Constitutive model functions. More...

#include <users_modules/gels/src/Gels.hpp>

Inheritance diagram for GelModule::Gel::ConstitutiveEquation< TYPE >:

Collaboration diagram for GelModule::Gel::ConstitutiveEquation< TYPE >:

Public Member Functions
	ConstitutiveEquation (map< int, BlockMaterialData > &data)

virtual	~ConstitutiveEquation ()

virtual PetscErrorCode	calculateCauchyDefromationTensor ()

virtual PetscErrorCode	calculateStrainTotal ()
	Calculate total strain. More...

virtual PetscErrorCode	calculateTraceStrainTotalDot ()

virtual PetscErrorCode	calculateStressAlpha ()
	Calculate stress in spring alpha. More...

virtual PetscErrorCode	calculateStressBeta ()
	Calculate stress in spring beta. More...

virtual PetscErrorCode	calculateStrainHatFlux ()
	Calculate rate of strain hat. More...

virtual PetscErrorCode	calculateStressBetaHat ()
	Calculate stress due to concentration of solvent molecules. More...

virtual PetscErrorCode	calculateStressTotal ()

virtual PetscErrorCode	calculateResidualStrainHat ()

virtual PetscErrorCode	calculateSolventFlux ()
	Calculate flux. More...

virtual PetscErrorCode	calculateSolventConcentrationDot ()
	Calculate solvent concentration rate. More...

Public Attributes
int	iD

map< int, BlockMaterialData > &	dAta

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	F
	Gradient of deformation. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	FDot
	Rate of gradient of deformation. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	strainHat
	Internal variable, strain in dashpot beta. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	strainHatDot
	Internal variable, strain in dashpot beta. More...

TYPE	mU
	Solvent concentration. More...

ublas::vector< TYPE, ublas::bounded_array< TYPE, 3 > >	gradientMu
	Gradient of solvent concentration. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	C
	Cauchy deformation. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	gradientU
	Gradient of displacements. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	strainTotal
	Total strain applied at integration point. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	stressAlpha
	Stress generated by spring alpha. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	stressBeta
	Stress generated by spring beta. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	strainHatFlux
	Rate of dashpot (beta) strain. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	stressBetaHat
	Stress as result of volume change due to solvent concentration. More...

TYPE	traceStrainTotal

TYPE	traceStrainHat

TYPE	traceStressBeta

TYPE	traceStrainTotalDot

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	stressTotal
	Total stress. More...

ublas::vector< TYPE, ublas::bounded_array< TYPE, 9 > >	solventFlux
	Solvent flux. More...

TYPE	solventConcentrationDot
	Volume rate change. More...

ublas::matrix< TYPE, ublas::row_major, ublas::bounded_array< TYPE, 9 > >	residualStrainHat
	Residual for calculation epsilon hat. More...

Detailed Description

template<typename TYPE>
struct GelModule::Gel::ConstitutiveEquation< TYPE >

Constitutive model functions.

Gel model

Definition at line 114 of file Gels.hpp.

Constructor & Destructor Documentation

◆ ConstitutiveEquation()

template<typename TYPE >

GelModule::Gel::ConstitutiveEquation< TYPE >::ConstitutiveEquation ( map< int, BlockMaterialData > & data )

inline

Definition at line 119 of file Gels.hpp.

                                                           :
     dAta(data) {
     }

◆ ~ConstitutiveEquation()

template<typename TYPE >

virtual GelModule::Gel::ConstitutiveEquation< TYPE >::~ConstitutiveEquation ( )

inlinevirtual

Definition at line 122 of file Gels.hpp.

122 {}

Member Function Documentation

◆ calculateCauchyDefromationTensor()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateCauchyDefromationTensor ( )

inlinevirtual

Definition at line 156 of file Gels.hpp.

                                                               {
       PetscFunctionBegin;
       C.resize(3,3);
       noalias(C) = prod(trans(F),F);
       PetscFunctionReturn(0);
     }

◆ calculateResidualStrainHat()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateResidualStrainHat ( )

inlinevirtual

Definition at line 301 of file Gels.hpp.

                                                         {
       PetscFunctionBegin;
       residualStrainHat.resize(3,3,false);
       noalias(residualStrainHat) =  strainHatDot - strainHatFlux;
       PetscFunctionReturn(0);
     }

◆ calculateSolventConcentrationDot()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateSolventConcentrationDot ( )

inlinevirtual

Calculate solvent concentration rate.

FIXME: For simplicity as first approximation set volume change as trace of gradient total strain

Definition at line 332 of file Gels.hpp.

                                                               {
       PetscFunctionBegin;
       solventConcentrationDot = traceStrainTotalDot/*/dAta[iD].oMega*/;
       PetscFunctionReturn(0);
     }

◆ calculateSolventFlux()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateSolventFlux ( )

inlinevirtual

Calculate flux.

\[ J_k = -\left( \frac{\kappa}{\eta\Omega^2} \right) \mu_{,i} \]

dAta[iD].oMega

Definition at line 319 of file Gels.hpp.

                                                   {
       PetscFunctionBegin;
       double a = dAta[iD].pErmeability/(dAta[iD].vIscosity*dAta[iD].oMega/**dAta[iD].oMega*/);
       solventFlux=a*gradientMu;
       PetscFunctionReturn(0);
     }

◆ calculateStrainHatFlux()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateStrainHatFlux ( )

inlinevirtual

Calculate rate of strain hat.

\[ \frac{\partial \hat{\varepsilon}_{ij}}{\partial t} = \frac{1}{2\hat{G}^\beta} \left( \sigma_{ij}^\beta - \frac{\hat{v}^\beta}{1+\hat{v}^\beta}\sigma_{kk}^\beta\delta_{ij} \right) \]

Definition at line 255 of file Gels.hpp.

                                                     {
       PetscFunctionBegin;
       traceStressBeta = 0;
       for(int ii = 0;ii<3;ii++) {
         traceStressBeta = stressBeta(ii,ii);
       }
       strainHatFlux.resize(3,3,false);
       double a = (1.0/(2.0*dAta[iD].gBetaHat));
       noalias(strainHatFlux) = a*stressBeta;
       double b = a*(dAta[iD].vBetaHat/(1.0+dAta[iD].vBetaHat));
       for(int ii = 0;ii<3;ii++) {
         strainHatFlux(ii,ii) -= b*traceStressBeta;
       }
       PetscFunctionReturn(0);
     }

◆ calculateStrainTotal()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateStrainTotal ( )

inlinevirtual

Calculate total strain.

Definition at line 166 of file Gels.hpp.

                                                   {
       PetscFunctionBegin;
       gradientU.resize(3,3,false);
       noalias(gradientU) = F;
       for(int ii = 0;ii<3;ii++) {
         gradientU(ii,ii) -= 1;
       }
       strainTotal.resize(3,3,false);
       noalias(strainTotal) = gradientU + trans(gradientU);
       strainTotal *= 0.5;
       PetscFunctionReturn(0);
     }

◆ calculateStressAlpha()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateStressAlpha ( )

inlinevirtual

Calculate stress in spring alpha.

\[ \sigma^\alpha_{ij} = 2G^\alpha\left(\varepsilon_{ij} + \frac{v^\alpha}{1-2v^\alpha}\varepsilon_{kk}\delta_{ij}\right) \]

Note: In general implementation for large strain this function should calculate Piola-Kirchhoff Stress I.

Definition at line 200 of file Gels.hpp.

                                                   {
       PetscFunctionBegin;
       traceStrainTotal = 0;
       for(int ii = 0;ii<3;ii++) {
         traceStrainTotal += strainTotal(ii,ii);
       }
       stressAlpha.resize(3,3,false);
       double a = 2.0*dAta[iD].gAlpha;
       double b = a*(dAta[iD].vAlpha/(1.0-2.0*dAta[iD].vAlpha));
       noalias(stressAlpha) = a*strainTotal;
       for(int ii = 0; ii<3; ii++){
         stressAlpha(ii,ii) += b*traceStrainTotal;
       }
       PetscFunctionReturn(0);
     }

◆ calculateStressBeta()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateStressBeta ( )

inlinevirtual

Calculate stress in spring beta.

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

Definition at line 226 of file Gels.hpp.

                                                  {
       PetscFunctionBegin;
       traceStrainTotal = 0;
       traceStrainHat = 0;
       for(int ii = 0;ii<3;ii++) {
         traceStrainHat += strainHat(ii,ii);
         traceStrainTotal += strainTotal(ii,ii);
       }
       stressBeta.resize(3,3,false);
       double a = 2.0*dAta[iD].gBeta;
       double b = a*(dAta[iD].vBeta/(1.0-2.0*dAta[iD].vBeta));
       noalias(stressBeta) = a*(strainTotal-strainHat);
       for(int ii = 0;ii<3;ii++) {
         stressBeta(ii,ii) += b*(traceStrainTotal-traceStrainHat);
       }
       PetscFunctionReturn(0);
     }

◆ calculateStressBetaHat()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateStressBetaHat ( )

inlinevirtual

Calculate stress due to concentration of solvent molecules.

\[ \hat{\sigma}_{ij}^\beta = \frac{\Delta\mu}{\Omega}\delta_{ij} \]

note that \(\Delta\mu = \mu-\mu_0\). In current version of code value of \(\Delta\mu\) is approximated.

Definition at line 280 of file Gels.hpp.

                                                     {
       PetscFunctionBegin;
       stressBetaHat.resize(3,3,false);
       stressBetaHat.clear();
       for(int ii=0; ii<3; ii++){
         stressBetaHat(ii,ii) = -(mU-dAta[iD].mU0)/dAta[iD].oMega;
       }
       PetscFunctionReturn(0);
     }

◆ calculateStressTotal()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateStressTotal ( )

inlinevirtual

Definition at line 292 of file Gels.hpp.

                                                   {
       PetscFunctionBegin;
       stressTotal.resize(3,3,false);
       noalias(stressTotal) = stressAlpha;
       noalias(stressTotal) += stressBeta;
       noalias(stressTotal) += stressBetaHat;
       PetscFunctionReturn(0);
     }

◆ calculateTraceStrainTotalDot()

template<typename TYPE >

virtual PetscErrorCode GelModule::Gel::ConstitutiveEquation< TYPE >::calculateTraceStrainTotalDot ( )

inlinevirtual

\berief Calculate trace of rate of gradient of deformation

Definition at line 181 of file Gels.hpp.

                                                           {
       PetscFunctionBegin;
       traceStrainTotalDot = 0;
       for(int ii = 0;ii<3;ii++) {
         traceStrainTotalDot += FDot(ii,ii);
       }
       PetscFunctionReturn(0);
     }

Member Data Documentation

◆ C

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::C

Cauchy deformation.

Definition at line 135 of file Gels.hpp.

◆ dAta

template<typename TYPE >

map<int,BlockMaterialData>& GelModule::Gel::ConstitutiveEquation< TYPE >::dAta

Definition at line 117 of file Gels.hpp.

◆ F

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::F

Gradient of deformation.

Definition at line 126 of file Gels.hpp.

◆ FDot

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::FDot

Rate of gradient of deformation.

Definition at line 127 of file Gels.hpp.

◆ gradientMu

template<typename TYPE >

ublas::vector<TYPE,ublas::bounded_array<TYPE,3> > GelModule::Gel::ConstitutiveEquation< TYPE >::gradientMu

Gradient of solvent concentration.

Definition at line 131 of file Gels.hpp.

◆ gradientU

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::gradientU

Gradient of displacements.

Definition at line 136 of file Gels.hpp.

◆ iD

template<typename TYPE >

int GelModule::Gel::ConstitutiveEquation< TYPE >::iD

Definition at line 116 of file Gels.hpp.

◆ mU

template<typename TYPE >

TYPE GelModule::Gel::ConstitutiveEquation< TYPE >::mU

Solvent concentration.

Definition at line 130 of file Gels.hpp.

◆ residualStrainHat

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::residualStrainHat

Residual for calculation epsilon hat.

Definition at line 154 of file Gels.hpp.

◆ solventConcentrationDot

template<typename TYPE >

TYPE GelModule::Gel::ConstitutiveEquation< TYPE >::solventConcentrationDot

Volume rate change.

Definition at line 153 of file Gels.hpp.

◆ solventFlux

template<typename TYPE >

ublas::vector<TYPE,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::solventFlux

Solvent flux.

Definition at line 152 of file Gels.hpp.

◆ strainHat

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::strainHat

Internal variable, strain in dashpot beta.

Definition at line 128 of file Gels.hpp.

◆ strainHatDot

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::strainHatDot

Internal variable, strain in dashpot beta.

Definition at line 129 of file Gels.hpp.

◆ strainHatFlux

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::strainHatFlux

Rate of dashpot (beta) strain.

Definition at line 141 of file Gels.hpp.

◆ strainTotal

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::strainTotal

Total strain applied at integration point.

Definition at line 137 of file Gels.hpp.

◆ stressAlpha

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::stressAlpha

Stress generated by spring alpha.

Definition at line 139 of file Gels.hpp.

◆ stressBeta

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::stressBeta

Stress generated by spring beta.

Definition at line 140 of file Gels.hpp.

◆ stressBetaHat

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::stressBetaHat

Stress as result of volume change due to solvent concentration.

Definition at line 142 of file Gels.hpp.

◆ stressTotal

template<typename TYPE >

ublas::matrix<TYPE,ublas::row_major,ublas::bounded_array<TYPE,9> > GelModule::Gel::ConstitutiveEquation< TYPE >::stressTotal

Total stress.

Definition at line 151 of file Gels.hpp.

◆ traceStrainHat

template<typename TYPE >

TYPE GelModule::Gel::ConstitutiveEquation< TYPE >::traceStrainHat

Definition at line 145 of file Gels.hpp.

◆ traceStrainTotal

template<typename TYPE >

TYPE GelModule::Gel::ConstitutiveEquation< TYPE >::traceStrainTotal

Definition at line 144 of file Gels.hpp.

◆ traceStrainTotalDot

template<typename TYPE >

TYPE GelModule::Gel::ConstitutiveEquation< TYPE >::traceStrainTotalDot

Definition at line 147 of file Gels.hpp.

◆ traceStressBeta

template<typename TYPE >

TYPE GelModule::Gel::ConstitutiveEquation< TYPE >::traceStressBeta

Definition at line 146 of file Gels.hpp.

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

users_modules/gels/src/Gels.hpp

Public Member Functions

Public Attributes

Detailed Description

template<typename TYPE> struct GelModule::Gel::ConstitutiveEquation< TYPE >

Constructor & Destructor Documentation

◆ ConstitutiveEquation()

◆ ~ConstitutiveEquation()

Member Function Documentation

◆ calculateCauchyDefromationTensor()

◆ calculateResidualStrainHat()

◆ calculateSolventConcentrationDot()

◆ calculateSolventFlux()

◆ calculateStrainHatFlux()

◆ calculateStrainTotal()

◆ calculateStressAlpha()

◆ calculateStressBeta()

◆ calculateStressBetaHat()

◆ calculateStressTotal()

◆ calculateTraceStrainTotalDot()

Member Data Documentation

◆ C

◆ dAta

◆ F

◆ FDot

◆ gradientMu

◆ gradientU

◆ iD

◆ mU

◆ residualStrainHat

◆ solventConcentrationDot

◆ solventFlux

◆ strainHat

◆ strainHatDot

◆ strainHatFlux

◆ strainTotal

◆ stressAlpha

◆ stressBeta

◆ stressBetaHat

◆ stressTotal

◆ traceStrainHat

◆ traceStrainTotal

◆ traceStrainTotalDot

◆ traceStressBeta

template<typename TYPE>
struct GelModule::Gel::ConstitutiveEquation< TYPE >