modified_mohr_coulomb_yield_surface.h

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// KRATOS  ___|  |                   |                   |
//       \___ \  __|  __| |   |  __| __| |   |  __| _` | |
//             | |   |    |   | (    |   |   | |   (   | |
//       _____/ \__|_|   \__,_|\___|\__|\__,_|_|  \__,_|_| MECHANICS
//
//  License:         BSD License
//                   license: structural_mechanics_application/license.txt
//
//  Main authors:    Alejandro Cornejo & Lucia Barbu
//
 
#pragma once
 
// System includes
 
// Project includes
#include "includes/checks.h"
#include "generic_yield_surface.h"
 
namespace Kratos
{
 
 
    // The size type definition
    typedef std::size_t SizeType;
 
 
 
 
template <class TPlasticPotentialType>
class ModifiedMohrCoulombYieldSurface
{
  public:
 
    typedef TPlasticPotentialType PlasticPotentialType;
 
    static constexpr SizeType Dimension = PlasticPotentialType::Dimension;
 
    static constexpr SizeType VoigtSize = PlasticPotentialType::VoigtSize;
 
    KRATOS_CLASS_POINTER_DEFINITION(ModifiedMohrCoulombYieldSurface);
 
    static constexpr double tolerance = std::numeric_limits<double>::epsilon();
 
 
    ModifiedMohrCoulombYieldSurface()
    {
    }
 
    ModifiedMohrCoulombYieldSurface(ModifiedMohrCoulombYieldSurface const &rOther)
    {
    }
 
    ModifiedMohrCoulombYieldSurface &operator=(ModifiedMohrCoulombYieldSurface const &rOther)
    {
        return *this;
    }
 
    virtual ~ModifiedMohrCoulombYieldSurface(){};
 
 
    static void CalculateEquivalentStress(
        const array_1d<double, VoigtSize>& rPredictiveStressVector,
        const Vector& rStrainVector,
        double& rEquivalentStress,
        ConstitutiveLaw::Parameters& rValues
        )
    {
        const Properties& r_material_properties = rValues.GetMaterialProperties();
 
        const bool has_symmetric_yield_stress = r_material_properties.Has(YIELD_STRESS);
        const double yield_compression = has_symmetric_yield_stress ? r_material_properties[YIELD_STRESS] : r_material_properties[YIELD_STRESS_COMPRESSION];
        const double yield_tension = has_symmetric_yield_stress ? r_material_properties[YIELD_STRESS] : r_material_properties[YIELD_STRESS_TENSION];
        double friction_angle = r_material_properties[FRICTION_ANGLE] * Globals::Pi / 180.0; // In radians!
 
        // Check input variables
        if (friction_angle < tolerance) {
            friction_angle = 32.0 * Globals::Pi / 180.0;
            KRATOS_WARNING("ModifiedMohrCoulombYieldSurface") << "Friction Angle not defined, assumed equal to 32 deg " << std::endl;
        }
 
        double theta;
        const double R = std::abs(yield_compression / yield_tension);
        const double Rmorh = std::pow(std::tan((Globals::Pi / 4.0) + friction_angle / 2.0), 2);
        const double alpha_r = R / Rmorh;
        const double sin_phi = std::sin(friction_angle);
 
        double I1, J2, J3;
        array_1d<double, VoigtSize> deviator = ZeroVector(VoigtSize);
        AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateI1Invariant(rPredictiveStressVector, I1);
        AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateJ2Invariant(rPredictiveStressVector, I1, deviator, J2);
        AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateJ3Invariant(deviator, J3);
 
        const double K1 = 0.5 * (1.0 + alpha_r) - 0.5 * (1.0 - alpha_r) * sin_phi;
        const double K2 = 0.5 * (1.0 + alpha_r) - 0.5 * (1.0 - alpha_r) / sin_phi;
        const double K3 = 0.5 * (1.0 + alpha_r) * sin_phi - 0.5 * (1.0 - alpha_r);
 
        // Check Modified Mohr-Coulomb criterion
        if (std::abs(I1) < tolerance) {
            rEquivalentStress = 0.0;
        } else {
            AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateLodeAngle(J2, J3, theta);
            rEquivalentStress = (2.0 * std::tan(Globals::Pi * 0.25 + friction_angle * 0.5) / std::cos(friction_angle)) * ((I1 * K3 / 3.0) +
                        std::sqrt(J2) * (K1 * std::cos(theta) - K2 * std::sin(theta) * sin_phi / std::sqrt(3.0)));
        }
    }
 
    static void GetInitialUniaxialThreshold(ConstitutiveLaw::Parameters& rValues, double& rThreshold)
    {
        const Properties& r_material_properties = rValues.GetMaterialProperties();
 
        const double yield_compression = r_material_properties.Has(YIELD_STRESS) ? r_material_properties[YIELD_STRESS] : r_material_properties[YIELD_STRESS_COMPRESSION];
        rThreshold = std::abs(yield_compression);
    }
 
    static void CalculatePlasticPotentialDerivative(
        const array_1d<double, VoigtSize>& rPredictiveStressVector,
        const array_1d<double, VoigtSize>& rDeviator,
        const double J2,
        array_1d<double, VoigtSize>& GFlux,
        ConstitutiveLaw::Parameters& rValues
        )
    {
        TPlasticPotentialType::CalculatePlasticPotentialDerivative(rPredictiveStressVector, rDeviator, J2, GFlux, rValues);
    }
 
    static void CalculateDamageParameter(
        ConstitutiveLaw::Parameters& rValues,
        double& rAParameter,
        const double CharacteristicLength
        )
    {
        const Properties& r_material_properties = rValues.GetMaterialProperties();
 
        const double fracture_energy = r_material_properties[FRACTURE_ENERGY];
        const double young_modulus = r_material_properties[YOUNG_MODULUS];
        const bool has_symmetric_yield_stress = r_material_properties.Has(YIELD_STRESS);
        const double yield_compression = has_symmetric_yield_stress ? r_material_properties[YIELD_STRESS] : r_material_properties[YIELD_STRESS_COMPRESSION];
        const double yield_tension = has_symmetric_yield_stress ? r_material_properties[YIELD_STRESS] : r_material_properties[YIELD_STRESS_TENSION];
        const double n = yield_compression / yield_tension;
 
        if (r_material_properties[SOFTENING_TYPE] == static_cast<int>(SofteningType::Exponential)) {
            rAParameter = 1.00 / (fracture_energy * n * n * young_modulus / (CharacteristicLength * std::pow(yield_compression, 2)) - 0.5);
            KRATOS_DEBUG_ERROR_IF(rAParameter < 0.0) << "Fracture energy is too low, increase FRACTURE_ENERGY..." << std::endl;
        } else { // linear
            rAParameter = -std::pow(yield_compression, 2) / (2.0 * young_modulus * fracture_energy * n * n / CharacteristicLength);
        }
    }
 
    static void CalculateYieldSurfaceDerivative(
        const array_1d<double, VoigtSize>& rPredictiveStressVector,
        const array_1d<double, VoigtSize>& rDeviator,
        const double J2,
        array_1d<double, VoigtSize>& rFFlux,
        ConstitutiveLaw::Parameters& rValues)
    {
        const Properties& r_material_properties = rValues.GetMaterialProperties();
 
        array_1d<double, VoigtSize> first_vector, second_vector, third_vector;
 
        AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateFirstVector(first_vector);
        AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateSecondVector(rDeviator, J2, second_vector);
        AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateThirdVector(rDeviator, J2, third_vector);
 
        double J3, lode_angle;
        AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateJ3Invariant(rDeviator, J3);
        AdvancedConstitutiveLawUtilities<VoigtSize>::CalculateLodeAngle(J2, J3, lode_angle);
 
        const double checker = std::abs(lode_angle * 180.0 / Globals::Pi);
 
        double c1, c2, c3;
        double friction_angle = r_material_properties[FRICTION_ANGLE] * Globals::Pi / 180.0;
 
        // Check input variables
        if (friction_angle < tolerance) {
            friction_angle = 32.0 * Globals::Pi / 180.0;
            KRATOS_WARNING("ModifiedMohrCoulombYieldSurface") << "Friction Angle not defined, assumed equal to 32 deg " << std::endl;
        }
 
        const double sin_phi = std::sin(friction_angle);
        const double cons_phi = std::cos(friction_angle);
        const double sin_theta = std::sin(lode_angle);
        const double cos_theta = std::cos(lode_angle);
        const double cos_3theta = std::cos(3.0 * lode_angle);
        const double tan_theta = std::tan(lode_angle);
        const double tan_3theta = std::tan(3.0 * lode_angle);
        const double Root3 = std::sqrt(3.0);
 
        const bool has_symmetric_yield_stress = r_material_properties.Has(YIELD_STRESS);
        const double compr_yield = has_symmetric_yield_stress ? r_material_properties[YIELD_STRESS] : r_material_properties[YIELD_STRESS_COMPRESSION];
        const double tens_yield = has_symmetric_yield_stress ? r_material_properties[YIELD_STRESS] : r_material_properties[YIELD_STRESS_TENSION];
        const double n = compr_yield / tens_yield;
 
        const double angle_phi = (Globals::Pi * 0.25) + friction_angle * 0.5;
        const double alpha = n / (std::tan(angle_phi) * std::tan(angle_phi));
 
        const double CFL = 2.0 * std::tan(angle_phi) / cons_phi;
 
        const double K1 = 0.5 * (1.0 + alpha) - 0.5 * (1.0 - alpha) * sin_phi;
        const double K2 = 0.5 * (1.0 + alpha) - 0.5 * (1.0 - alpha) / sin_phi;
        const double K3 = 0.5 * (1.0 + alpha) * sin_phi - 0.5 * (1.0 - alpha);
 
        if (std::abs(sin_phi) > tolerance)
            c1 = CFL * K3 / 3.0;
        else
            c1 = 0.0; // check
 
        if (std::abs(checker) < 29.0) { // Lode angle not greater than pi/6
            c2 = cos_theta * CFL * (K1 * (1.0 + tan_theta * tan_3theta) + K2 * sin_phi * (tan_3theta - tan_theta) / Root3);
            c3 = CFL * (K1 * Root3 * sin_theta + K2 * sin_phi * cos_theta) / (2.0 * J2 * cos_3theta);
        } else {
            c3 = 0.0;
            double aux = 1.0;
            if (lode_angle > tolerance)
                aux = -1.0;
            c2 = 0.5 * CFL * (K1 * Root3 + aux * K2 * sin_phi / Root3);
        }
        noalias(rFFlux) = c1 * first_vector + c2 * second_vector + c3 * third_vector;
    }
 
    static int Check(const Properties& rMaterialProperties)
    {
        KRATOS_ERROR_IF_NOT(rMaterialProperties.Has(FRICTION_ANGLE)) << "FRICTION_ANGLE is not a defined value" << std::endl;
        if (!rMaterialProperties.Has(YIELD_STRESS)) {
            KRATOS_ERROR_IF_NOT(rMaterialProperties.Has(YIELD_STRESS_TENSION)) << "YIELD_STRESS_TENSION is not a defined value" << std::endl;
            KRATOS_ERROR_IF_NOT(rMaterialProperties.Has(YIELD_STRESS_COMPRESSION)) << "YIELD_STRESS_COMPRESSION is not a defined value" << std::endl;
 
            const double yield_compression = rMaterialProperties[YIELD_STRESS_COMPRESSION];
            const double yield_tension = rMaterialProperties[YIELD_STRESS_TENSION];
 
            KRATOS_ERROR_IF(yield_compression < tolerance) << "Yield stress in compression almost zero or negative, include YIELD_STRESS_COMPRESSION in definition";
            KRATOS_ERROR_IF(yield_tension < tolerance) << "Yield stress in tension almost zero or negative, include YIELD_STRESS_TENSION in definition";
        } else {
            const double yield_stress = rMaterialProperties[YIELD_STRESS];
 
            KRATOS_ERROR_IF(yield_stress < tolerance) << "Yield stress almost zero or negative, include YIELD_STRESS in definition";
        }
        KRATOS_ERROR_IF_NOT(rMaterialProperties.Has(FRACTURE_ENERGY)) << "FRACTURE_ENERGY is not a defined value" << std::endl;
        KRATOS_ERROR_IF_NOT(rMaterialProperties.Has(YOUNG_MODULUS)) << "YOUNG_MODULUS is not a defined value" << std::endl;
 
        return TPlasticPotentialType::Check(rMaterialProperties);
    }
 
    static bool IsWorkingWithTensionThreshold()
    {
        return false;
    }
 
    static double GetScaleFactorTension(const Properties& rMaterialProperties)
    {
        const double yield_compression = rMaterialProperties[YIELD_STRESS_COMPRESSION];
        const double yield_tension = rMaterialProperties[YIELD_STRESS_TENSION];
        return yield_compression / yield_tension;
    }
 
 
 
 
 
 
 
  protected:
 
 
 
 
 
 
 
  private:
 
 
 
 
 
 
 
 
}; // Class ModifiedMohrCoulombYieldSurface
 
 
 
 
 
} // namespace Kratos.