero();
if (eqv_stress > _strength[qp])
{ val = 1.5/eqv_stress * _ce[qp] * pk2_dev * _ce[qp];
//val = 1.5/eqv_stress*pk2_dev*_ce[qp];
// val = dirnew;
//
//
}
return true;
}
Real
PorousFlowDispersiveFlux::computeQpResidual()
{
RealVectorValue flux = 0.0;
RealVectorValue velocity;
Real velocity_abs;
RankTwoTensor v2;
RankTwoTensor dispersion;
dispersion.zero();
Real diffusion;
for (unsigned int ph = 0; ph < _num_phases; ++ph)
{
// Diffusive component
diffusion = _porosity_qp[_qp] * _tortuosity[_qp][ph] * _diffusion_coeff[_qp][ph][_fluid_component];
// Calculate Darcy velocity
velocity = (_permeability[_qp] * (_grad_p[_qp][ph] - _fluid_density_qp[_qp][ph] *
_gravity) * _relative_permeability[_qp][ph] / _fluid_viscosity[_qp][ph]);
velocity_abs = std::sqrt(velocity * velocity);
if (velocity_abs > 0.0)
{
v2.vectorOuterProduct(velocity, velocity);
// Add longitudinal dispersion to diffusive component
diffusion += _disp_trans[ph] * velocity_abs;
dispersion = (_disp_long[ph] - _disp_trans[ph]) * v2 / velocity_abs;
}
flux += _fluid_density_qp[_qp][ph] * (diffusion * _identity_tensor + dispersion) * _grad_mass_frac[_qp][ph][_fluid_component];
}
return _grad_test[_i][_qp] * flux;
}
bool
HEVPFlowRatePowerLawJ2::computeDirection(unsigned int qp, RankTwoTensor & val) const
{
RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
Real eqv_stress = computeEqvStress(pk2_dev, _ce[qp]);
val.zero();
if (eqv_stress > 0.0)
val = 1.5 / eqv_stress * _ce[qp] * pk2_dev * _ce[qp];
return true;
}
bool
FlowRateModel::computeFlowDirection(RankTwoTensor & flow_dirn,
const RankTwoTensor & pk2,
const RankTwoTensor & ce,
const std::vector<Real> & /*internal_var*/,
const unsigned int /*start_index*/,
const unsigned int /*size*/) const
{
RankTwoTensor pk2_dev = computePK2Deviatoric(pk2, ce);
Real eqv_stress = computeEqvStress(pk2_dev, ce);
flow_dirn.zero();
if (eqv_stress > 0.0)
flow_dirn = 3.0/(2.0 * eqv_stress) * ce * pk2_dev * ce;
return true;
}
bool
stzRHEVPFlowRatePowerLawJ2::computeTensorDerivative(unsigned int qp, const std::string & coupled_var_name, RankTwoTensor & val) const
{
val.zero();
if (_pk2_prop_name == coupled_var_name)
{
RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
Real eqv_stress = computeEqvStress(pk2_dev, _ce[qp]);
Real dflowrate_dseqv;
if (eqv_stress>_strength[qp])
// dflowrate_dseqv = 1/_t_tau*std::exp(-1/_chiv[qp])*std::exp(eqv_stress/_grain_pressure/_chiv[qp])* \
(1.0/(_grain_pressure*_chiv[qp])*(1.0-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress));
dflowrate_dseqv = _v*std::exp(-1/_chiv[qp])*(1.0-1.0/(eqv_stress*eqv_stress));
RankTwoTensor tau = pk2_dev * _ce[qp];
RankTwoTensor dseqv_dpk2dev;
dseqv_dpk2dev.zero();
if (eqv_stress > _strength[qp])
dseqv_dpk2dev = 1.5/eqv_stress * tau * _ce[qp];
RankTwoTensor ce_inv = _ce[qp].inverse();
RankFourTensor dpk2dev_dpk2;
for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
for (unsigned int l = 0; l < LIBMESH_DIM; ++l)
{
dpk2dev_dpk2(i, j, k, l) = 0.0;
if (i==k && j==l)
dpk2dev_dpk2(i, j, k, l) = 1.0;
dpk2dev_dpk2(i, j, k, l) -= ce_inv(i, j) * _ce[qp](k, l)/3.0;
}
val = dflowrate_dseqv * dpk2dev_dpk2.transposeMajor() * dseqv_dpk2dev;
}
return true;
}
bool
HEVPFlowRatePowerLawJ2::computeTensorDerivative(unsigned int qp,
const std::string & coupled_var_name,
RankTwoTensor & val) const
{
val.zero();
if (_pk2_prop_name == coupled_var_name)
{
RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
Real eqv_stress = computeEqvStress(pk2_dev, _ce[qp]);
Real dflowrate_dseqv = _ref_flow_rate * _flow_rate_exponent *
std::pow(eqv_stress / _strength[qp], _flow_rate_exponent - 1.0) /
_strength[qp];
RankTwoTensor tau = pk2_dev * _ce[qp];
RankTwoTensor dseqv_dpk2dev;
dseqv_dpk2dev.zero();
if (eqv_stress > 0.0)
dseqv_dpk2dev = 1.5 / eqv_stress * tau * _ce[qp];
RankTwoTensor ce_inv = _ce[qp].inverse();
RankFourTensor dpk2dev_dpk2;
for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
for (unsigned int l = 0; l < LIBMESH_DIM; ++l)
{
dpk2dev_dpk2(i, j, k, l) = 0.0;
if (i == k && j == l)
dpk2dev_dpk2(i, j, k, l) = 1.0;
dpk2dev_dpk2(i, j, k, l) -= ce_inv(i, j) * _ce[qp](k, l) / 3.0;
}
val = dflowrate_dseqv * dpk2dev_dpk2.transposeMajor() * dseqv_dpk2dev;
}
return true;
}
void
RecomputeRadialReturn::computeStress(RankTwoTensor & strain_increment,
RankTwoTensor & inelastic_strain_increment,
RankTwoTensor & stress_new)
{
// Given the stretching, update the inelastic strain
// Compute the stress in the intermediate configuration while retaining the stress history
// compute the deviatoric trial stress and trial strain from the current intermediate configuration
RankTwoTensor deviatoric_trial_stress = stress_new.deviatoric();
// compute the effective trial stress
Real dev_trial_stress_squared = deviatoric_trial_stress.doubleContraction(deviatoric_trial_stress);
Real effective_trial_stress = std::sqrt(3.0 / 2.0 * dev_trial_stress_squared);
//If the effective trial stress is zero, so should the inelastic strain increment be zero
//In that case skip the entire iteration if the effective trial stress is zero
if (effective_trial_stress != 0.0)
{
computeStressInitialize(effective_trial_stress);
// Use Newton sub-iteration to determine the scalar effective inelastic strain increment
Real scalar_effective_inelastic_strain = 0;
unsigned int iteration = 0;
Real residual = 10; // use a large number here to guarantee at least one loop through while
Real norm_residual = 10;
Real first_norm_residual = 10;
// create an output string with iteration information when errors occur
std::string iteration_output;
while (iteration < _max_its &&
norm_residual > _absolute_tolerance &&
(norm_residual/first_norm_residual) > _relative_tolerance)
{
iterationInitialize(scalar_effective_inelastic_strain);
residual = computeResidual(effective_trial_stress, scalar_effective_inelastic_strain);
norm_residual = std::abs(residual);
if (iteration == 0)
{
first_norm_residual = norm_residual;
if (first_norm_residual == 0)
first_norm_residual = 1;
}
Real derivative = computeDerivative(effective_trial_stress, scalar_effective_inelastic_strain);
scalar_effective_inelastic_strain -= residual / derivative;
if (_output_iteration_info || _output_iteration_info_on_error)
{
iteration_output = "In the element " + Moose::stringify(_current_elem->id()) +
+ " and the qp point " + Moose::stringify(_qp) + ": \n" +
+ " iteration = " + Moose::stringify(iteration ) + "\n" +
+ " effective trial stress = " + Moose::stringify(effective_trial_stress) + "\n" +
+ " scalar effective inelastic strain = " + Moose::stringify(scalar_effective_inelastic_strain) +"\n" +
+ " relative residual = " + Moose::stringify(norm_residual/first_norm_residual) + "\n" +
+ " relative tolerance = " + Moose::stringify(_relative_tolerance) + "\n" +
+ " absolute residual = " + Moose::stringify(norm_residual) + "\n" +
+ " absolute tolerance = " + Moose::stringify(_absolute_tolerance) + "\n";
}
iterationFinalize(scalar_effective_inelastic_strain);
++iteration;
}
if (_output_iteration_info)
_console << iteration_output << std::endl;
if (iteration == _max_its &&
norm_residual > _absolute_tolerance &&
(norm_residual/first_norm_residual) > _relative_tolerance)
{
if (_output_iteration_info_on_error)
Moose::err << iteration_output;
mooseError("Exceeded maximum iterations in RecomputeRadialReturn solve for material: " << _name << ". Rerun with 'output_iteration_info_on_error = true' for more information.");
}
// compute inelastic strain increments while avoiding a potential divide by zero
inelastic_strain_increment = deviatoric_trial_stress;
inelastic_strain_increment *= (3.0 / 2.0 * scalar_effective_inelastic_strain / effective_trial_stress);
}
else
inelastic_strain_increment.zero();
strain_increment -= inelastic_strain_increment;
stress_new = _elasticity_tensor[_qp] * (strain_increment + _elastic_strain_old[_qp]);
computeStressFinalize(inelastic_strain_increment);
}
void mooseSetToZero<RankTwoTensor>(RankTwoTensor & v)
{
v.zero();
}
bool
TensorMechanicsPlasticTensileMulti::doReturnMap(const RankTwoTensor & trial_stress, const 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
{
mooseAssert(dpm.size() == 3, "TensorMechanicsPlasticTensileMulti size of dpm should be 3 but it is " << dpm.size());
std::vector<Real> eigvals;
RankTwoTensor eigvecs;
trial_stress.symmetricEigenvaluesEigenvectors(eigvals, eigvecs);
eigvals[0] += _shift;
eigvals[2] -= _shift;
Real str = tensile_strength(intnl_old);
yf.resize(3);
yf[0] = eigvals[0] - str;
yf[1] = eigvals[1] - str;
yf[2] = eigvals[2] - str;
if (yf[0] <= _f_tol && yf[1] <= _f_tol && yf[2] <= _f_tol)
{
// purely elastic (trial_stress, intnl_old)
trial_stress_inadmissible = false;
return true;
}
trial_stress_inadmissible = true;
delta_dp.zero();
returned_stress.zero();
// In the following i often assume that E_ijkl is
// for an isotropic situation. This reduces FLOPS
// substantially which is important since the returnMap
// is potentially the most compute-intensive function
// of a simulation.
// In many comments i write the general expression, and
// i hope that might guide future coders if they are
// generalising to a non-istropic E_ijkl
// n[alpha] = E_ijkl*r[alpha]_kl expressed in principal stress space
// (alpha = 0, 1, 2, corresponding to the three surfaces)
// Note that in principal stress space, the flow
// directions are, expressed in 'vector' form,
// r[0] = (1,0,0), r[1] = (0,1,0), r[2] = (0,0,1).
// Similar for _n:
// so _n[0] = E_ij00*r[0], _n[1] = E_ij11*r[1], _n[2] = E_ij22*r[2]
// In the following I assume that the E_ijkl is
// for an isotropic situation.
// In the anisotropic situation, we couldn't express
// the flow directions as vectors in the same principal
// stress space as the stress: they'd be full rank-2 tensors
std::vector<std::vector<Real> > n(3);
for (unsigned i = 0 ; i < 3 ; ++i)
n[i].resize(3);
n[0][0] = E_ijkl(0,0,0,0);
n[0][1] = E_ijkl(1,1,0,0);
n[0][2] = E_ijkl(2,2,0,0);
n[1][0] = E_ijkl(0,0,1,1);
n[1][1] = E_ijkl(1,1,1,1);
n[1][2] = E_ijkl(2,2,1,1);
n[2][0] = E_ijkl(0,0,2,2);
n[2][1] = E_ijkl(1,1,2,2);
n[2][2] = E_ijkl(2,2,2,2);
// With non-zero Poisson's ratio and hardening
// it is not computationally cheap to know whether
// the trial stress will return to the tip, edge,
// or plane. The following is correct for zero
// Poisson's ratio and no hardening, and at least
// gives a not-completely-stupid guess in the
// more general case.
// trial_order[0] = type of return to try first
// trial_order[1] = type of return to try second
// trial_order[2] = type of return to try third
std::vector<int> trial_order(3);
if (yf[0] > 0) // all the yield functions are positive, since eigvals are ordered eigvals[0] <= eigvals[1] <= eigvals[2]
{
trial_order[0] = tip;
trial_order[1] = edge;
trial_order[2] = plane;
}
else if (yf[1] > 0) // two yield functions are positive
{
trial_order[0] = edge;
trial_order[1] = tip;
trial_order[2] = plane;
}
else
{
trial_order[0] = plane;
trial_order[1] = edge;
trial_order[2] = tip;
}
unsigned trial;
bool nr_converged;
for (trial = 0 ; trial < 3 ; ++trial)
{
switch (trial_order[trial])
{
case tip:
nr_converged = returnTip(eigvals, n, dpm, returned_stress, intnl_old, 0);
break;
case edge:
nr_converged = returnEdge(eigvals, n, dpm, returned_stress, intnl_old, 0);
break;
case plane:
nr_converged = returnPlane(eigvals, n, dpm, returned_stress, intnl_old, 0);
break;
}
str = tensile_strength(intnl_old + dpm[0] + dpm[1] + dpm[2]);
if (nr_converged && KuhnTuckerOK(returned_stress, dpm, str))
break;
}
if (trial == 3)
{
Moose::err << "Trial stress = \n";
trial_stress.print(Moose::err);
Moose::err << "Internal parameter = " << intnl_old << "\n";
mooseError("TensorMechanicsPlasticTensileMulti: FAILURE! You probably need to implement a line search\n");
// failure - must place yield function values at trial stress into yf
str = tensile_strength(intnl_old);
yf[0] = eigvals[0] - str;
yf[1] = eigvals[1] - str;
yf[2] = eigvals[2] - str;
return false;
}
// success
returned_intnl = intnl_old;
for (unsigned i = 0 ; i < 3 ; ++i)
{
yf[i] = returned_stress(i, i) - str;
delta_dp(i, i) = dpm[i];
returned_intnl += dpm[i];
}
returned_stress = eigvecs*returned_stress*(eigvecs.transpose());
delta_dp = eigvecs*delta_dp*(eigvecs.transpose());
return true;
}
bool
stznewHEVPFlowRatePowerLawJ2::computeTensorDerivative(unsigned int qp, const std::string & coupled_var_name, RankTwoTensor & val) const
{
val.zero();
if (_pk2_prop_name == coupled_var_name)
{
RankTwoTensor pk2_dev = computePK2Deviatoric(_pk2[qp], _ce[qp]);
// Real s_xx = _tensor[qp](0,0);
// Real s_yy = _tensor[qp](1,1);
// Real tau_xy= _tensor[qp](0,1);
// Real s_mean = 1.0/3.0*(s_xx+s_yy);
// Real PI = 3.1415926;
// Real tau_max = std::pow((s_xx-s_yy)/2*(s_xx-s_yy)/2+tau_xy*tau_xy,0.5);
// Real eqv_stress = tau_max ;
Real eqv_stress = computeEqvStress(pk2_dev, _ce[qp]);
Real _pressure_eff=_grain_pressure-_biot*_pf[qp];
// Real _t_taunew = _agrain[qp]/std::sqrt(_grain_pressure/_rho);
Real _t_taunew = _agrain[qp]/std::sqrt(_pressure_eff/_rho);
// Real dflowrate_dseqv = _ref_flow_rate * _flow_rate_exponent * std::pow(eqv_stress/_strength[qp],_flow_rate_exponent-1.0)/_strength[qp];
// stz
// Real dflowrate_dseqv = 1/_t_tau*std::exp(-1/_chiv[qp])*std::exp(eqv_stress/_grain_pressure/_chiv[qp])* \
// (1/(_grain_pressure*_chiv[qp])*(1-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress))*(eqv_stress>_strength[qp]);
//
Real dflowrate_dseqv;
if (eqv_stress>_strength[qp])
// dflowrate_dseqv = 1/_t_tau*std::exp(-1/_chiv[qp])*std::exp(eqv_stress/_grain_pressure/_chiv[qp])* \
(1.0/(_grain_pressure*_chiv[qp])*(1.0-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress));
// Original Stuff
{
dflowrate_dseqv = 1/_t_taunew*std::exp(-1/_chiv[qp])*std::exp(eqv_stress/_pressure_eff/_chiv[qp])* \
(1.0/(_pressure_eff*_chiv[qp])*(1.0-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress));
} // Modified
// {
//dflowrate_dseqv = 1.0/_t_taunew*std::exp(-1.0/_chiv[qp])*(-1.0*_strength[qp])/(eqv_stress*eqv_stress);
// } // dflowrate_dseqv = 1/_t_tau*std::exp(-1/_chi)*std::exp(eqv_stress/_grain_pressure/_chi)* \
// (1.0/(_grain_pressure*_chi)*(1.0-_strength[qp]/eqv_stress)+_strength[qp]/(eqv_stress*eqv_stress));
RankTwoTensor tau = pk2_dev * _ce[qp];
RankTwoTensor dseqv_dpk2dev;
dseqv_dpk2dev.zero();
if (eqv_stress > _strength[qp])
dseqv_dpk2dev = 1.5/eqv_stress * tau * _ce[qp];
RankTwoTensor ce_inv = _ce[qp].inverse();
RankFourTensor dpk2dev_dpk2;
for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
for (unsigned int k = 0; k < LIBMESH_DIM; ++k)
for (unsigned int l = 0; l < LIBMESH_DIM; ++l)
{
dpk2dev_dpk2(i, j, k, l) = 0.0;
if (i==k && j==l)
dpk2dev_dpk2(i, j, k, l) = 1.0;
dpk2dev_dpk2(i, j, k, l) -= ce_inv(i, j) * _ce[qp](k, l)/3.0;
}
val = dflowrate_dseqv * dpk2dev_dpk2.transposeMajor() * dseqv_dpk2dev;
}
return true;
}
void
InteractionIntegral::computeAuxFields(RankTwoTensor & aux_stress, RankTwoTensor & grad_disp)
{
RealVectorValue k(0.0);
if (_sif_mode == SifMethod::KI)
k(0) = 1.0;
else if (_sif_mode == SifMethod::KII)
k(1) = 1.0;
else if (_sif_mode == SifMethod::KIII)
k(2) = 1.0;
Real t = _theta;
Real t2 = _theta / 2.0;
Real tt2 = 3.0 * _theta / 2.0;
Real st = std::sin(t);
Real ct = std::cos(t);
Real st2 = std::sin(t2);
Real ct2 = std::cos(t2);
Real stt2 = std::sin(tt2);
Real ctt2 = std::cos(tt2);
Real ct2sq = Utility::pow<2>(ct2);
Real ct2cu = Utility::pow<3>(ct2);
Real sqrt2PiR = std::sqrt(2.0 * libMesh::pi * _r);
// Calculate auxiliary stress tensor
aux_stress.zero();
aux_stress(0, 0) =
1.0 / sqrt2PiR * (k(0) * ct2 * (1.0 - st2 * stt2) - k(1) * st2 * (2.0 + ct2 * ctt2));
aux_stress(1, 1) = 1.0 / sqrt2PiR * (k(0) * ct2 * (1.0 + st2 * stt2) + k(1) * st2 * ct2 * ctt2);
aux_stress(0, 1) = 1.0 / sqrt2PiR * (k(0) * ct2 * st2 * ctt2 + k(1) * ct2 * (1.0 - st2 * stt2));
aux_stress(0, 2) = -1.0 / sqrt2PiR * k(2) * st2;
aux_stress(1, 2) = 1.0 / sqrt2PiR * k(2) * ct2;
// plane stress
// Real s33 = 0;
// plane strain
aux_stress(2, 2) = _poissons_ratio * (aux_stress(0, 0) + aux_stress(1, 1));
aux_stress(1, 0) = aux_stress(0, 1);
aux_stress(2, 0) = aux_stress(0, 2);
aux_stress(2, 1) = aux_stress(1, 2);
// Calculate x1 derivative of auxiliary displacements
grad_disp.zero();
grad_disp(0, 0) = k(0) / (4.0 * _shear_modulus * sqrt2PiR) *
(ct * ct2 * _kappa + ct * ct2 - 2.0 * ct * ct2cu + st * st2 * _kappa +
st * st2 - 6.0 * st * st2 * ct2sq) +
k(1) / (4.0 * _shear_modulus * sqrt2PiR) *
(ct * st2 * _kappa + ct * st2 + 2.0 * ct * st2 * ct2sq - st * ct2 * _kappa +
3.0 * st * ct2 - 6.0 * st * ct2cu);
grad_disp(0, 1) = k(0) / (4.0 * _shear_modulus * sqrt2PiR) *
(ct * st2 * _kappa + ct * st2 - 2.0 * ct * st2 * ct2sq - st * ct2 * _kappa -
5.0 * st * ct2 + 6.0 * st * ct2cu) +
k(1) / (4.0 * _shear_modulus * sqrt2PiR) *
(-ct * ct2 * _kappa + 3.0 * ct * ct2 - 2.0 * ct * ct2cu -
st * st2 * _kappa + 3.0 * st * st2 - 6.0 * st * st2 * ct2sq);
grad_disp(0, 2) = k(2) / (_shear_modulus * sqrt2PiR) * (st2 * ct - ct2 * st);
}
void
ComputeMultipleInelasticStress::updateQpState(RankTwoTensor & elastic_strain_increment,
RankTwoTensor & combined_inelastic_strain_increment)
{
if (_output_iteration_info == true)
{
_console << std::endl
<< "iteration output for ComputeMultipleInelasticStress solve:"
<< " time=" << _t << " int_pt=" << _qp << std::endl;
}
Real l2norm_delta_stress;
Real first_l2norm_delta_stress = 1.0;
unsigned int counter = 0;
std::vector<RankTwoTensor> inelastic_strain_increment;
inelastic_strain_increment.resize(_num_models);
for (unsigned i_rmm = 0; i_rmm < _models.size(); ++i_rmm)
inelastic_strain_increment[i_rmm].zero();
RankTwoTensor stress_max, stress_min;
do
{
for (unsigned i_rmm = 0; i_rmm < _num_models; ++i_rmm)
{
_models[i_rmm]->setQp(_qp);
// initially assume the strain is completely elastic
elastic_strain_increment = _strain_increment[_qp];
// and subtract off all inelastic strain increments calculated so far
// except the one that we're about to calculate
for (unsigned j_rmm = 0; j_rmm < _num_models; ++j_rmm)
if (i_rmm != j_rmm)
elastic_strain_increment -= inelastic_strain_increment[j_rmm];
// form the trial stress, with the check for changed elasticity constants
if (_is_elasticity_tensor_guaranteed_isotropic || !_perform_finite_strain_rotations)
{
_stress[_qp] =
_elasticity_tensor[_qp] * (_elastic_strain_old[_qp] + elastic_strain_increment);
// InitialStress Deprecation: remove these lines
if (_perform_finite_strain_rotations)
rotateQpInitialStress();
addQpInitialStress();
}
else
_stress[_qp] = _stress_old[_qp] + _elasticity_tensor[_qp] * elastic_strain_increment;
// given a trial stress (_stress[_qp]) and a strain increment (elastic_strain_increment)
// let the i^th model produce an admissible stress (as _stress[_qp]), and decompose
// the strain increment into an elastic part (elastic_strain_increment) and an
// inelastic part (inelastic_strain_increment[i_rmm])
computeAdmissibleState(i_rmm,
elastic_strain_increment,
inelastic_strain_increment[i_rmm],
_consistent_tangent_operator[i_rmm]);
if (i_rmm == 0)
{
stress_max = _stress[_qp];
stress_min = _stress[_qp];
}
else
{
for (unsigned int i = 0; i < LIBMESH_DIM; ++i)
{
for (unsigned int j = 0; j < LIBMESH_DIM; ++j)
{
if (_stress[_qp](i, j) > stress_max(i, j))
stress_max(i, j) = _stress[_qp](i, j);
else if (stress_min(i, j) > _stress[_qp](i, j))
stress_min(i, j) = _stress[_qp](i, j);
}
}
}
}
// now check convergence in the stress:
// once the change in stress is within tolerance after each recompute material
// consider the stress to be converged
l2norm_delta_stress = (stress_max - stress_min).L2norm();
if (counter == 0 && l2norm_delta_stress > 0.0)
first_l2norm_delta_stress = l2norm_delta_stress;
if (_output_iteration_info == true)
{
_console << "stress iteration number = " << counter << "\n"
<< " relative l2 norm delta stress = "
<< (0 == first_l2norm_delta_stress ? 0
: l2norm_delta_stress / first_l2norm_delta_stress)
<< "\n"
<< " stress convergence relative tolerance = " << _relative_tolerance << "\n"
<< " absolute l2 norm delta stress = " << l2norm_delta_stress << "\n"
<< " stress convergence absolute tolerance = " << _absolute_tolerance << std::endl;
}
++counter;
} while (counter < _max_iterations && l2norm_delta_stress > _absolute_tolerance &&
(l2norm_delta_stress / first_l2norm_delta_stress) > _relative_tolerance &&
_num_models != 1);
if (counter == _max_iterations && l2norm_delta_stress > _absolute_tolerance &&
(l2norm_delta_stress / first_l2norm_delta_stress) > _relative_tolerance)
throw MooseException("Max stress iteration hit during ComputeMultipleInelasticStress solve!");
combined_inelastic_strain_increment.zero();
for (unsigned i_rmm = 0; i_rmm < _num_models; ++i_rmm)
combined_inelastic_strain_increment +=
_inelastic_weights[i_rmm] * inelastic_strain_increment[i_rmm];
if (_fe_problem.currentlyComputingJacobian())
computeQpJacobianMult();
_matl_timestep_limit[_qp] = 0.0;
for (unsigned i_rmm = 0; i_rmm < _num_models; ++i_rmm)
_matl_timestep_limit[_qp] += 1.0 / _models[i_rmm]->computeTimeStepLimit();
if (MooseUtils::absoluteFuzzyEqual(_matl_timestep_limit[_qp], 0.0))
{
_matl_timestep_limit[_qp] = std::numeric_limits<Real>::max();
}
else
{
_matl_timestep_limit[_qp] = 1.0 / _matl_timestep_limit[_qp];
}
}
bool
TensorMechanicsPlasticMohrCoulombMulti::doReturnMap(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
{
mooseAssert(dpm.size() == 6, "TensorMechanicsPlasticMohrCoulombMulti size of dpm should be 6 but it is " << dpm.size());
std::vector<Real> eigvals;
RankTwoTensor eigvecs;
trial_stress.symmetricEigenvaluesEigenvectors(eigvals, eigvecs);
eigvals[0] += _shift;
eigvals[2] -= _shift;
Real sinphi = std::sin(phi(intnl_old));
Real cosphi = std::cos(phi(intnl_old));
Real coh = cohesion(intnl_old);
Real cohcos = coh*cosphi;
yieldFunctionEigvals(eigvals[0], eigvals[1], eigvals[2], sinphi, cohcos, yf);
if (yf[0] <= _f_tol && yf[1] <= _f_tol && yf[2] <= _f_tol && yf[3] <= _f_tol && yf[4] <= _f_tol && yf[5] <= _f_tol)
{
// purely elastic (trial_stress, intnl_old)
trial_stress_inadmissible = false;
return true;
}
trial_stress_inadmissible = true;
delta_dp.zero();
returned_stress = RankTwoTensor();
// these are the normals to the 6 yield surfaces, which are const because of the assumption of no psi hardening
std::vector<RealVectorValue> norm(6);
const Real sinpsi = std::sin(psi(intnl_old));
const Real oneminus = 0.5*(1 - sinpsi);
const Real oneplus = 0.5*(1 + sinpsi);
norm[0](0) = oneplus; norm[0](1) = -oneminus; norm[0](2) = 0;
norm[1](0) = -oneminus; norm[1](1) = oneplus; norm[1](2) = 0;
norm[2](0) = oneplus; norm[2](1) = 0; norm[2](2) = -oneminus;
norm[3](0) = -oneminus; norm[3](1) = 0; norm[3](2) = oneplus;
norm[4](0) = 0; norm[4](1) = oneplus; norm[4](2) = -oneminus;
norm[5](0) = 0; norm[5](1) = -oneminus; norm[5](2) = oneplus;
// the flow directions are these norm multiplied by Eijkl.
// I call the flow directions "n".
// In the following I assume that the Eijkl is
// for an isotropic situation. Then I don't have to
// rotate to the principal-stress frame, and i don't
// have to worry about strange off-diagonal things
std::vector<RealVectorValue> n(6);
for (unsigned ys = 0; ys < 6; ++ys)
for (unsigned i = 0; i < 3; ++i)
for (unsigned j = 0; j < 3; ++j)
n[ys](i) += E_ijkl(i,i,j,j)*norm[ys](j);
const Real mag_E = E_ijkl(0, 0, 0, 0);
// With non-zero Poisson's ratio and hardening
// it is not computationally cheap to know whether
// the trial stress will return to the tip, edge,
// or plane. The following at least
// gives a not-completely-stupid guess
// trial_order[0] = type of return to try first
// trial_order[1] = type of return to try second
// trial_order[2] = type of return to try third
// trial_order[3] = type of return to try fourth
// trial_order[4] = type of return to try fifth
// In the following the "binary" stuff indicates the
// deactive (0) and active (1) surfaces, eg
// 110100 means that surfaces 0, 1 and 3 are active
// and 2, 4 and 5 are deactive
const unsigned int number_of_return_paths = 5;
std::vector<int> trial_order(number_of_return_paths);
if (yf[1] > _f_tol && yf[3] > _f_tol && yf[5] > _f_tol)
{
trial_order[0] = tip110100;
trial_order[1] = edge010100;
trial_order[2] = plane000100;
trial_order[3] = edge000101;
trial_order[4] = tip010101;
}
else if (yf[1] <= _f_tol && yf[3] > _f_tol && yf[5] > _f_tol)
{
trial_order[0] = edge000101;
trial_order[1] = plane000100;
trial_order[2] = tip110100;
trial_order[3] = tip010101;
trial_order[4] = edge010100;
}
else if (yf[1] <= _f_tol && yf[3] > _f_tol && yf[5] <= _f_tol)
{
trial_order[0] = plane000100;
trial_order[1] = edge000101;
trial_order[2] = edge010100;
trial_order[3] = tip110100;
trial_order[4] = tip010101;
}
else
{
trial_order[0] = edge010100;
trial_order[1] = plane000100;
trial_order[2] = edge000101;
trial_order[3] = tip110100;
trial_order[4] = tip010101;
}
unsigned trial;
bool nr_converged = false;
bool kt_success = false;
std::vector<RealVectorValue> ntip(3);
std::vector<Real> dpmtip(3);
for (trial = 0; trial < number_of_return_paths; ++trial)
{
switch (trial_order[trial])
{
case tip110100:
for (unsigned int i = 0; i < 3; ++i)
{
ntip[0](i) = n[0](i);
ntip[1](i) = n[1](i);
ntip[2](i) = n[3](i);
}
kt_success = returnTip(eigvals, ntip, dpmtip, returned_stress, intnl_old, sinphi, cohcos, 0, nr_converged, ep_plastic_tolerance, yf);
if (nr_converged && kt_success)
{
dpm[0] = dpmtip[0];
dpm[1] = dpmtip[1];
dpm[3] = dpmtip[2];
dpm[2] = dpm[4] = dpm[5] = 0;
}
break;
case tip010101:
for (unsigned int i = 0; i < 3; ++i)
{
ntip[0](i) = n[1](i);
ntip[1](i) = n[3](i);
ntip[2](i) = n[5](i);
}
kt_success = returnTip(eigvals, ntip, dpmtip, returned_stress, intnl_old, sinphi, cohcos, 0, nr_converged, ep_plastic_tolerance, yf);
if (nr_converged && kt_success)
{
dpm[1] = dpmtip[0];
dpm[3] = dpmtip[1];
dpm[5] = dpmtip[2];
dpm[0] = dpm[2] = dpm[4] = 0;
}
break;
case edge000101:
kt_success = returnEdge000101(eigvals, n, dpm, returned_stress, intnl_old, sinphi, cohcos, 0, mag_E, nr_converged, ep_plastic_tolerance, yf);
break;
case edge010100:
kt_success = returnEdge010100(eigvals, n, dpm, returned_stress, intnl_old, sinphi, cohcos, 0, mag_E, nr_converged, ep_plastic_tolerance, yf);
break;
case plane000100:
kt_success = returnPlane(eigvals, n, dpm, returned_stress, intnl_old, sinphi, cohcos, 0, nr_converged, ep_plastic_tolerance, yf);
break;
}
if (nr_converged && kt_success)
break;
}
if (trial == number_of_return_paths)
{
sinphi = std::sin(phi(intnl_old));
cosphi = std::cos(phi(intnl_old));
coh = cohesion(intnl_old);
cohcos = coh*cosphi;
yieldFunctionEigvals(eigvals[0], eigvals[1], eigvals[2], sinphi, cohcos, yf);
Moose::err << "Trial stress = \n";
trial_stress.print(Moose::err);
Moose::err << "which has eigenvalues = " << eigvals[0] << " " << eigvals[1] << " " << eigvals[2] << "\n";
Moose::err << "and yield functions = " << yf[0] << " " << yf[1] << " " << yf[2] << " " << yf[3] << " " << yf[4] << " " << yf[5] << "\n";
Moose::err << "Internal parameter = " << intnl_old << "\n";
mooseError("TensorMechanicsPlasticMohrCoulombMulti: FAILURE! You probably need to implement a line search if your hardening is too severe, or you need to tune your tolerances (eg, yield_function_tolerance should be a little smaller than (young modulus)*ep_plastic_tolerance).\n");
return false;
}
// success
returned_intnl = intnl_old;
for (unsigned i = 0; i < 6; ++i)
returned_intnl += dpm[i];
for (unsigned i = 0; i < 6; ++i)
for (unsigned j = 0; j < 3; ++j)
delta_dp(j, j) += dpm[i]*norm[i](j);
returned_stress = eigvecs*returned_stress*(eigvecs.transpose());
delta_dp = eigvecs*delta_dp*(eigvecs.transpose());
return true;
}
Real
PorousFlowDispersiveFlux::computeQpJac(unsigned int jvar) const
{
// If the variable is not a valid PorousFlow variable, set the Jacobian to 0
if (_dictator.notPorousFlowVariable(jvar))
return 0.0;
const unsigned int pvar = _dictator.porousFlowVariableNum(jvar);
RealVectorValue velocity;
Real velocity_abs;
RankTwoTensor v2;
RankTwoTensor dispersion;
dispersion.zero();
Real diffusion;
RealVectorValue flux = 0.0;
RealVectorValue dflux = 0.0;
for (unsigned int ph = 0; ph < _num_phases; ++ph)
{
// Diffusive component
diffusion = _porosity_qp[_qp] * _tortuosity[_qp][ph] * _diffusion_coeff[_qp][ph][_fluid_component];
// Calculate Darcy velocity
velocity = (_permeability[_qp] * (_grad_p[_qp][ph] - _fluid_density_qp[_qp][ph] *
_gravity) * _relative_permeability[_qp][ph] / _fluid_viscosity[_qp][ph]);
velocity_abs = std::sqrt(velocity * velocity);
if (velocity_abs > 0.0)
{
v2.vectorOuterProduct(velocity, velocity);
// Add longitudinal dispersion to diffusive component
diffusion += _disp_trans[ph] * velocity_abs;
dispersion = (_disp_long[ph] - _disp_trans[ph]) * v2 / velocity_abs;
}
// Derivative of Darcy velocity
RealVectorValue dvelocity = _dpermeability_dvar[_qp][pvar] * _phi[_j][_qp] * (_grad_p[_qp][ph] - _fluid_density_qp[_qp][ph]*_gravity);
for (unsigned i = 0; i < LIBMESH_DIM; ++i)
dvelocity += _dpermeability_dgradvar[_qp][i][pvar] * _grad_phi[_j][_qp](i) * (_grad_p[_qp][ph] - _fluid_density_qp[_qp][ph] * _gravity);
dvelocity += _permeability[_qp] * (_grad_phi[_j][_qp] * _dgrad_p_dgrad_var[_qp][ph][pvar] - _phi[_j][_qp] * _dfluid_density_qp_dvar[_qp][ph][pvar] * _gravity);
dvelocity += _permeability[_qp] * (_dgrad_p_dvar[_qp][ph][pvar] * _phi[_j][_qp]);
Real dvelocity_abs = 0.0;
if (velocity_abs > 0.0)
dvelocity_abs = velocity * dvelocity / velocity_abs;
// Derivative of diffusion term (note: dispersivity is assumed constant)
Real ddiffusion = _phi[_j][_qp] * _dporosity_qp_dvar[_qp][pvar] * _tortuosity[_qp][ph] * _diffusion_coeff[_qp][ph][_fluid_component];
ddiffusion += _phi[_j][_qp] * _porosity_qp[_qp] * _dtortuosity_dvar[_qp][ph][pvar] * _diffusion_coeff[_qp][ph][_fluid_component];
ddiffusion += _phi[_j][_qp] * _porosity_qp[_qp] * _tortuosity[_qp][ph] * _ddiffusion_coeff_dvar[_qp][ph][_fluid_component][pvar];
ddiffusion += _disp_trans[ph] * dvelocity_abs;
// Derivative of dispersion term (note: dispersivity is assumed constant)
RankTwoTensor ddispersion;
ddispersion.zero();
if (velocity_abs > 0.0)
{
RankTwoTensor dv2a, dv2b;
dv2a.vectorOuterProduct(velocity, dvelocity);
dv2b.vectorOuterProduct(dvelocity, velocity);
ddispersion = (_disp_long[ph] - _disp_trans[ph]) * (dv2a + dv2b) / velocity_abs;
ddispersion -= (_disp_long[ph] - _disp_trans[ph]) * v2 * dvelocity_abs / velocity_abs / velocity_abs;
}
dflux += _phi[_j][_qp] * _dfluid_density_qp_dvar[_qp][ph][pvar] * (diffusion * _identity_tensor + dispersion) * _grad_mass_frac[_qp][ph][_fluid_component];
dflux += _fluid_density_qp[_qp][ph] * (ddiffusion * _identity_tensor + ddispersion) * _grad_mass_frac[_qp][ph][_fluid_component];
dflux += _fluid_density_qp[_qp][ph] * (diffusion * _identity_tensor + dispersion) * _dmass_frac_dvar[_qp][ph][_fluid_component][pvar] * _grad_phi[_j][_qp];
}
return _grad_test[_i][_qp] * dflux;
}