Real
volumetricStrain(const SymmTensor & symm_strain)
{
Real value = symm_strain.trace();
value += symm_strain.xx() * symm_strain.yy() + symm_strain.yy() * symm_strain.zz() +
symm_strain.zz() * symm_strain.xx() +
symm_strain.xx() * symm_strain.yy() * symm_strain.zz();
return value;
}
void
CardiacHolzapfel2009Material::computeQpStressProperties(const SymmTensor &C, const SymmTensor & /*E*/)
{
const SymmTensor CC(square(C));
// invariants (We will not need all of them. However, defining them avoids to forget any.)
const Real I1(C.trace());
/*const Real I2(0.5*(I1*I1-CC.trace()));*/
/*const Real I3(_J[_qp]); */
const Real I4f(_Ef[_qp]*(C*_Ef[_qp]));
const Real I4s(_Es[_qp]*(C*_Es[_qp]));
/*const Real I4n(_En[_qp]*(C*_En[_qp])); */
/*const Real I5f(_Ef[_qp]*(CC*_Ef[_qp]));*/
/*const Real I5s(_Es[_qp]*(CC*_Es[_qp]));*/
/*const Real I5n(_En[_qp]*(CC*_En[_qp]));*/
const Real I8fs(_Ef[_qp]*(C*_Es[_qp]));
/*const Real I8fn(_Ef[_qp]*(C*_En[_qp]));*/
/*const Real I8sn(_Es[_qp]*(C*_En[_qp]));*/
// the following will be needed in the stress as well as in the energy and stress_derivative
const Real i_term( _p[A1 ]*std::exp(_p[B1 ]*(I1 -3) ) );
const Real f_term( 2*_p[Af ]*std::exp(_p[Bf ]*(I4f-1)*(I4f-1)) );
const Real s_term( 2*_p[As ]*std::exp(_p[Bs ]*(I4s-1)*(I4s-1)) );
const Real fs_term( _p[Afs]*std::exp(_p[Bfs]* I8fs * I8fs ) );
// elastic energy contribution
_W[_qp] = i_term /(2*_p[B1 ])
+ ( f_term - 2*_p[Af ])/(2*_p[Bf ])
+ ( s_term - 2*_p[As ])/(2*_p[Bs ])
+ (fs_term - 2*_p[Afs])/(2*_p[Bfs]);
// tensors for constructing stress and stress_derivative
const SymmTensor EfEf(kron(_Ef[_qp]));
const SymmTensor EsEs(kron(_Es[_qp]));
const SymmTensor EfEs(kronSym(_Ef[_qp],_Es[_qp]));
// stress
_stress[_qp] = scaledID(i_term) + EfEf*(I4f-1)*f_term + EsEs*(I4s-1)*s_term + EfEs*I8fs*fs_term;
// stress derivative /* fancy lambda function syntax makes things much easier here */
_stress_derivative[_qp].fill_from_minor_iter( [&](const unsigned int M,
const unsigned int N,
const unsigned int P,
const unsigned int Q) -> Real { return _p[B1 ] * i_term * _id(M,N) * _id(P,Q)
+ (1 + (I4f-1)*(I4f-1)*2*_p[Bf ]) * f_term * EfEf(M,N) * EfEf(P,Q)
+ (1 + (I4f-1)*(I4f-1)*2*_p[Bf ]) * s_term * EsEs(M,N) * EsEs(P,Q)
+ (1 + I8fs *2*_p[Bfs]) * fs_term * EfEs(M,N) * EfEs(P,Q); } );
}
void
PLC_LSH::computeLSH( const SymmTensor & strain_increment,
SymmTensor & plastic_strain_increment,
SymmTensor & stress_new )
{
// compute deviatoric trial stress
SymmTensor dev_trial_stress(stress_new);
dev_trial_stress.addDiag( -stress_new.trace()/3 );
// effective trial stress
Real dts_squared = dev_trial_stress.doubleContraction(dev_trial_stress);
Real effective_trial_stress = std::sqrt(1.5 * dts_squared);
// determine if yield condition is satisfied
Real yield_condition = effective_trial_stress - _hardening_variable_old[_qp] - _yield_stress;
_hardening_variable[_qp] = _hardening_variable_old[_qp];
_plastic_strain[_qp] = _plastic_strain_old[_qp];
if (yield_condition > 0) // then use newton iteration to determine effective plastic strain increment
{
unsigned int it = 0;
Real plastic_residual = 0;
Real norm_plas_residual = 10;
Real first_norm_plas_residual = 10;
Real scalar_plastic_strain_increment = 0;
while (it < _max_its &&
norm_plas_residual > _absolute_tolerance &&
(norm_plas_residual/first_norm_plas_residual) > _relative_tolerance)
{
plastic_residual = effective_trial_stress - (3. * _shear_modulus * scalar_plastic_strain_increment) -
_hardening_variable[_qp] - _yield_stress;
norm_plas_residual = std::abs(plastic_residual);
if (it == 0)
{
first_norm_plas_residual = norm_plas_residual;
}
scalar_plastic_strain_increment += plastic_residual / (3. * _shear_modulus + _hardening_constant);
_hardening_variable[_qp] = _hardening_variable_old[_qp] + (_hardening_constant * scalar_plastic_strain_increment);
if (_output_iteration_info == true)
{
_console
<< "pls_it=" << it
<< " trl_strs=" << effective_trial_stress
<< " del_p=" << scalar_plastic_strain_increment
<< " harden=" << _hardening_variable[_qp]
<< " rel_res=" << norm_plas_residual/first_norm_plas_residual
<< " rel_tol=" << _relative_tolerance
<< " abs_res=" << norm_plas_residual
<< " abs_tol=" << _absolute_tolerance
<< std::endl;
}
++it;
}
if (it == _max_its &&
norm_plas_residual > _absolute_tolerance &&
(norm_plas_residual/first_norm_plas_residual) > _relative_tolerance)
{
mooseError("Max sub-newton iteration hit during plasticity increment solve!");
}
if (effective_trial_stress < 0.01)
{
effective_trial_stress = 0.01;
}
plastic_strain_increment = dev_trial_stress;
plastic_strain_increment *= (1.5*scalar_plastic_strain_increment/effective_trial_stress);
SymmTensor elastic_strain_increment(strain_increment);
elastic_strain_increment -= plastic_strain_increment;
// compute stress increment
stress_new = *elasticityTensor() * elastic_strain_increment;
// update stress and plastic strain
stress_new += _stress_old;
_plastic_strain[_qp] += plastic_strain_increment;
} // end of if statement
}
void
ReturnMappingModel::computeStress(const Elem & /*current_elem*/,
const SymmElasticityTensor & elasticityTensor,
const SymmTensor & stress_old,
SymmTensor & strain_increment,
SymmTensor & stress_new,
SymmTensor & inelastic_strain_increment)
{
// compute deviatoric trial stress
SymmTensor dev_trial_stress(stress_new);
dev_trial_stress.addDiag(-dev_trial_stress.trace() / 3.0);
// compute effective trial stress
Real dts_squared = dev_trial_stress.doubleContraction(dev_trial_stress);
Real effective_trial_stress = std::sqrt(1.5 * dts_squared);
// compute effective strain increment
SymmTensor dev_strain_increment(strain_increment);
dev_strain_increment.addDiag(-strain_increment.trace() / 3.0);
_effective_strain_increment = dev_strain_increment.doubleContraction(dev_strain_increment);
_effective_strain_increment = std::sqrt(2.0 / 3.0 * _effective_strain_increment);
const SymmIsotropicElasticityTensor * iso_e_t =
dynamic_cast<const SymmIsotropicElasticityTensor *>(&elasticityTensor);
if (!iso_e_t)
mooseError("Models derived from ReturnMappingModel require a SymmIsotropicElasticityTensor");
_three_shear_modulus = 3.0 * iso_e_t->shearModulus();
computeStressInitialize(effective_trial_stress, elasticityTensor);
Real scalar;
returnMappingSolve(effective_trial_stress, scalar, _console);
// compute inelastic and elastic strain increments
if (_legacy_return_mapping)
{
if (effective_trial_stress < 0.01)
effective_trial_stress = 0.01;
inelastic_strain_increment = dev_trial_stress;
inelastic_strain_increment *= (1.5 * scalar / effective_trial_stress);
}
else
{
if (scalar != 0.0)
inelastic_strain_increment = dev_trial_stress * (1.5 * scalar / effective_trial_stress);
else
inelastic_strain_increment = 0.0;
}
strain_increment -= inelastic_strain_increment;
_effective_inelastic_strain[_qp] = _effective_inelastic_strain_old[_qp] + scalar;
// compute stress increment
stress_new = elasticityTensor * strain_increment;
// update stress
stress_new += stress_old;
computeStressFinalize(inelastic_strain_increment);
}
bool FractureElasticityVoigt::evalStress (double lambda, double mu, double Gc,
const SymmTensor& epsil, double* Phi,
SymmTensor* sigma, Matrix* dSdE,
bool postProc, bool printElm) const
{
PROFILE3("FractureEl::evalStress");
unsigned short int a = 0, b = 0;
// Define a Lambda-function to set up the isotropic constitutive matrix
auto&& setIsotropic = [this,a,b](Matrix& C, double lambda, double mu) mutable
{
for (a = 1; a <= C.rows(); a++)
if (a > nsd)
C(a,a) = mu;
else
{
C(a,a) = 2.0*mu;
for (b = 1; b <= nsd; b++)
C(a,b) += lambda;
}
};
// Define some material constants
double trEps = epsil.trace();
double C0 = trEps >= -epsZ ? Gc*lambda : lambda;
double Cp = Gc*mu;
if (trEps >= -epsZ && trEps <= epsZ)
{
// No strains, stress free configuration
Phi[0] = 0.0;
if (postProc)
Phi[1] = Phi[2] = Phi[3] = 0.0;
if (sigma)
*sigma = 0.0;
if (dSdE)
setIsotropic(*dSdE,C0,Cp);
return true;
}
// Calculate principal strains and the associated directions
Vec3 eps;
std::vector<SymmTensor> M(nsd,SymmTensor(nsd));
{
PROFILE4("Tensor::principal");
if (!epsil.principal(eps,M.data()))
return false;
}
// Split the strain tensor into positive and negative parts
SymmTensor ePos(nsd), eNeg(nsd);
for (a = 0; a < nsd; a++)
if (eps[a] > 0.0)
ePos += eps[a]*M[a];
else if (eps[a] < 0.0)
eNeg += eps[a]*M[a];
if (sigma)
{
// Evaluate the stress tensor
*sigma = C0*trEps;
*sigma += 2.0*mu*(Gc*ePos + eNeg);
}
// Evaluate the tensile energy
Phi[0] = mu*(ePos*ePos).trace();
if (trEps > 0.0) Phi[0] += 0.5*lambda*trEps*trEps;
if (postProc)
{
// Evaluate the compressive energy
Phi[1] = mu*(eNeg*eNeg).trace();
if (trEps < 0.0) Phi[1] += 0.5*lambda*trEps*trEps;
// Evaluate the total strain energy
Phi[2] = Gc*Phi[0] + Phi[1];
// Evaluate the bulk energy
Phi[3] = Gc*(Phi[0] + Phi[1]);
}
else if (sigmaC > 0.0) // Evaluate the crack driving function
Phi[0] = this->MieheCrit56(eps,lambda,mu);
#if INT_DEBUG > 4
std::cout <<"eps_p = "<< eps <<"\n";
for (a = 0; a < nsd; a++)
std::cout <<"M("<< 1+a <<") =\n"<< M[a];
std::cout <<"ePos =\n"<< ePos <<"eNeg =\n"<< eNeg;
if (sigma) std::cout <<"sigma =\n"<< *sigma;
std::cout <<"Phi = "<< Phi[0];
if (postProc) std::cout <<" "<< Phi[1] <<" "<< Phi[2] <<" "<< Phi[3];
std::cout << std::endl;
#else
if (printElm)
{
std::cout <<"g(c) = "<< Gc
<<"\nepsilon =\n"<< epsil <<"eps_p = "<< eps
<<"\nePos =\n"<< ePos <<"eNeg =\n"<< eNeg;
if (sigma) std::cout <<"sigma =\n"<< *sigma;
std::cout <<"Phi = "<< Phi[0];
if (postProc) std::cout <<" "<< Phi[1] <<" "<< Phi[2] <<" "<< Phi[3];
std::cout << std::endl;
}
#endif
if (!dSdE)
return true;
else if (eps[0] == eps[nsd-1])
{
// Hydrostatic pressure
setIsotropic(*dSdE, C0, eps.x > 0.0 ? Cp : mu);
return true;
}
typedef unsigned short int s_ind; // Convenience type definition
// Define a Lambda-function to calculate (lower triangle of) the matrix Qa
auto&& getQ = [this](Matrix& Q, const SymmTensor& Ma, double C)
{
if (C == 0.0) return;
auto&& Mult = [Ma](s_ind i, s_ind j, s_ind k, s_ind l)
{
return Ma(i,j)*Ma(k,l);
};
s_ind i, j, k, l, is, js;
// Normal stresses and strains
for (i = 1; i <= nsd; i++)
for (j = 1; j <= i; j++)
Q(i,j) += C*Mult(i,i,j,j);
is = nsd+1;
for (i = 1; i < nsd; i++)
for (j = i+1; j <= nsd; j++, is++)
{
// Shear stress coupled to normal strain
for (k = 1; k <= nsd; k++)
Q(is,k) += C*Mult(i,j,k,k);
// Shear stress coupled to shear strain
js = nsd+1;
for (k = 1; k < nsd; k++)
for (l = k+1; js <= is; l++, js++)
Q(is,js) += C*Mult(i,j,k,l);
}
};
// Define a Lambda-function to calculate (lower triangle of) the matrix Gab
auto&& getG = [this](Matrix& G, const SymmTensor& Ma,
const SymmTensor& Mb, double C)
{
if (C == 0.0) return;
auto&& Mult = [Ma,Mb](s_ind i, s_ind j, s_ind k, s_ind l)
{
return Ma(i,k)*Mb(j,l) + Ma(i,l)*Mb(j,k) +
Mb(i,k)*Ma(j,l) + Mb(i,l)*Ma(j,k);
};
s_ind i, j, k, l, is, js;
// Normal stresses and strains
for (i = 1; i <= nsd; i++)
for (j = 1; j <= i; j++)
G(i,j) += C*Mult(i,i,j,j);
is = nsd+1;
for (i = 1; i < nsd; i++)
for (j = i+1; j <= nsd; j++, is++)
{
// Shear stress coupled to normal strain
for (k = 1; k <= nsd; k++)
G(is,k) += C*Mult(i,j,k,k);
// Shear stress coupled to shear strain
js = nsd+1;
for (k = 1; k < nsd; k++)
for (l = k+1; js <= is; l++, js++)
G(is,js) += C*Mult(i,j,k,l);
}
};
// Evaluate the stress tangent assuming Voigt notation and symmetry
for (a = 1; a <= nsd; a++)
for (b = 1; b <= a; b++)
(*dSdE)(a,b) = C0;
for (a = 0; a < nsd; a++)
{
double C1 = eps[a] >= 0.0 ? Cp : mu;
getQ(*dSdE, M[a], 2.0*C1);
if (eps[a] != 0.0)
for (b = 0; b < nsd; b++)
if (a != b && eps[a] != eps[b])
getG(*dSdE,M[a],M[b],C1/(1.0-eps[b]/eps[a]));
}
// Account for symmetry
for (b = 2; b <= dSdE->rows(); b++)
for (a = 1; a < b; a++)
(*dSdE)(a,b) = (*dSdE)(b,a);
return true;
}
void
Linear::computeStrain( const unsigned qp,
const SymmTensor & total_strain_old,
SymmTensor & total_strain_new,
SymmTensor & strain_increment )
{
strain_increment.xx( _grad_disp_x[qp](0) );
strain_increment.yy( _grad_disp_y[qp](1) );
strain_increment.zz( _grad_disp_z[qp](2) );
strain_increment.xy( 0.5*(_grad_disp_x[qp](1)+_grad_disp_y[qp](0)) );
strain_increment.yz( 0.5*(_grad_disp_y[qp](2)+_grad_disp_z[qp](1)) );
strain_increment.zx( 0.5*(_grad_disp_z[qp](0)+_grad_disp_x[qp](2)) );
if (_large_strain)
{
strain_increment.xx() += 0.5*(_grad_disp_x[qp](0)*_grad_disp_x[qp](0) +
_grad_disp_y[qp](0)*_grad_disp_y[qp](0) +
_grad_disp_z[qp](0)*_grad_disp_z[qp](0));
strain_increment.yy() += 0.5*(_grad_disp_x[qp](1)*_grad_disp_x[qp](1) +
_grad_disp_y[qp](1)*_grad_disp_y[qp](1) +
_grad_disp_z[qp](1)*_grad_disp_z[qp](1));
strain_increment.zz() += 0.5*(_grad_disp_x[qp](2)*_grad_disp_x[qp](2) +
_grad_disp_y[qp](2)*_grad_disp_y[qp](2) +
_grad_disp_z[qp](2)*_grad_disp_z[qp](2));
strain_increment.xy() += 0.5*(_grad_disp_x[qp](0)*_grad_disp_x[qp](1) +
_grad_disp_y[qp](0)*_grad_disp_y[qp](1) +
_grad_disp_z[qp](0)*_grad_disp_z[qp](1));
strain_increment.yz() += 0.5*(_grad_disp_x[qp](1)*_grad_disp_x[qp](2) +
_grad_disp_y[qp](1)*_grad_disp_y[qp](2) +
_grad_disp_z[qp](1)*_grad_disp_z[qp](2));
strain_increment.zx() += 0.5*(_grad_disp_x[qp](2)*_grad_disp_x[qp](0) +
_grad_disp_y[qp](2)*_grad_disp_y[qp](0) +
_grad_disp_z[qp](2)*_grad_disp_z[qp](0));
}
if (_volumetric_locking_correction)
{
// volumetric locking correction - averaging the volumertic strain over the element
Real volumetric_strain = 0.0;
Real volume = 0.0;
for (unsigned int qp_loop = 0; qp_loop < _solid_model.qrule()->n_points(); ++qp_loop)
{
volumetric_strain += (_grad_disp_x[qp_loop](0) + _grad_disp_y[qp_loop](1) + _grad_disp_z[qp_loop](2)) / 3.0 * _solid_model.JxW(qp_loop);
volume += _solid_model.JxW(qp_loop);
if (_large_strain)
{
volumetric_strain += 0.5 * (_grad_disp_x[qp](0) * _grad_disp_x[qp](0) +
_grad_disp_y[qp](0) * _grad_disp_y[qp](0) +
_grad_disp_z[qp](0) * _grad_disp_z[qp](0)) / 3.0 * _solid_model.JxW(qp_loop);
volumetric_strain += 0.5 * (_grad_disp_x[qp](1) * _grad_disp_x[qp](1) +
_grad_disp_y[qp](1) * _grad_disp_y[qp](1) +
_grad_disp_z[qp](1) * _grad_disp_z[qp](1)) / 3.0 * _solid_model.JxW(qp_loop);
volumetric_strain += 0.5 * (_grad_disp_x[qp](2) * _grad_disp_x[qp](2) +
_grad_disp_y[qp](2) * _grad_disp_y[qp](2) +
_grad_disp_z[qp](2) * _grad_disp_z[qp](2)) / 3.0 * _solid_model.JxW(qp_loop);
}
}
volumetric_strain /= volume; // average volumetric strain
// strain increment at _qp
Real trace = strain_increment.trace();
strain_increment.xx() += volumetric_strain - trace / 3.0;
strain_increment.yy() += volumetric_strain - trace / 3.0;
strain_increment.zz() += volumetric_strain - trace / 3.0;
}
total_strain_new = strain_increment;
strain_increment -= total_strain_old;
}
Real
firstInvariant(const SymmTensor & symm_tensor)
{
return symm_tensor.trace();
}
Real
hydrostatic(const SymmTensor & symm_tensor)
{
return symm_tensor.trace() / 3.0;
}
void
PlaneStrain::computeStrain( const unsigned qp,
const SymmTensor & total_strain_old,
SymmTensor & total_strain_new,
SymmTensor & strain_increment )
{
strain_increment.xx() = _grad_disp_x[qp](0);
strain_increment.yy() = _grad_disp_y[qp](1);
if (_have_strain_zz)
strain_increment.zz() = _strain_zz[qp];
else if (_have_scalar_strain_zz && _scalar_strain_zz.size()>0)
strain_increment.zz() = _scalar_strain_zz[0];
else
strain_increment.zz() = 0;
strain_increment.xy() = 0.5*(_grad_disp_x[qp](1) + _grad_disp_y[qp](0));
strain_increment.yz() = 0;
strain_increment.zx() = 0;
if (_large_strain)
{
strain_increment.xx() += 0.5*(_grad_disp_x[qp](0)*_grad_disp_x[qp](0) +
_grad_disp_y[qp](0)*_grad_disp_y[qp](0));
strain_increment.yy() += 0.5*(_grad_disp_x[qp](1)*_grad_disp_x[qp](1) +
_grad_disp_y[qp](1)*_grad_disp_y[qp](1));
strain_increment.xy() += 0.5*(_grad_disp_x[qp](0)*_grad_disp_x[qp](1) +
_grad_disp_y[qp](0)*_grad_disp_y[qp](1));
}
if (_volumetric_locking_correction)
{
// volumetric locking correction
Real volumetric_strain = 0.0;
Real volume = 0.0;
Real dim = 3.0;
for (unsigned int qp_loop = 0; qp_loop < _solid_model.qrule()->n_points(); ++qp_loop)
{
if (_have_strain_zz)
volumetric_strain += (_grad_disp_x[qp_loop](0) + _grad_disp_y[qp_loop](1) + _strain_zz[qp_loop]) / dim * _solid_model.JxW(qp_loop);
else if (_have_scalar_strain_zz && _scalar_strain_zz.size() > 0)
volumetric_strain += (_grad_disp_x[qp_loop](0) + _grad_disp_y[qp_loop](1) + _scalar_strain_zz[0]) / dim * _solid_model.JxW(qp_loop);
else
volumetric_strain += (_grad_disp_x[qp_loop](0) + _grad_disp_y[qp_loop](1)) / dim * _solid_model.JxW(qp_loop);
volume += _solid_model.JxW(qp_loop);
if (_large_strain)
{
volumetric_strain += 0.5 * (_grad_disp_x[qp_loop](0) * _grad_disp_x[qp_loop](0) +
_grad_disp_y[qp_loop](0) * _grad_disp_y[qp_loop](0)) / dim * _solid_model.JxW(qp_loop);
volumetric_strain += 0.5 * (_grad_disp_x[qp_loop](1) * _grad_disp_x[qp_loop](1) +
_grad_disp_y[qp_loop](1) * _grad_disp_y[qp_loop](1)) / dim * _solid_model.JxW(qp_loop);
}
}
volumetric_strain /= volume; // average volumetric strain
// strain increment at _qp
Real trace = strain_increment.trace();
strain_increment.xx() += volumetric_strain - trace / dim;
strain_increment.yy() += volumetric_strain - trace / dim;
strain_increment.zz() += volumetric_strain - trace / dim;
}
total_strain_new = strain_increment;
strain_increment -= total_strain_old;
}
void
ReturnMappingModel::computeStress(const Elem & /*current_elem*/, unsigned qp,
const SymmElasticityTensor & elasticityTensor,
const SymmTensor & stress_old,
SymmTensor & strain_increment,
SymmTensor & stress_new,
SymmTensor & inelastic_strain_increment)
{
// compute deviatoric trial stress
SymmTensor dev_trial_stress(stress_new);
dev_trial_stress.addDiag(-dev_trial_stress.trace()/3.0);
// compute effective trial stress
Real dts_squared = dev_trial_stress.doubleContraction(dev_trial_stress);
Real effective_trial_stress = std::sqrt(1.5 * dts_squared);
// compute effective strain increment
SymmTensor dev_strain_increment(strain_increment);
dev_strain_increment.addDiag(-strain_increment.trace()/3.0);
_effective_strain_increment = dev_strain_increment.doubleContraction(dev_strain_increment);
_effective_strain_increment = std::sqrt(2.0/3.0 * _effective_strain_increment);
computeStressInitialize(qp, effective_trial_stress, elasticityTensor);
// Use Newton sub-iteration to determine inelastic strain increment
Real scalar = 0;
unsigned int it = 0;
Real residual = 10;
Real norm_residual = 10;
Real first_norm_residual = 10;
std::string iter_output;
while (it < _max_its &&
norm_residual > _absolute_tolerance &&
(norm_residual/first_norm_residual) > _relative_tolerance)
{
iterationInitialize(qp, scalar);
residual = computeResidual(qp, effective_trial_stress, scalar);
norm_residual = std::abs(residual);
if (it == 0)
{
first_norm_residual = norm_residual;
if (first_norm_residual == 0)
{
first_norm_residual = 1;
}
}
scalar -= residual / computeDerivative(qp, effective_trial_stress, scalar);
if (_output_iteration_info == true ||
_output_iteration_info_on_error == true)
{
iter_output = "In the element " + Moose::stringify(_current_elem->id()) +
+ " and the qp point " + Moose::stringify(qp) + ": \n" +
+ " iteration = " + Moose::stringify(it ) + "\n" +
+ " effective trial stress = " + Moose::stringify(effective_trial_stress) + "\n" +
+ " scalar effective inelastic strain = " + Moose::stringify(scalar) +"\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(qp, scalar);
++it;
}
if (_output_iteration_info)
_console << iter_output;
if (it == _max_its &&
norm_residual > _absolute_tolerance &&
(norm_residual/first_norm_residual) > _relative_tolerance)
{
if (_output_iteration_info_on_error)
{
Moose::err << iter_output;
}
mooseError("Exceeded maximum iterations in ReturnMappingModel solve for material: " << _name << ". Rerun with 'output_iteration_info_on_error = true' for more information.");
}
// compute inelastic and elastic strain increments (avoid potential divide by zero - how should this be done)?
if (effective_trial_stress < 0.01)
{
effective_trial_stress = 0.01;
}
inelastic_strain_increment = dev_trial_stress;
inelastic_strain_increment *= (1.5*scalar/effective_trial_stress);
strain_increment -= inelastic_strain_increment;
// compute stress increment
stress_new = elasticityTensor * strain_increment;
// update stress
stress_new += stress_old;
computeStressFinalize(qp, inelastic_strain_increment);
}
void
ReturnMappingModel::computeStress( const Elem & /*current_elem*/, unsigned qp,
const SymmElasticityTensor & elasticityTensor,
const SymmTensor & stress_old,
SymmTensor & strain_increment,
SymmTensor & stress_new,
SymmTensor & inelastic_strain_increment )
{
// compute deviatoric trial stress
SymmTensor dev_trial_stress(stress_new);
dev_trial_stress.addDiag( -dev_trial_stress.trace()/3.0 );
// compute effective trial stress
Real dts_squared = dev_trial_stress.doubleContraction(dev_trial_stress);
Real effective_trial_stress = std::sqrt(1.5 * dts_squared);
// compute effective strain increment
SymmTensor dev_strain_increment(strain_increment);
dev_strain_increment.addDiag( -strain_increment.trace()/3.0);
_effective_strain_increment = dev_strain_increment.doubleContraction(dev_strain_increment);
_effective_strain_increment = std::sqrt(2.0/3.0 * _effective_strain_increment);
computeStressInitialize(qp, effective_trial_stress, elasticityTensor);
// Use Newton sub-iteration to determine inelastic strain increment
Real scalar = 0;
unsigned int it = 0;
Real residual = 10;
Real norm_residual = 10;
Real first_norm_residual = 10;
std::stringstream iter_output;
while (it < _max_its &&
norm_residual > _absolute_tolerance &&
(norm_residual/first_norm_residual) > _relative_tolerance)
{
iterationInitialize( qp, scalar );
residual = computeResidual(qp, effective_trial_stress, scalar);
norm_residual = std::abs(residual);
if (it == 0)
{
first_norm_residual = norm_residual;
if (first_norm_residual == 0)
{
first_norm_residual = 1;
}
}
scalar -= residual / computeDerivative(qp, effective_trial_stress, scalar);
if (_output_iteration_info == true ||
_output_iteration_info_on_error == true)
{
iter_output
<< " it=" << it
<< " trl_strs=" << effective_trial_stress
<< " scalar=" << scalar
<< " rel_res=" << norm_residual/first_norm_residual
<< " rel_tol=" << _relative_tolerance
<< " abs_res=" << norm_residual
<< " abs_tol=" << _absolute_tolerance
<< std::endl;
}
iterationFinalize( qp, scalar );
++it;
}
if (_output_iteration_info)
_console << iter_output.str();
if (it == _max_its &&
norm_residual > _absolute_tolerance &&
(norm_residual/first_norm_residual) > _relative_tolerance)
{
if (_output_iteration_info_on_error)
{
Moose::err << iter_output.str();
}
mooseError("Max sub-newton iteration hit during nonlinear constitutive model solve! (" << _name << ")");
}
// compute inelastic and elastic strain increments (avoid potential divide by zero - how should this be done)?
if (effective_trial_stress < 0.01)
{
effective_trial_stress = 0.01;
}
inelastic_strain_increment = dev_trial_stress;
inelastic_strain_increment *= (1.5*scalar/effective_trial_stress);
strain_increment -= inelastic_strain_increment;
// compute stress increment
stress_new = elasticityTensor * strain_increment;
// update stress
stress_new += stress_old;
computeStressFinalize(qp, inelastic_strain_increment);
}
Real
MaterialTensorAux::getTensorQuantity(const SymmTensor & tensor,
const MTA_ENUM quantity,
const MooseEnum & quantity_moose_enum,
const int index,
const Point * curr_point,
const Point * p1,
const Point * p2)
{
Real value(0);
if (quantity == MTA_COMPONENT)
{
value = tensor.component(index);
}
else if ( quantity == MTA_VONMISES )
{
value = std::sqrt(0.5*(
std::pow(tensor.xx() - tensor.yy(), 2) +
std::pow(tensor.yy() - tensor.zz(), 2) +
std::pow(tensor.zz() - tensor.xx(), 2) + 6 * (
std::pow(tensor.xy(), 2) +
std::pow(tensor.yz(), 2) +
std::pow(tensor.zx(), 2))));
}
else if ( quantity == MTA_PLASTICSTRAINMAG )
{
value = std::sqrt(2.0/3.0 * tensor.doubleContraction(tensor));
}
else if ( quantity == MTA_HYDROSTATIC )
{
value = tensor.trace()/3.0;
}
else if ( quantity == MTA_HOOP )
{
// This is the location of the stress. A vector from the cylindrical axis to this point will define the x' axis.
Point p0( *curr_point );
// The vector p1 + t*(p2-p1) defines the cylindrical axis. The point along this
// axis closest to p0 is found by the following for t:
const Point p2p1( *p2 - *p1 );
const Point p2p0( *p2 - p0 );
const Point p1p0( *p1 - p0 );
const Real t( -(p1p0*p2p1)/p2p1.size_sq() );
// The nearest point on the cylindrical axis to p0 is p.
const Point p( *p1 + t * p2p1 );
Point xp( p0 - p );
xp /= xp.size();
Point yp( p2p1/p2p1.size() );
Point zp( xp.cross( yp ));
//
// The following works but does more than we need
//
// // Rotation matrix R
// ColumnMajorMatrix R(3,3);
// // Fill with direction cosines
// R(0,0) = xp(0);
// R(1,0) = xp(1);
// R(2,0) = xp(2);
// R(0,1) = yp(0);
// R(1,1) = yp(1);
// R(2,1) = yp(2);
// R(0,2) = zp(0);
// R(1,2) = zp(1);
// R(2,2) = zp(2);
// // Rotate
// ColumnMajorMatrix tensor( _tensor[_qp].columnMajorMatrix() );
// ColumnMajorMatrix tensorp( R.transpose() * ( tensor * R ));
// // Hoop stress is the zz stress
// value = tensorp(2,2);
//
// Instead, tensorp(2,2) = R^T(2,:)*tensor*R(:,2)
//
const Real zp0( zp(0) );
const Real zp1( zp(1) );
const Real zp2( zp(2) );
value = (zp0*tensor(0,0)+zp1*tensor(1,0)+zp2*tensor(2,0))*zp0 +
(zp0*tensor(0,1)+zp1*tensor(1,1)+zp2*tensor(2,1))*zp1 +
(zp0*tensor(0,2)+zp1*tensor(1,2)+zp2*tensor(2,2))*zp2;
}
else if ( quantity == MTA_RADIAL )
{
// This is the location of the stress. A vector from the cylindrical axis to this point will define the x' axis
// which is the radial direction in which we want the stress.
Point p0( *curr_point );
// The vector p1 + t*(p2-p1) defines the cylindrical axis. The point along this
// axis closest to p0 is found by the following for t:
const Point p2p1( *p2 - *p1 );
const Point p2p0( *p2 - p0 );
const Point p1p0( *p1 - p0 );
const Real t( -(p1p0*p2p1)/p2p1.size_sq() );
// The nearest point on the cylindrical axis to p0 is p.
const Point p( *p1 + t * p2p1 );
Point xp( p0 - p );
xp /= xp.size();
const Real xp0( xp(0) );
const Real xp1( xp(1) );
const Real xp2( xp(2) );
value = (xp0*tensor(0,0)+xp1*tensor(1,0)+xp2*tensor(2,0))*xp0 +
(xp0*tensor(0,1)+xp1*tensor(1,1)+xp2*tensor(2,1))*xp1 +
(xp0*tensor(0,2)+xp1*tensor(1,2)+xp2*tensor(2,2))*xp2;
}
else if ( quantity == MTA_AXIAL )
{
// The vector p2p1=(p2-p1) defines the axis, which is the direction in which we want the stress.
Point p2p1( *p2 - *p1 );
p2p1 /= p2p1.size();
const Real axis0( p2p1(0) );
const Real axis1( p2p1(1) );
const Real axis2( p2p1(2) );
value = (axis0*tensor(0,0)+axis1*tensor(1,0)+axis2*tensor(2,0))*axis0 +
(axis0*tensor(0,1)+axis1*tensor(1,1)+axis2*tensor(2,1))*axis1 +
(axis0*tensor(0,2)+axis1*tensor(1,2)+axis2*tensor(2,2))*axis2;
}
else if ( quantity == MTA_MAXPRINCIPAL )
{
value = principalValue( tensor, 0 );
}
else if ( quantity == MTA_MEDPRINCIPAL )
{
value = principalValue( tensor, 1 );
}
else if ( quantity == MTA_MINPRINCIPAL )
{
value = principalValue( tensor, 2 );
}
else if ( quantity == MTA_FIRSTINVARIANT )
{
value = tensor.trace();
}
else if ( quantity == MTA_SECONDINVARIANT )
{
value =
tensor.xx()*tensor.yy() +
tensor.yy()*tensor.zz() +
tensor.zz()*tensor.xx() -
tensor.xy()*tensor.xy() -
tensor.yz()*tensor.yz() -
tensor.zx()*tensor.zx();
}
else if ( quantity == MTA_THIRDINVARIANT )
{
value =
tensor.xx()*tensor.yy()*tensor.zz() -
tensor.xx()*tensor.yz()*tensor.yz() +
tensor.xy()*tensor.zx()*tensor.yz() -
tensor.xy()*tensor.xy()*tensor.zz() +
tensor.zx()*tensor.xy()*tensor.yz() -
tensor.zx()*tensor.zx()*tensor.yy();
}
else if ( quantity == MTA_TRIAXIALITY )
{
Real hydrostatic = tensor.trace()/3.0;
Real von_mises = std::sqrt(0.5*(
std::pow(tensor.xx() - tensor.yy(), 2) +
std::pow(tensor.yy() - tensor.zz(), 2) +
std::pow(tensor.zz() - tensor.xx(), 2) + 6 * (
std::pow(tensor.xy(), 2) +
std::pow(tensor.yz(), 2) +
std::pow(tensor.zx(), 2))));
value = std::abs(hydrostatic / von_mises);
}
else if ( quantity == MTA_VOLUMETRICSTRAIN )
{
value =
tensor.trace() +
tensor.xx()*tensor.yy() +
tensor.yy()*tensor.zz() +
tensor.zz()*tensor.xx() +
tensor.xx()*tensor.yy()*tensor.zz();
}
else
{
mooseError("Unknown quantity in MaterialTensorAux: " + quantity_moose_enum.operator std::string());
}
return value;
}