MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim > Class Template Reference

Detailed Description

template<int DisplacementDim>
class MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >

The cohesive zone delamination model for mode I fracture introduced herein follows a bilinear traction-separation law which is characterized by four basic parameters: the initial normal and shear stiffness \(K_n\), \(K_s\), the fracture toughness \(G_c\) (also referred to as critical energy release rate), and the peak tensile normal traction \(t_{n,p}\).

Definition at line 125 of file CohesiveZoneModeI.h.

#include <CohesiveZoneModeI.h>

Inheritance diagram for MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >:

Collaboration diagram for MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >:

Public Member Functions
std::unique_ptr< typename FractureModelBase< DisplacementDim >::MaterialStateVariables >	createMaterialStateVariables () override
	CohesiveZoneModeI (double const penalty_aperture_cutoff, bool const tension_cutoff, MaterialPropertiesParameters material_properties)
void	computeConstitutiveRelation (double const t, ParameterLib::SpatialPosition const &x, double const aperture0, Eigen::Ref< Eigen::VectorXd const > sigma0, Eigen::Ref< Eigen::VectorXd const > w_prev, Eigen::Ref< Eigen::VectorXd const > w, Eigen::Ref< Eigen::VectorXd const > sigma_prev, Eigen::Ref< Eigen::VectorXd > sigma, Eigen::Ref< Eigen::MatrixXd > C, typename FractureModelBase< DisplacementDim >::MaterialStateVariables &material_state_variables) override
MaterialProperties	evaluatedMaterialProperties (double const t, ParameterLib::SpatialPosition const &x) const
Public Member Functions inherited from MaterialLib::Fracture::FractureModelBase< DisplacementDim >
virtual	~FractureModelBase ()=default
virtual void	computeConstitutiveRelation (double const t, ParameterLib::SpatialPosition const &x, double const aperture0, Eigen::Ref< Eigen::VectorXd const > sigma0, Eigen::Ref< Eigen::VectorXd const > w_prev, Eigen::Ref< Eigen::VectorXd const > w, Eigen::Ref< Eigen::VectorXd const > sigma_prev, Eigen::Ref< Eigen::VectorXd > sigma, Eigen::Ref< Eigen::MatrixXd > C, MaterialStateVariables &material_state_variables)=0

Private Attributes
double const	_penalty_aperture_cutoff
bool const	_tension_cutoff
MaterialPropertiesParameters	_mp

Constructor & Destructor Documentation

CohesiveZoneModeI()

template<int DisplacementDim>

MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::CohesiveZoneModeI ( double const penalty_aperture_cutoff, bool const tension_cutoff, MaterialPropertiesParameters material_properties )

inlineexplicit

Definition at line 137 of file CohesiveZoneModeI.h.

        : _penalty_aperture_cutoff(penalty_aperture_cutoff),
          _tension_cutoff(tension_cutoff),
          _mp(std::move(material_properties))
    {
    }

Member Function Documentation

computeConstitutiveRelation()

template<int DisplacementDim>

void MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::computeConstitutiveRelation ( double const t, ParameterLib::SpatialPosition const & x, double const aperture0, Eigen::Ref< Eigen::VectorXd const > sigma0, Eigen::Ref< Eigen::VectorXd const > w_prev, Eigen::Ref< Eigen::VectorXd const > w, Eigen::Ref< Eigen::VectorXd const > sigma_prev, Eigen::Ref< Eigen::VectorXd > sigma, Eigen::Ref< Eigen::MatrixXd > C, typename FractureModelBase< DisplacementDim >::MaterialStateVariables & material_state_variables )

override

Computation of the constitutive relation for the Cohesive Zone Mode I model.

Parameters

t	current time
x	current position in space
aperture0	initial fracture's aperture
sigma0	initial stress
w_prev	fracture displacement at previous time step
w	fracture displacement at current time step
sigma_prev	stress at previous time step
sigma	stress at current time step
C	tangent matrix for stress and fracture displacements
material_state_variables	material state variables

Undamaged stiffness used in compression.

Definition at line 36 of file CohesiveZoneModeI.cpp.

{
    assert(dynamic_cast<StateVariables<DisplacementDim> const*>(
               &material_state_variables) != nullptr);
 
    auto& state =
        static_cast<StateVariables<DisplacementDim>&>(material_state_variables);
    // reset damage in each iteration
    state.setInitialConditions();
 
    auto const mp = evaluatedMaterialProperties(t, x);
 
    C.setZero();
 
    // Separately compute shear and normal stresses because of the penalty for
    // the normal component.
    const int index_ns = DisplacementDim - 1;
    double const w_n = w[index_ns];
    for (int i = 0; i < index_ns; i++)
    {
        C(i, i) = mp.Ks;
    }
 
    sigma.noalias() = C * w;
 
    double const aperture = w_n + aperture0;
 
    sigma.coeffRef(index_ns) =
        mp.Kn * w_n * logPenalty(aperture0, aperture, _penalty_aperture_cutoff);
 
    C(index_ns, index_ns) =
        mp.Kn *
        logPenaltyDerivative(aperture0, aperture, _penalty_aperture_cutoff);
 
    sigma.noalias() += sigma0;
 
    // Exit if fracture is closing
    if (sigma[index_ns] < 0)
    {
        return;  
    }
 
    //
    // Continue with fracture opening.
    //
    // effective opening calculated by shift to state corresponding to sigma0=0
    const double w_n_effective = w_n + sigma0[index_ns] / mp.Kn;
    double degradation = 0.0;
    if (mp.w_nf == 0.0)  // can be used to model tension-cutoff
    {
        state.damage_prev = 1.0;
        state.damage = 1.0;
    }
    else
    {
        state.damage =
            computeDamage(state.damage_prev, w_n_effective, mp.w_np, mp.w_nf);
        degradation = ((1 - state.damage) * mp.w_np) /
                      (mp.w_np + state.damage * (mp.w_nf - mp.w_np));
    }
 
    // Degrade stiffness tensor in tension.
    C = C * degradation;
    // Create effective relative displacement vector
    Eigen::VectorXd w_eff = w;
    // Only origin of normal entry is shifted, shear unaffected
    w_eff[index_ns] = w_n_effective;
    sigma = C * w_eff;
 
    if (state.damage > state.damage_prev)
    {
        // If damage is increasing, provide extension to consistent tangent.
 
        Eigen::Matrix<double, DisplacementDim, 1> dd_dw =
            Eigen::Matrix<double, DisplacementDim, 1>::Zero();
 
        double const tmp = mp.w_np + state.damage * (mp.w_nf - mp.w_np);
        dd_dw[index_ns] =
            (mp.w_np * mp.w_nf) / ((mp.w_nf - mp.w_np) * (tmp * tmp));
 
        C -= C * w_eff * (dd_dw).transpose();
    }
 
    // TODO (nagel) Initial stress not considered, yet.
    // sigma.noalias() += sigma0;
}

References MaterialLib::Fracture::logPenalty(), MaterialLib::Fracture::logPenaltyDerivative(), and MaterialLib::Fracture::CohesiveZoneModeI::StateVariables< DisplacementDim >::setInitialConditions().

createMaterialStateVariables()

template<int DisplacementDim>

std::unique_ptr< typename FractureModelBase< DisplacementDim >::MaterialStateVariables > MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::createMaterialStateVariables ( )

inlineoverridevirtual

Polymorphic creator for MaterialStateVariables objects specific for a material model.

Implements MaterialLib::Fracture::FractureModelBase< DisplacementDim >.

Definition at line 130 of file CohesiveZoneModeI.h.

    {
        return std::make_unique<StateVariables<DisplacementDim>>();
    }

evaluatedMaterialProperties()

template<int DisplacementDim>

MaterialProperties MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::evaluatedMaterialProperties ( double const t, ParameterLib::SpatialPosition const & x ) const

inline

Definition at line 180 of file CohesiveZoneModeI.h.

    {
        return MaterialProperties(t, x, _mp);
    }

References MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::_mp.

Member Data Documentation

_mp

template<int DisplacementDim>

MaterialPropertiesParameters MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::_mp

private

Definition at line 197 of file CohesiveZoneModeI.h.

Referenced by MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::evaluatedMaterialProperties().

_penalty_aperture_cutoff

template<int DisplacementDim>

double const MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::_penalty_aperture_cutoff

private

Compressive normal displacements above this value will not enter the computation of the normal stiffness modulus of the fracture.

Note

Setting this to the initial aperture value allows negative apertures.

Definition at line 191 of file CohesiveZoneModeI.h.

_tension_cutoff

template<int DisplacementDim>

bool const MaterialLib::Fracture::CohesiveZoneModeI::CohesiveZoneModeI< DisplacementDim >::_tension_cutoff

private

If set no resistance to open the fracture over the initial aperture is opposed.

Definition at line 195 of file CohesiveZoneModeI.h.

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

• MaterialLib/FractureModels/CohesiveZoneModeI.h
• MaterialLib/FractureModels/CohesiveZoneModeI.cpp