KelvinVoigtDamper::ConstitutiveEquation< TYPE > Struct Template Reference

Constitutive model functions. More...

#include <users_modules/basic_finite_elements/src/KelvinVoigtDamper.hpp>

Inheritance diagram for KelvinVoigtDamper::ConstitutiveEquation< TYPE >:

Collaboration diagram for KelvinVoigtDamper::ConstitutiveEquation< TYPE >:

Public Member Functions
	ConstitutiveEquation (BlockMaterialData &data, bool is_displacement=true)
virtual	~ConstitutiveEquation ()=default
virtual MoFEMErrorCode	calculateEngineeringStrainDot ()
	Calculate strain rate. More...
virtual MoFEMErrorCode	calculateDashpotCauchyStress ()
	Calculate Cauchy dashpot stress. More...
virtual MoFEMErrorCode	calculateFirstPiolaKirchhoffStress ()
	Calculate First Piola-Kirchhoff Stress Dashpot stress. More...

Public Attributes
FTensor::Index< 'i', 3 >	i
FTensor::Index< 'j', 3 >	j
FTensor::Index< 'k', 3 >	k
BlockMaterialData &	dAta
bool	isDisplacement
MatrixBoundedArray< TYPE, 9 >	F
	Gradient of deformation. More...
MatrixBoundedArray< TYPE, 9 >	FDot
	Rate of gradient of deformation. More...
MatrixBoundedArray< TYPE, 9 >	gradientUDot
	Rate of gradient of displacements. More...
MatrixBoundedArray< TYPE, 9 >	engineringStrainDot
MatrixBoundedArray< TYPE, 9 >	dashpotCauchyStress
	Stress generated by spring beta. More...
MatrixBoundedArray< TYPE, 9 >	dashpotFirstPiolaKirchhoffStress
	Stress generated by spring beta. More...
MatrixBoundedArray< TYPE, 9 >	invF
	Inverse of gradient of deformation. More...
TYPE	traceEngineeringStrainDot
TYPE	J
	Jacobian of gradient of deformation. More...

Detailed Description

template<typename TYPE>
struct KelvinVoigtDamper::ConstitutiveEquation< TYPE >

Constitutive model functions.

Examples

nonlinear_dynamics.cpp.

Definition at line 43 of file KelvinVoigtDamper.hpp.

Constructor & Destructor Documentation

ConstitutiveEquation()

template<typename TYPE >

KelvinVoigtDamper::ConstitutiveEquation< TYPE >::ConstitutiveEquation ( BlockMaterialData &  data, bool  is_displacement = true  )

inline

Definition at line 52 of file KelvinVoigtDamper.hpp.

        : dAta(data), isDisplacement(is_displacement) {}

~ConstitutiveEquation()

template<typename TYPE >

virtual KelvinVoigtDamper::ConstitutiveEquation< TYPE >::~ConstitutiveEquation ( )

virtualdefault

Member Function Documentation

calculateDashpotCauchyStress()

template<typename TYPE >

virtual MoFEMErrorCode KelvinVoigtDamper::ConstitutiveEquation< TYPE >::calculateDashpotCauchyStress ( )

inlinevirtual

Calculate Cauchy dashpot stress.

Calculate dashpot Cauchy stress. It has to be pull back to reference configuration before use in total Lagrangian formulation.

\[ \sigma^\beta_{ij} = 2G^\beta\left[ \dot{\varepsilon}_{ij} + \frac{v^\beta}{1-2v^\beta}\dot{\varepsilon}_{kk}\delta_{ij} \right] \]

Definition at line 113 of file KelvinVoigtDamper.hpp.

                                                          {
      MoFEMFunctionBegin;
      dashpotCauchyStress.resize(3, 3, false);
      double a = 2.0 * dAta.gBeta;
      double b = a * (dAta.vBeta / (1.0 - 2.0 * dAta.vBeta));
      noalias(dashpotCauchyStress) = a * engineringStrainDot;
      for (int ii = 0; ii < 3; ii++) {
        dashpotCauchyStress(ii, ii) += b * traceEngineeringStrainDot;
      }
      MoFEMFunctionReturn(0);
    }

calculateEngineeringStrainDot()

template<typename TYPE >

virtual MoFEMErrorCode KelvinVoigtDamper::ConstitutiveEquation< TYPE >::calculateEngineeringStrainDot ( )

inlinevirtual

Calculate strain rate.

\[ \dot{\varepsilon}_{ij} = \frac{1}{2} \left( \frac{\partial v_i}{\partial X_j} + \frac{\partial v_j}{\partial X_i} \right) \]

Definition at line 82 of file KelvinVoigtDamper.hpp.

                                                           {
      MoFEMFunctionBegin;
      gradientUDot.resize(3, 3, false);
      noalias(gradientUDot) = FDot;
 
      // for (int ii = 0; ii < 3; ii++)
      //   gradientUDot(ii, ii) -= 1;
        
      traceEngineeringStrainDot = 0;
      for (int ii = 0; ii < 3; ii++) {
        traceEngineeringStrainDot += gradientUDot(ii, ii);
      }
      engineringStrainDot.resize(3, 3, false);
      noalias(engineringStrainDot) = gradientUDot + trans(gradientUDot);
      engineringStrainDot *= 0.5;
      MoFEMFunctionReturn(0);
    }

calculateFirstPiolaKirchhoffStress()

template<typename TYPE >

virtual MoFEMErrorCode KelvinVoigtDamper::ConstitutiveEquation< TYPE >::calculateFirstPiolaKirchhoffStress ( )

inlinevirtual

Calculate First Piola-Kirchhoff Stress Dashpot stress.

\[ P^\beta_{ij} = J \sigma^\beta_{ik} F^{-1}_{jk} \]

Definition at line 132 of file KelvinVoigtDamper.hpp.

                                                                {
      MoFEMFunctionBegin;
      dashpotFirstPiolaKirchhoffStress.resize(3, 3, false);
      if (dAta.lInear) {
        noalias(dashpotFirstPiolaKirchhoffStress) = dashpotCauchyStress;
      } else {
 
        invF.resize(3, 3, false);
 
        auto t_dashpotFirstPiolaKirchhoffStress = getFTensor2FromArray3by3(
            dashpotFirstPiolaKirchhoffStress, FTensor::Number<0>(), 0);
        auto t_dashpotCauchyStress = getFTensor2FromArray3by3(
            dashpotCauchyStress, FTensor::Number<0>(), 0);
        auto t_F = getFTensor2FromArray3by3(F, FTensor::Number<0>(), 0);
        auto t_invF = getFTensor2FromArray3by3(invF, FTensor::Number<0>(), 0);
        if (isDisplacement) {
          t_F(0, 0) += 1;
          t_F(1, 1) += 1;
          t_F(2, 2) += 1;
        }
 
        J = determinantTensor3by3(t_F);
        CHKERR invertTensor3by3(t_F, J, t_invF);
        t_dashpotFirstPiolaKirchhoffStress(i, j) =
            J * (t_dashpotCauchyStress(i, k) * t_invF(j, k));
      }
      MoFEMFunctionReturn(0);
    }

Member Data Documentation

dashpotCauchyStress

template<typename TYPE >

MatrixBoundedArray<TYPE, 9> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::dashpotCauchyStress

Stress generated by spring beta.

Definition at line 62 of file KelvinVoigtDamper.hpp.

dashpotFirstPiolaKirchhoffStress

template<typename TYPE >

MatrixBoundedArray<TYPE, 9> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::dashpotFirstPiolaKirchhoffStress

Stress generated by spring beta.

Definition at line 64 of file KelvinVoigtDamper.hpp.

dAta

template<typename TYPE >

BlockMaterialData& KelvinVoigtDamper::ConstitutiveEquation< TYPE >::dAta

Definition at line 49 of file KelvinVoigtDamper.hpp.

engineringStrainDot

template<typename TYPE >

MatrixBoundedArray<TYPE, 9> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::engineringStrainDot

Definition at line 60 of file KelvinVoigtDamper.hpp.

F

template<typename TYPE >

MatrixBoundedArray<TYPE, 9> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::F

Gradient of deformation.

Definition at line 56 of file KelvinVoigtDamper.hpp.

FDot

template<typename TYPE >

MatrixBoundedArray<TYPE, 9> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::FDot

Rate of gradient of deformation.

Definition at line 57 of file KelvinVoigtDamper.hpp.

gradientUDot

template<typename TYPE >

MatrixBoundedArray<TYPE, 9> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::gradientUDot

Rate of gradient of displacements.

Definition at line 59 of file KelvinVoigtDamper.hpp.

i

template<typename TYPE >

FTensor::Index<'i', 3> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::i

Definition at line 45 of file KelvinVoigtDamper.hpp.

invF

template<typename TYPE >

MatrixBoundedArray<TYPE, 9> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::invF

Inverse of gradient of deformation.

Definition at line 65 of file KelvinVoigtDamper.hpp.

isDisplacement

template<typename TYPE >

bool KelvinVoigtDamper::ConstitutiveEquation< TYPE >::isDisplacement

Definition at line 50 of file KelvinVoigtDamper.hpp.

j

template<typename TYPE >

FTensor::Index<'j', 3> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::j

Definition at line 46 of file KelvinVoigtDamper.hpp.

J

template<typename TYPE >

TYPE KelvinVoigtDamper::ConstitutiveEquation< TYPE >::J

Jacobian of gradient of deformation.

Definition at line 68 of file KelvinVoigtDamper.hpp.

k

template<typename TYPE >

FTensor::Index<'k', 3> KelvinVoigtDamper::ConstitutiveEquation< TYPE >::k

Definition at line 47 of file KelvinVoigtDamper.hpp.

traceEngineeringStrainDot

template<typename TYPE >

TYPE KelvinVoigtDamper::ConstitutiveEquation< TYPE >::traceEngineeringStrainDot

Definition at line 67 of file KelvinVoigtDamper.hpp.

---

The documentation for this struct was generated from the following file:

• users_modules/basic_finite_elements/src/KelvinVoigtDamper.hpp