void HyperElasticUP3DLaw::CalculateMaterialResponsePK2 (Parameters& rValues)
{
//-----------------------------//
//a.-Check if the constitutive parameters are passed correctly to the law calculation
CheckParameters(rValues);
//b.- Get Values to compute the constitutive law:
Flags &Options=rValues.GetOptions();
const Properties& MaterialProperties = rValues.GetMaterialProperties();
const Matrix& DeformationGradientF = rValues.GetDeformationGradientF();
const double& DeterminantF = rValues.GetDeterminantF();
const GeometryType& DomainGeometry = rValues.GetElementGeometry ();
const Vector& ShapeFunctions = rValues.GetShapeFunctionsValues ();
Vector& StrainVector = rValues.GetStrainVector();
Vector& StressVector = rValues.GetStressVector();
Matrix& ConstitutiveMatrix = rValues.GetConstitutiveMatrix();
//-----------------------------//
//0.- Initialize parameters
MaterialResponseVariables ElasticVariables;
ElasticVariables.Identity = identity_matrix<double> ( 3 );
ElasticVariables.SetElementGeometry(DomainGeometry);
ElasticVariables.SetShapeFunctionsValues(ShapeFunctions);
// Initialize Splited Parts: Isochoric and Volumetric stresses and constitutive tensors
double voigtsize = StressVector.size();
VectorSplit SplitStressVector;
MatrixSplit SplitConstitutiveMatrix;
//1.- Lame constants
const double& YoungModulus = MaterialProperties[YOUNG_MODULUS];
const double& PoissonCoefficient = MaterialProperties[POISSON_RATIO];
ElasticVariables.LameLambda = (YoungModulus*PoissonCoefficient)/((1+PoissonCoefficient)*(1-2*PoissonCoefficient));
ElasticVariables.LameMu = YoungModulus/(2*(1+PoissonCoefficient));
//2.- Thermal constants
if( MaterialProperties.Has(THERMAL_EXPANSION_COEFFICIENT) )
ElasticVariables.ThermalExpansionCoefficient = MaterialProperties[THERMAL_EXPANSION_COEFFICIENT];
else
ElasticVariables.ThermalExpansionCoefficient = 0;
if( MaterialProperties.Has(REFERENCE_TEMPERATURE) )
ElasticVariables.ReferenceTemperature = MaterialProperties[REFERENCE_TEMPERATURE];
else
ElasticVariables.ReferenceTemperature = 0;
//3.-DeformationGradient Tensor 3D
ElasticVariables.DeformationGradientF = DeformationGradientF;
ElasticVariables.DeformationGradientF = Transform2DTo3D( ElasticVariables.DeformationGradientF );
//4.-Determinant of the Total Deformation Gradient
ElasticVariables.DeterminantF = DeterminantF;
//5.-Right Cauchy Green tensor C
Matrix RightCauchyGreen = prod(trans(ElasticVariables.DeformationGradientF),ElasticVariables.DeformationGradientF);
//6.-Inverse of the Right Cauchy-Green tensor C: (stored in the CauchyGreenMatrix)
ElasticVariables.traceCG = 0;
ElasticVariables.CauchyGreenMatrix( 3, 3 );
MathUtils<double>::InvertMatrix( RightCauchyGreen, ElasticVariables.CauchyGreenMatrix, ElasticVariables.traceCG);
//8.-Green-Lagrange Strain:
if(Options.Is( ConstitutiveLaw::COMPUTE_STRAIN ))
{
this->CalculateGreenLagrangeStrain(RightCauchyGreen, StrainVector);
}
//9.-Calculate Total PK2 stress
SplitStressVector.Isochoric = ZeroVector(voigtsize);
if( Options.Is(ConstitutiveLaw::COMPUTE_STRESS ) || Options.Is(ConstitutiveLaw::COMPUTE_CONSTITUTIVE_TENSOR ) )
this->CalculateIsochoricStress( ElasticVariables, StressMeasure_PK2, SplitStressVector.Isochoric );
Vector IsochoricStressVector = SplitStressVector.Isochoric;
if( Options.Is( ConstitutiveLaw::COMPUTE_STRESS ) )
{
SplitStressVector.Volumetric = ZeroVector(voigtsize);
this->CalculateVolumetricStress ( ElasticVariables, SplitStressVector.Volumetric );
//PK2 Stress:
StressVector = SplitStressVector.Isochoric + SplitStressVector.Volumetric;
if( Options.Is(ConstitutiveLaw::ISOCHORIC_TENSOR_ONLY ) )
{
StressVector = SplitStressVector.Isochoric;
}
else if( Options.Is(ConstitutiveLaw::VOLUMETRIC_TENSOR_ONLY ) )
{
StressVector = SplitStressVector.Volumetric;
}
}
//10.-Calculate Constitutive Matrix related to Total PK2 stress
if( Options.Is( ConstitutiveLaw::COMPUTE_CONSTITUTIVE_TENSOR ) )
{
//initialize constitutive tensors
ConstitutiveMatrix.clear();
SplitConstitutiveMatrix.Isochoric = ConstitutiveMatrix;
SplitConstitutiveMatrix.Volumetric = ConstitutiveMatrix;
Matrix IsoStressMatrix = MathUtils<double>::StressVectorToTensor( IsochoricStressVector );
this->CalculateIsochoricConstitutiveMatrix ( ElasticVariables, IsoStressMatrix, SplitConstitutiveMatrix.Isochoric );
this->CalculateVolumetricConstitutiveMatrix ( ElasticVariables, SplitConstitutiveMatrix.Volumetric );
//if( Options.Is(ConstitutiveLaw::TOTAL_TENSOR ) )
ConstitutiveMatrix = SplitConstitutiveMatrix.Isochoric + SplitConstitutiveMatrix.Volumetric;
if( Options.Is(ConstitutiveLaw::ISOCHORIC_TENSOR_ONLY ) )
{
ConstitutiveMatrix = SplitConstitutiveMatrix.Isochoric;
}
else if( Options.Is(ConstitutiveLaw::VOLUMETRIC_TENSOR_ONLY ) )
{
ConstitutiveMatrix = SplitConstitutiveMatrix.Volumetric;
}
}
// std::cout<<" Constitutive "<<ConstitutiveMatrix<<std::endl;
// std::cout<<" Stress "<<StressVector<<std::endl;
//-----------------------------//
}
void LinearElastic3DLaw::CalculateMaterialResponseKirchhoff (Parameters& rValues)
{
//-----------------------------//
//a.-Check if the constitutive parameters are passed correctly to the law calculation
//CheckParameters(rValues);
//b.- Get Values to compute the constitutive law:
Flags &Options=rValues.GetOptions();
const Properties& MaterialProperties = rValues.GetMaterialProperties();
Vector& StrainVector = rValues.GetStrainVector();
Vector& StressVector = rValues.GetStressVector();
//-----------------------------//
//1.- Lame constants
const double& YoungModulus = MaterialProperties[YOUNG_MODULUS];
const double& PoissonCoefficient = MaterialProperties[POISSON_RATIO];
// //1.1- Thermal constants
// double ThermalExpansionCoefficient = 0;
// if( MaterialProperties.Has(THERMAL_EXPANSION_COEFFICIENT) )
// ThermalExpansionCoefficient = MaterialProperties[THERMAL_EXPANSION_COEFFICIENT];
// double ReferenceTemperature = 0;
// if( MaterialProperties.Has(REFERENCE_TEMPERATURE) )
// ReferenceTemperature = MaterialProperties[REFERENCE_TEMPERATURE];
if(Options.Is( ConstitutiveLaw::COMPUTE_STRAIN )) //large strains
{
//1.-Compute total deformation gradient
const Matrix& DeformationGradientF = rValues.GetDeformationGradientF();
//2.-Left Cauchy-Green tensor b
Matrix LeftCauchyGreenMatrix = prod(DeformationGradientF,trans(DeformationGradientF));
//3.-Almansi Strain:
//e= 0.5*(1-invFT*invF)
this->CalculateAlmansiStrain(LeftCauchyGreenMatrix,StrainVector);
//LARGE STRAINS OBJECTIVE MESURE KIRCHHOFF MATERIAL:
// Kirchhoff model is set with S = CE
this->CalculateMaterialResponsePK2 (rValues);
//1.- Obtain parameters
const double& DeterminantF = rValues.GetDeterminantF();
//2.-Almansi Strain:
// if(Options.Is( ConstitutiveLaw::COMPUTE_STRAIN ))
// {
// TransformStrains (StrainVector, DeformationGradientF, StrainMeasure_GreenLagrange, StrainMeasure_Almansi);
// }
//3.-Calculate Total Kirchhoff stress
if( Options.Is( ConstitutiveLaw::COMPUTE_STRESS ) )
{
TransformStresses(StressVector, DeformationGradientF, DeterminantF, StressMeasure_PK2, StressMeasure_Kirchhoff);
}
// COMMENTED BECAUSE THE CONVERGENCE IS NOT IMPROVED AND IS TIME CONSUMING:
//4.-Calculate Cauchy constitutive tensor
// if( Options.Is( ConstitutiveLaw::COMPUTE_CONSTITUTIVE_TENSOR ) )
// {
// Matrix& ConstitutiveMatrix = rValues.GetConstitutiveMatrix();
// PushForwardConstitutiveMatrix(ConstitutiveMatrix, DeformationGradientF);
// }
if( Options.Is( ConstitutiveLaw::COMPUTE_STRAIN_ENERGY ) )
{
mStrainEnergy *= DeterminantF;
}
}
else{ //small strains
//7.-Calculate total Kirchhoff stress
if( Options.Is( ConstitutiveLaw::COMPUTE_STRESS ) ){
if( Options.Is( ConstitutiveLaw::COMPUTE_CONSTITUTIVE_TENSOR ) ){
Matrix& ConstitutiveMatrix = rValues.GetConstitutiveMatrix();
this->CalculateLinearElasticMatrix( ConstitutiveMatrix, YoungModulus, PoissonCoefficient );
this->CalculateStress( StrainVector, ConstitutiveMatrix, StressVector );
}
else {
Matrix ConstitutiveMatrix = ZeroMatrix( StrainVector.size() ,StrainVector.size());
this->CalculateLinearElasticMatrix( ConstitutiveMatrix, YoungModulus, PoissonCoefficient );
this->CalculateStress( StrainVector, ConstitutiveMatrix, StressVector );
}
}
else if( Options.IsNot( ConstitutiveLaw::COMPUTE_STRESS ) && Options.Is( ConstitutiveLaw::COMPUTE_CONSTITUTIVE_TENSOR ) )
{
Matrix& ConstitutiveMatrix = rValues.GetConstitutiveMatrix();
this->CalculateLinearElasticMatrix( ConstitutiveMatrix, YoungModulus, PoissonCoefficient );
}
if( Options.Is( ConstitutiveLaw::COMPUTE_STRAIN_ENERGY ) )
{
if( Options.IsNot( ConstitutiveLaw::COMPUTE_STRESS ) ){
if(Options.Is( ConstitutiveLaw::COMPUTE_CONSTITUTIVE_TENSOR )){
Matrix ConstitutiveMatrix = ZeroMatrix( StrainVector.size(), StrainVector.size());
this->CalculateLinearElasticMatrix( ConstitutiveMatrix, YoungModulus, PoissonCoefficient );
this->CalculateStress( StrainVector, ConstitutiveMatrix, StressVector );
}
else{
Matrix& ConstitutiveMatrix = rValues.GetConstitutiveMatrix();
this->CalculateStress( StrainVector, ConstitutiveMatrix, StressVector );
}
}
mStrainEnergy = 0.5 * inner_prod(StrainVector,StressVector); //Belytschko Nonlinear Finite Elements pag 226 (5.4.3) : w = 0.5*E:C:E
}
}
//std::cout<<" Strain "<<StrainVector<<std::endl;
//std::cout<<" Stress "<<StressVector<<std::endl;
//Matrix& ConstitutiveMatrix = rValues.GetConstitutiveMatrix();
//std::cout<<" Constitutive "<<ConstitutiveMatrix<<std::endl;
}