Functions
template<typename FunctorType , typename MeshType , typename MapType >
void	saveVectorAccordingToFunctor (const std::shared_ptr< FESpace< MeshType, MapType > > dispFESpace, const FunctorType functor, const VectorEpetra &originVector, const std::shared_ptr< VectorEpetra > statusVector, const std::shared_ptr< VectorEpetra > saveVector, const UInt offset)
	Save displacement according to a functor. More...

template<typename FunctorType , typename MeshType , typename MapType >
void	saveBooleanVectorAccordingToFunctor (const std::shared_ptr< FESpace< MeshType, MapType > > dispFESpace, const FunctorType &functor, const std::shared_ptr< VectorEpetra > originVector, std::shared_ptr< VectorEpetra > saveVector, const UInt offset)

void	computeGradientLocalDisplacement (boost::multi_array< Real, 3 > &gradientLocalDisplacement, const VectorElemental &uk_loc, const CurrentFE &fe)
	Gradient of the displacement on the local element. More...

void	computeLocalDeformationGradient (const VectorElemental &uk_loc, std::vector< Epetra_SerialDenseMatrix > &tensorF, const CurrentFE &fe)
	Deformation Gradient on the local element. More...

void	computeLocalDeformationGradientWithoutIdentity (const VectorElemental &uk_loc, std::vector< Epetra_SerialDenseMatrix > &tensorF, const CurrentFE &fe)
	Gradient on the local element. More...

void	stiff_derdiv (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	METHODS SHARED BETWEEN LINEAR ELASTIC MODEL AND ST.VENANT-KIRCHHOFF MODEL These two methods are implemented in AssemblyElemental.cpp. More...

void	stiff_dergradbis (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary second term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference) More...

void	stiff_divgrad (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary third term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference) More...

void	stiff_gradgrad (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fourth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference) More...

void	stiff_dergrad_gradbis (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fifth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference) More...

void	stiff_dergrad_gradbis_Tr (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fifth-2 term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference) More...

void	stiff_gradgradTr_gradbis (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary sixth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference) More...

void	stiff_dergrad (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	METHODS FOR THE JACOBIAN MATRIX. More...

void	stiff_divgrad_2 (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary second term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference) More...

void	stiff_gradgrad_2 (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary third term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference) More...

void	stiff_dergrad_gradbis_2 (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fourth term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference) More...

void	stiff_dergrad_gradbis_Tr_2 (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fifth term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference) More...

void	stiff_gradgradTr_gradbis_2 (Real coef, const boost::multi_array< Real, 3 > &gradientLocalDisplacement, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary sixth term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference) More...

void	stiff_gradgradTr_gradbis_3 (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary seventh term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference) More...

void	source_Pvol (Real coef, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, VectorElemental &elvec, const CurrentFE &fe)
	METHODS SHARED BETWEEN NEO-HOOKEAN AND EXPONENTIAL MODELS The volumetric part for Neo-Hookean and Exponential models is the same Methods for the volumetric part of the stiffness vector. More...

void	stiff_Jac_Pvol_1term (Real coef, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, MatrixElemental &elmat, const CurrentFE &fe)
	Methods for the volumetric part of the Jacobian matrix. More...

void	stiff_Jac_Pvol_2term (Real coef, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary second volumetric term of the nonlinear Jacobian matrix of the Neo-Hookean and Exponential models (see the reference) More...

void	source_P1iso_NH (Real coef, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, VectorElemental &elvec, const CurrentFE &fe)
	METHODS FOR NEO-HOOKEAN MODEL Methods for the isochoric part of the stiffness vector. More...

void	computeInvariantsRightCauchyGreenTensor (std::vector< LifeV::Real > &invariants, const Epetra_SerialDenseMatrix &tensorF, Epetra_SerialDenseMatrix &cofactorF)
	METHODS FOR TENSORIAL CALCULUS In this part of the namespace, the methods to perform basics operations on tensors are defined. More...

void	computeInvariantsRightCauchyGreenTensor (std::vector< LifeV::Real > &invariants, const Epetra_SerialDenseMatrix &tensorF)
	Computation of the Right Cauchy Green tensor given the tensor F. More...

void	computeCauchyStressTensor (Epetra_SerialDenseMatrix &cauchy, Epetra_SerialDenseMatrix &firstPiola, LifeV::Real det, Epetra_SerialDenseMatrix &tensorF)

void	computeEigenvalues (const Epetra_SerialDenseMatrix &cauchy, std::vector< LifeV::Real > &eigenvaluesR, std::vector< LifeV::Real > &eigenvaluesI)

void	stiff_Jac_P1iso_NH_1term (Real coef, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, MatrixElemental &elmat, const CurrentFE &fe)
	Methods for the isochoric part of the Jacobian matrix. More...

void	stiff_Jac_P1iso_NH_2term (Real coef, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary second nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference) More...

void	stiff_Jac_P1iso_NH_3term (Real coef, const std::vector< Real > &Jk, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary third nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference) More...

void	stiff_Jac_P1iso_NH_4term (Real coef, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fourth nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference) More...

void	stiff_Jac_P1iso_NH_5term (Real coef, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fifth nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference) More...

void	source_P1iso_Exp (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, VectorElemental &elvec, const CurrentFE &fe)
	METHODS FOR EXPONENTIAL MODEL Methods for the isochoric part of the stiffness vector. More...

void	stiff_Jac_P1iso_Exp_1term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Methods for the isochoric part of the Jacobian matrix. More...

void	stiff_Jac_P1iso_Exp_2term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary second nonlinear isochoric Jacobian matrix for Exponential model (see the reference) More...

void	stiff_Jac_P1iso_Exp_3term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary third nonlinear isochoric Jacobian matrix for Exponential model (see the reference) More...

void	stiff_Jac_P1iso_Exp_4term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fourth nonlinear isochoric Jacobian matrix for Exponential model (see the reference) More...

void	stiff_Jac_P1iso_Exp_5term (Real coef, Real coefExp, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fifth nonlinear isochoric Jacobian matrix for Exponential model (see the reference) More...

void	stiff_Jac_P1iso_Exp_6term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary sixth nonlinear isochoric Jacobian matrix for Exponential model (see the reference) More...

void	source_P1iso_VKPenalized (Real lambda, Real mu, const boost::multi_array< Real, 3 > &FkMinusTransposed, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Ic_isok, const std::vector< Real > &Ic_k, const std::vector< Real > &Jack_k, VectorElemental &elvec, const CurrentFE &fe)
	METHOD FOR THE ST. More...

void	source_P2iso_VKPenalized (Real mu, const boost::multi_array< Real, 3 > &FkMinusTransposed, const boost::multi_array< Real, 3 > &FkCk, const std::vector< Real > &Ic_Squared, const std::vector< Real > &Jk, VectorElemental &elvec, const CurrentFE &fe)
	Elementary nonlinear isochoric stiffness vector for St. Venant-Kirchhoff Penalized model. More...

void	stiff_Jac_P1iso_VKPenalized_0term (Real lambda, Real mu, const boost::multi_array< Real, 3 > &FkMinusTransposed, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_k, const std::vector< Real > &IcIso_k, MatrixElemental &elmat, const CurrentFE &fe)
	Methdos for the Jacobian of the St. More...

void	stiff_Jac_P1iso_VKPenalized_1term (Real coeff, const boost::multi_array< Real, 3 > &FkMinusTransposed, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_k, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary first nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_2term (Real coef, const boost::multi_array< Real, 3 > &FkMinusTransposed, const std::vector< Real > &Jk, const std::vector< Real > &Ic_k, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary third nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_3term (Real coef, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary second nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_4term (Real coef, const boost::multi_array< Real, 3 > &FkMinusTransposed, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_k, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fourth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_5term (Real coef, Real secondCoef, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fifth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_6term (Real coef, Real secondCoef, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, const boost::multi_array< Real, 3 > &Fk, const boost::multi_array< Real, 3 > &FkMinusTransposed, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary sixth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_7term (Real coef, Real secondCoef, const boost::multi_array< Real, 3 > &FkMinusTransposed, const std::vector< Real > &Ic_isok, const std::vector< Real > &Ic_k, const std::vector< Real > &Jk, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary seventh nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_8term (Real coef, const std::vector< Real > &Jack_k, const boost::multi_array< Real, 3 > &FkMinusTransposed, const boost::multi_array< Real, 3 > &FkCk, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary seventh nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_9term (Real coef, const std::vector< Real > &Jack_k, const std::vector< Real > &Ic_kSquared, const boost::multi_array< Real, 3 > &FkMinusTransposed, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary seventh nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_10term (Real coef, const std::vector< Real > &Jack_k, const boost::multi_array< Real, 3 > &Ck, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary eigth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_11term (Real coef, const std::vector< Real > &Jk, const boost::multi_array< Real, 3 > &Fk, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary sixth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_12term (Real coef, const std::vector< Real > &Jk, const boost::multi_array< Real, 3 > &Fk, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary tenth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_13term (Real coef, const std::vector< Real > &Jk, const std::vector< Real > &Ic_kSquared, const boost::multi_array< Real, 3 > &FkMinusTransposed, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary eleventh nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	stiff_Jac_P1iso_VKPenalized_14term (Real coef, const std::vector< Real > &Jk, const boost::multi_array< Real, 3 > &FkCk, const boost::multi_array< Real, 3 > &FkMinusTransposed, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary twelveth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference) More...

void	source_P1iso_SecondOrderExponential (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &trCisok, VectorElemental &elvec, const CurrentFE &fe)
	Methods for second order exponential law Methods for the first Piola-Kirchhoff tensor. More...

void	stiff_Jac_P1iso_SecondOrderExp_1term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Methods for the Jacobian matrix Elementary first nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference) More...

void	stiff_Jac_P1iso_SecondOrderExp_2term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary second nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference) More...

void	stiff_Jac_P1iso_SecondOrderExp_3term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary third nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference) More...

void	stiff_Jac_P1iso_SecondOrderExp_4term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const boost::multi_array< Real, 3 > &Fk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, const std::vector< Real > &Ic_k, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fourth nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference) More...

void	stiff_Jac_P1iso_SecondOrderExp_5term (Real coef, Real coefExp, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary fifth nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference) More...

void	stiff_Jac_P1iso_SecondOrderExp_6term (Real coef, Real coefExp, const boost::multi_array< Real, 3 > &CofFk, const std::vector< Real > &Jk, const std::vector< Real > &Ic_isok, MatrixElemental &elmat, const CurrentFE &fe)
	Elementary sixth nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference) More...

Detailed Description

/namespace AssemblyElementalStructure

This namespace is specially designed to contain the elementary operations (corresponding to differential operators) that build the local contributions to be used in the assembly procedures.

Function Documentation

◆ saveVectorAccordingToFunctor()

void saveVectorAccordingToFunctor	(	const std::shared_ptr< FESpace< MeshType, MapType > >	dispFESpace,
		const FunctorType	functor,
		const VectorEpetra &	originVector,
		const std::shared_ptr< VectorEpetra >	statusVector,
		const std::shared_ptr< VectorEpetra >	saveVector,
		const UInt	offset
	)

Save displacement according to a functor.

Parameters

FE	the finite element space
fct	the functor for the saving
originVector	the vector from which the values are taken
saveVector	the vector from which the values are saved

Definition at line 90 of file structure/fem/AssemblyElementalStructure.hpp.

◆ saveBooleanVectorAccordingToFunctor()

void saveBooleanVectorAccordingToFunctor	(	const std::shared_ptr< FESpace< MeshType, MapType > >	dispFESpace,
		const FunctorType &	functor,
		const std::shared_ptr< VectorEpetra >	originVector,
		std::shared_ptr< VectorEpetra >	saveVector,
		const UInt	offset
	)

Definition at line 131 of file structure/fem/AssemblyElementalStructure.hpp.

◆ computeGradientLocalDisplacement()

void computeGradientLocalDisplacement	(	boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		const VectorElemental &	uk_loc,
		const CurrentFE &	fe
	)

Gradient of the displacement on the local element.

This function assembles the local tensor of the gradient of the displacement field

Parameters

uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
fe	The current finite element

Definition at line 48 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ computeLocalDeformationGradient()

void computeLocalDeformationGradient	(	const VectorElemental &	uk_loc,
		std::vector< Epetra_SerialDenseMatrix > &	tensorF,
		const CurrentFE &	fe
	)

Deformation Gradient on the local element.

This function assembles the local deformation gradient

Parameters

uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
fe	The current finite element

Definition at line 77 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ computeLocalDeformationGradientWithoutIdentity()

void computeLocalDeformationGradientWithoutIdentity	(	const VectorElemental &	uk_loc,
		std::vector< Epetra_SerialDenseMatrix > &	tensorF,
		const CurrentFE &	fe
	)

Gradient on the local element.

This function assembles the local gradient

Parameters

uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
fe	The current finite element

Definition at line 107 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_derdiv()

void stiff_derdiv	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

METHODS SHARED BETWEEN LINEAR ELASTIC MODEL AND ST.VENANT-KIRCHHOFF MODEL These two methods are implemented in AssemblyElemental.cpp.

Methods for St.

METHODS FOR ST.VENANT-KIRCHHOFF MODEL Methods for the Stiffness matrix ( evaluate the RHS or the residuals ) Elementary first term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference)

This function assembles the local first term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Venant Kirchhoff model Methods for the stiffness matrix $coef \cdot ( trace { [\nabla u^k]^T \nabla u }, \nabla\cdot v )$

Definition at line 138 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_dergradbis()

void stiff_dergradbis	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary second term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference)

$coef \cdot ( [\nabla u^k]^T \nabla u : \nabla v )$

This function assembles the local second term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 173 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_divgrad()

void stiff_divgrad	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary third term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference)

This function assembles the local third term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 209 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_gradgrad()

void stiff_gradgrad	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fourth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference)

This function assembles the local fourth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the fourth term of the nonlinear stiffness matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary stiffness matrix of the current volume
fe	The current finite element

Definition at line 260 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_dergrad_gradbis()

void stiff_dergrad_gradbis	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fifth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference)

This function assembles the local fifth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 312 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_dergrad_gradbis_Tr()

void stiff_dergrad_gradbis_Tr	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fifth-2 term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference)

This function assembles the local fifth-2 term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 350 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_gradgradTr_gradbis()

void stiff_gradgradTr_gradbis	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary sixth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model (see the reference)

This function assembles the local sixth term of the nonlinear stiffness matrix for St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

u^k [ u^k]^T at each quadrature poInt

Definition at line 387 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_dergrad()

void stiff_dergrad	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

METHODS FOR THE JACOBIAN MATRIX.

Methods for the jacobian (St. Venant-Kirchhoff material)

Elementary first term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference)

This function assembles the local first term of the Jacobian matrix of the nonlinear stiffness matrix of the St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

$coef \cdot ( [\nabla u]^T \nabla u^k + [\nabla u^k]^T \nabla u : \nabla v )$

Definition at line 452 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_divgrad_2()

void stiff_divgrad_2	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary second term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference)

This function assembles the local second term of the Jacobian matrix of the nonlinear stiffness matrix of the St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 487 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_gradgrad_2()

void stiff_gradgrad_2	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary third term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference)

This function assembles the local third term of the Jacobian matrix of the nonlinear stiffness matrix of the St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 521 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_dergrad_gradbis_2()

void stiff_dergrad_gradbis_2	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fourth term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference)

This function assembles the local fourth term of the Jacobian matrix of the nonlinear stiffness matrix of the St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 554 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_dergrad_gradbis_Tr_2()

void stiff_dergrad_gradbis_Tr_2	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fifth term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference)

This function assembles the local fifth term of the Jacobian matrix of the nonlinear stiffness matrix of the St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 590 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_gradgradTr_gradbis_2()

void stiff_gradgradTr_gradbis_2	(	Real	coef,
		const boost::multi_array< Real, 3 > &	gradientLocalDisplacement,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary sixth term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference)

This function assembles the local sixth term of the Jacobian matrix of the nonlinear stiffness matrix of the St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 630 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_gradgradTr_gradbis_3()

void stiff_gradgradTr_gradbis_3	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary seventh term of the Jacobian matrix for the nonlinear stiffness matrix of the St.Venant-Kirchhoff model (see the reference)

This function assembles the local seventh term of the Jacobian matrix of the nonlinear stiffness matrix of the St.Venant-Kirchhoff model.

Parameters

coef	The constant coefficient of the matrix
uk_loc	The local displacement (remark: the nonlinear matrix depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Definition at line 670 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ source_Pvol()

void source_Pvol	(	Real	coef,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

METHODS SHARED BETWEEN NEO-HOOKEAN AND EXPONENTIAL MODELS The volumetric part for Neo-Hookean and Exponential models is the same Methods for the volumetric part of the stiffness vector.

METHODS SHARED BETWEEN NEO-HOOKEAN AND EXPONENTIAL MODELS

The volumetric part is the same for Neo-Hookean and Expoential models is the same

Elementary volumetric term of the nonlinear stiffness vector of the Neo-Hookean and Exponential models (see the reference)

This function assembles the volumetric term of the nonlinear stiffness vector of the Neo-Hookean and Exponential models.

Parameters

coef	The constant coefficient of the volumetric term of the nonlinear stiffness vector
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elvec	The elementary vector of the current volume
fe	The current finite element

STIFFFNESS VECTOR --------------------------------------------------------------------------— Volumetric part-----------------------------------------------------------------------------— Source term source_Pvol: Int { coef /2* (J^2 - J + log(J) ) * 1/J * (CofF : v) }

Definition at line 748 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_Pvol_1term()

void stiff_Jac_Pvol_1term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Methods for the volumetric part of the Jacobian matrix.

JACOBIAN MATRIX -------------------------------------------------------------------------—— Volumetric part--------------------------------------------------------------------------——.

Elementary first volumetric term of the nonlinear Jacobian matrix of the Neo-Hookean and Exponential models (see the reference)

This function assembles the local first volumetric term of the Jacobian matrix of the nonlinear volumetric stiffness vector of the Neo-Hookean and Exponential models.

Parameters

coef	The constant coefficient of the matrix
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elvec	The elementary matrix of the current volume
fe	The current finite element

Jacobian matrix: Int { 1/2 * coef * ( 2 - 1/J + 1/J^2 ) * ( CofF : ) (CofF : v) }

Definition at line 780 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_Pvol_2term()

void stiff_Jac_Pvol_2term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary second volumetric term of the nonlinear Jacobian matrix of the Neo-Hookean and Exponential models (see the reference)

This function assembles the local second volumetric term of the Jacobian matrix of the nonlinear volumetric stiffness vector of the Neo-Hookean and Exponential models.

Parameters

coef	The constant coefficient of the matrix
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness matrix: Int { 1/2 * coef * ( 1/J - 1 - log(J)/J^2 ) * ( CofF [ ]^t CofF ) : v }

Definition at line 820 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ source_P1iso_NH()

void source_P1iso_NH	(	Real	coef,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

METHODS FOR NEO-HOOKEAN MODEL Methods for the isochoric part of the stiffness vector.

METHODS FOR NEO-HOOKEAN MODEL

Stiffness vector isochoric part ---------------------------------------------------------——

Elementary nonlinear isochoric stiffness vector for Neo-Hookean model (see the reference)

This function assembles the nonlinear isochoric part of the stiffness vector for Neo-Hookean model.

Parameters

coef	The coefficient of the vector
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elvec	The elementary vector of the current volume
fe	The current finite element

Source term source_P1iso_NH: Int { coef * ( J^(-2/3) * (F : v) - 1/3 * (Ic_iso / J) (CofF : v) ) }

Definition at line 864 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ computeInvariantsRightCauchyGreenTensor() [1/2]

void computeInvariantsRightCauchyGreenTensor	(	std::vector< LifeV::Real > &	invariants,
		const Epetra_SerialDenseMatrix &	tensorF,
		Epetra_SerialDenseMatrix &	cofactorF
	)

METHODS FOR TENSORIAL CALCULUS In this part of the namespace, the methods to perform basics operations on tensors are defined.

END OF EXPONENTIAL MODEL

The operations are: tensorial products, computations of invariants

This function computes the invariants of the right Cauchy Green tensor and the cofactor of F

Parameters

invariants	vector of invariants of C
tensorF	deformation gradient tensor

METHODS FOR TENSORIAL CALCULUS

Computation of the Right Cauchy Green tensor given the tensor F.

Definition at line 1404 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ computeInvariantsRightCauchyGreenTensor() [2/2]

void computeInvariantsRightCauchyGreenTensor	(	std::vector< LifeV::Real > &	invariants,
		const Epetra_SerialDenseMatrix &	tensorF
	)

Computation of the Right Cauchy Green tensor given the tensor F.

Definition at line 1444 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ computeCauchyStressTensor()

void computeCauchyStressTensor	(	Epetra_SerialDenseMatrix &	cauchy,
		Epetra_SerialDenseMatrix &	firstPiola,
		LifeV::Real	det,
		Epetra_SerialDenseMatrix &	tensorF
	)

This function computes the Cauchy stress tensor given the detF, first Piola Kirchhoff and tensorF

Parameters

cauchy	Cauchy stress tensor
firstPiola	first Piola-Kirchhoff tensor
invariants	vector of invariants of C
tensorF	deformation gradient tensor

Definition at line 1456 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ computeEigenvalues()

void computeEigenvalues	(	const Epetra_SerialDenseMatrix &	cauchy,
		std::vector< LifeV::Real > &	eigenvaluesR,
		std::vector< LifeV::Real > &	eigenvaluesI
	)

This function computes the eigenvalues of

Parameters

cauchy	Cauchy stress tensor
eigenvalues	vector of principal tensions

Definition at line 1467 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_NH_1term()

void stiff_Jac_P1iso_NH_1term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Methods for the isochoric part of the Jacobian matrix.

Elementary first nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference)

This function assembles the local first nonlinear isochooric Jacobian matrix for Neo-Hookean model.

Parameters

coef	The coefficient of the matrix
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Jacobian matrix isochoric part ----------------------------------------------------------—— 1. Jacobian matrix : Int { -2/3 * coef * J^(-5/3) *( CofF : ) ( F : ) }

Definition at line 906 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_NH_2term()

void stiff_Jac_P1iso_NH_2term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary second nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference)

This function assembles the local second nonlinear isochooric Jacobian matrix for Neo-Hookean model.

Parameters

coef	The coefficient of the matrix
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness matrix: Int { 2/9 * coef * ( Ic_iso / J^2 )( CofF : ) ( CofF : ) }

Definition at line 947 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_NH_3term()

void stiff_Jac_P1iso_NH_3term	(	Real	coef,
		const std::vector< Real > &	Jk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary third nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference)

This function assembles the local third nonlinear isochooric Jacobian matrix for Neo-Hookean model.

Parameters

coef	The coefficient of the matrix
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness matrix : Int { coef * J^(-2/3) ( : )}

assembling diagonal block

copy of diagonal block

assembling diagonal block

copy of diagonal block

assembling diagonal block

copy of diagonal block

assembling diagonal block

copy of diagonal block

Definition at line 988 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_NH_4term()

void stiff_Jac_P1iso_NH_4term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fourth nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference)

This function assembles the local fourth nonlinear isochooric Jacobian matrix for Neo-Hookean model.

Parameters

coef	The coefficient of the matrix
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness matrix : Int { -2/3 * coef * J^(-5/3) ( F : ) ( CofF : ) }

Definition at line 1024 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_NH_5term()

void stiff_Jac_P1iso_NH_5term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fifth nonlinear isochoric Jacobian matrix for Neo-Hookean model (see the reference)

This function assembles the local fifth nonlinear isochooric Jacobian matrix for Neo-Hookean model.

Parameters

coef	The coefficient of the matrix
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness matrix : Int { 1/3 * coef * J^(-2) * Ic_iso * (CofF [ ]^t CofF ) : }

Definition at line 1065 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ source_P1iso_Exp()

void source_P1iso_Exp	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

METHODS FOR EXPONENTIAL MODEL Methods for the isochoric part of the stiffness vector.

END OF NEO-HOOKEAN MODEL

Elementary nonlinear isochoric stiffness vector for Exponential model (see the reference)

This function assembles the local nonlinear isochoric stiffness vector for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elvec	The elementary vector of the current volume
fe	The current finite element

METHODS FOR EXPONENTIAL MODEL

Stiffness vector isochoric part ------------------------------------------------------------—

Definition at line 1113 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_Exp_1term()

void stiff_Jac_P1iso_Exp_1term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Methods for the isochoric part of the Jacobian matrix.

Jacobian matrix isochoric part ----------------------------------------------------------——.

Elementary first nonlinear isochoric Jacobian matrix for Exponential model (see the reference)

This function assembles the local first nonlinear isochoric Jacobian matrix for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : Int { - 2/3 coef * J^(-5/3) * exp( coefExp( Ic_iso - 3) )* ( 1. + coefExp * Ic_iso ) * ( CofF : ) ( F : ) }

Definition at line 1153 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_Exp_2term()

void stiff_Jac_P1iso_Exp_2term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary second nonlinear isochoric Jacobian matrix for Exponential model (see the reference)

This function assembles the local second nonlinear isochoric Jacobian matrix for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : Int { 2 * coef * coefExp * J^(-4/3) * exp( coefExp*( Ic_iso - 3) ) * ( F : ) ( F : )}

Definition at line 1196 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_Exp_3term()

void stiff_Jac_P1iso_Exp_3term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary third nonlinear isochoric Jacobian matrix for Exponential model (see the reference)

This function assembles the local third nonlinear isochoric Jacobian matrix for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term: Int { 2.0/9.0 * coef * J^-2 * Ic_iso * exp( coefExp*( Ic_iso - 3) ) * ( 1. + coefExp * Ic_iso )( CofF : ) ( CofF : )}

Definition at line 1236 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_Exp_4term()

void stiff_Jac_P1iso_Exp_4term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fourth nonlinear isochoric Jacobian matrix for Exponential model (see the reference)

This function assembles the local fourth nonlinear isochoric Jacobian matrix for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term: Int { -2.0/3.0 * coef * J^(-5/3) * exp( coefExp*( Ic_iso - 3) ) * ( 1. + coefExp * Ic_iso )( F : ) ( CofF : ) }

Definition at line 1277 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_Exp_5term()

void stiff_Jac_P1iso_Exp_5term	(	Real	coef,
		Real	coefExp,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fifth nonlinear isochoric Jacobian matrix for Exponential model (see the reference)

This function assembles the local fifth nonlinear isochoric Jacobian matrix for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : Int {coef * J^(-2/3) * exp( coefExp*( Ic_iso - 3)) ( : )}

copy of diagonal block

Definition at line 1319 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_Exp_6term()

void stiff_Jac_P1iso_Exp_6term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary sixth nonlinear isochoric Jacobian matrix for Exponential model (see the reference)

This function assembles the local sixth nonlinear isochoric Jacobian matrix for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : Int { 1.0/3.0 * coef * J^(-2) * Ic_iso * exp(coefExp( Ic_iso - 3)) * (CofF [ ]^t CofF ) : }

Definition at line 1355 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ source_P1iso_VKPenalized()

void source_P1iso_VKPenalized	(	Real	lambda,
		Real	mu,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Ic_isok,
		const std::vector< Real > &	Ic_k,
		const std::vector< Real > &	Jack_k,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

METHOD FOR THE ST.

METHODS FOR THE ST.

VENANT-KIRCHHOFF LAW IN THE ISOCHORIC AND VOLUMETRIC DECOUPLED VERSION This law uses, for the volumetric part, the one used by the exponential and neohookean model. The isochoric part is, of course, completely new and, consequently its jacobian. Elementary nonlinear isochoric stiffness vector for St. Venant-Kirchhoff Penalized model

This function assembles the local nonlinear isochoric stiffness vector for St. Venant-Kirchhoff Penalized model

Parameters

lambda	first Lame Coefficient
mu	shear modulus
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elvec	The elementary vector of the current volume
fe	The current finite element

VENANT KIRCHHOFF PENALIZED LAW

Stiffness vector isochoric part ------------------------------------------------------------—

Definition at line 1529 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ source_P2iso_VKPenalized()

void source_P2iso_VKPenalized	(	Real	mu,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		const boost::multi_array< Real, 3 > &	FkCk,
		const std::vector< Real > &	Ic_Squared,
		const std::vector< Real > &	Jk,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

Elementary nonlinear isochoric stiffness vector for St. Venant-Kirchhoff Penalized model.

This function assembles the local nonlinear isochoric stiffness vector for St. Venant-Kirchhoff Penalized model

Parameters

mu	shear modulus
Fk^-T
FkCk	The product FC
Jk	The determinant of F
Ic_Squared	The trace of C^2
elvec	The elementary vector of the current volume
fe	The current finite element

Definition at line 1564 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_0term()

void stiff_Jac_P1iso_VKPenalized_0term	(	Real	lambda,
		Real	mu,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_k,
		const std::vector< Real > &	IcIso_k,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Methdos for the Jacobian of the St.

Jacobian matrix of the first Piola-Kirchhoff tensor for the VK Penalized law.

Venant-Kirchhoff Penalized law. Elementary first nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local first nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

lambda	the first Lame coefficient
FkMinusTransposed	The matrix F^-T
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_k	The trace of C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { -(2.0/3.0) * Jk^(-2.0/3.0) * ( (lambda/2) * Ic_isok - ( (3/2)*lambda + mu ) ) * F^-T: ) * ( F - (1.0/3.0) * Ic_k * F^-T ): }

Definition at line 1595 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_1term()

void stiff_Jac_P1iso_VKPenalized_1term	(	Real	coeff,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_k,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary first nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local first nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

lambda	the first Lame coefficient
FkMinusTransposed	The matrix F^-T
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_k	The trace of C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term :int{ J^(-2/3) * (lambda / 2) * ( (-2/3) * Ic_k * J^(-2/3) * F^-T: ) * ( F : )}

Definition at line 1636 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_2term()

void stiff_Jac_P1iso_VKPenalized_2term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_k,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary third nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local third nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	lambda / 2 where lambda is the first Lame constant
FKMinusTransposed	The matrix F^-T
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_k	The first invariant of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term:int { J^(-2/3) * (lambda / 2) * ( ( 2/9 ) * J^(-2/3) * Ic_k^2 ) * ( F^-T : ) ( F^-T : ) }

Definition at line 1676 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_3term()

void stiff_Jac_P1iso_VKPenalized_3term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary second nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local second nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	(lambda/2) where lambda is the first Lame coefficient
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : Int { J^(-2/3) * coeff * ( 2 * J^(-2/3) ) * ( F : ) ( F : )}

Definition at line 1715 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_4term()

void stiff_Jac_P1iso_VKPenalized_4term	(	Real	coef,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_k,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fourth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local fourth nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	(lambda/2) where lamba is the first Lame coefficient
FkMinusTransposed	The tensor F^-T
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_k	The first invariant of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term:int{J^(-2/3) * (lambda/2) * ( -2.0/3.0 * J^(-2/3) * Ic_k ) * ( F : )*(F^-T : )}

Definition at line 1753 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_5term()

void stiff_Jac_P1iso_VKPenalized_5term	(	Real	coef,
		Real	secondCoef,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fifth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local fifth nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	lambda first lame coefficient
coef2	mu shear modulus
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { J^(-2.0/3.0) * ( (lambda/2) * Ic_isok - ( (3/2)*lambda + mu ) ) * : v }

copy of diagonal block

Definition at line 1793 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_6term()

void stiff_Jac_P1iso_VKPenalized_6term	(	Real	coef,
		Real	secondCoef,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		const boost::multi_array< Real, 3 > &	Fk,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary sixth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local sixth nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	lambda first Lame coefficient
coef2	mu sheat modulus
Ic_k	The first invariant of the right Cauchy-Green tensor C
Fk	The deformation gradient that depends on the local displacement uk_loc
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term: int { J^(-2.0/3.0) * ( (lambda/2) * Ic_isok - ( (3/2)*lambda + mu ) ) * ( (-2/3) * ( F : ) ) * ( F^-T : v ) }

Definition at line 1829 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_7term()

void stiff_Jac_P1iso_VKPenalized_7term	(	Real	coef,
		Real	secondCoef,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		const std::vector< Real > &	Ic_isok,
		const std::vector< Real > &	Ic_k,
		const std::vector< Real > &	Jk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary seventh nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local seventh nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	lambda the first Lame coefficient
coef2	mu the shear modulus
FkMinusTransposed	The tensor F^-T
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
Ic_k	The first invariant of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { ( J^(-2/3) * (lambda/2) * Ic_isok - ( (3/2)*lambda + mu ) ) * ( (1/3) * Ic_k * ( F^-T ^T F-T ) : v }

Definition at line 1869 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_8term()

void stiff_Jac_P1iso_VKPenalized_8term	(	Real	coef,
		const std::vector< Real > &	Jack_k,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		const boost::multi_array< Real, 3 > &	FkCk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary seventh nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local seventh nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	lambda the first Lame coefficient
coef2	mu the shear modulus
FkMinusTransposed	The tensor F^-T
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
Ic_k	The first invariant of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { ( -4.0/3.0) * ( mu * J^(-4/3) ) * ( F^-T: ) * ( F C ) : v }

Definition at line 1910 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_9term()

void stiff_Jac_P1iso_VKPenalized_9term	(	Real	coef,
		const std::vector< Real > &	Jack_k,
		const std::vector< Real > &	Ic_kSquared,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary seventh nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local seventh nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	lambda the first Lame coefficient
coef2	mu the shear modulus
FkMinusTransposed	The tensor F^-T
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
Ic_k	The first invariant of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { ( 4.0/9.0) * ( mu * J^(-4/3) ) Ic_kSquared * (F^-T : ) * F^-T : }

Definition at line 1950 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_10term()

void stiff_Jac_P1iso_VKPenalized_10term	(	Real	coef,
		const std::vector< Real > &	Jack_k,
		const boost::multi_array< Real, 3 > &	Ck,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary eigth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local eigth nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	mu the shear modulus
Ck	The right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { ( mu * J^(-4/3) ) * ( * C ) : v }

Definition at line 1990 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_11term()

void stiff_Jac_P1iso_VKPenalized_11term	(	Real	coef,
		const std::vector< Real > &	Jk,
		const boost::multi_array< Real, 3 > &	Fk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary sixth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local sixth nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	mu the shear modulus
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation tensor
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { ( mu * J^(-4/3) ) * (F [ ]^T F ) : }

Definition at line 2024 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_12term()

void stiff_Jac_P1iso_VKPenalized_12term	(	Real	coef,
		const std::vector< Real > &	Jk,
		const boost::multi_array< Real, 3 > &	Fk,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary tenth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local tenth nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	mu the shear modulus
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation tensor
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { ( mu * J^(-4/3) ) * (F * F^T * [ ] ) : }

Definition at line 2061 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_13term()

void stiff_Jac_P1iso_VKPenalized_13term	(	Real	coef,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_kSquared,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary eleventh nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local eleventh nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	mu the shear modulus
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the right Cauchy-Green tensor C^2
FkMinusTransposed	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { ( mu * J^(-4/3) * ( (1/3) * Ic_SquaredK * ( F^-T [ ]^T F^-T) : v ) }

Definition at line 2098 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_VKPenalized_14term()

void stiff_Jac_P1iso_VKPenalized_14term	(	Real	coef,
		const std::vector< Real > &	Jk,
		const boost::multi_array< Real, 3 > &	FkCk,
		const boost::multi_array< Real, 3 > &	FkMinusTransposed,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary twelveth nonlinear isochoric Jacobian matrix for VK-Penalized model (see the reference)

This function assembles the local twelveth nonlinear isochoric Jacobian matrix for VK-Penalized model.

Parameters

coef	mu the shear modulus
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ck	The first invariant of the right Cauchy-Green tensor C^2
Fk	The deformation gradient matrix
FkMinusTransposed	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : int { ( mu * J^(-4/3) ) * ( (-4.0/3.0) * ( FkCk : ) ) * F^-T : v ) }

Definition at line 2138 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ source_P1iso_SecondOrderExponential()

void source_P1iso_SecondOrderExponential	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

Methods for second order exponential law Methods for the first Piola-Kirchhoff tensor.

END OF VENANT-KIRCHHOFF PENALIZED MODEL

SECOND ORDER EXPONENTIAL MODEL

Methods for the Second Order Exponential law Assemble the first Piola-Kirchhoff tensor

Definition at line 2186 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_SecondOrderExp_1term()

void stiff_Jac_P1iso_SecondOrderExp_1term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Methods for the Jacobian matrix Elementary first nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference)

This function assembles the local first nonlinear isochoric Jacobian matrix for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : Int { ( - 4/3 coef * J^(-5/3) * exp( coefExp( Ic_iso - 3)^2 ) * ( tr_isoCk + ( tr_isoCk - 3 ) * ( 2 *coefExp * ( tr_isoCk - 3 ) + 1 ) ) ) * ( CofF : ) ( F : ) }

Definition at line 2219 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_SecondOrderExp_2term()

void stiff_Jac_P1iso_SecondOrderExp_2term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary second nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference)

This function assembles the local second nonlinear isochoric Jacobian matrix for Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : Int { 4 * coef * J^(-4/3) * exp( coefExp*( Ic_iso - 3)*( Ic_iso - 3) ) * ( 1.0 + 2 * coefExp * (Ic_isoK - 3)^2 ) * ( F : ) ( F : )}

Definition at line 2263 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_SecondOrderExp_3term()

void stiff_Jac_P1iso_SecondOrderExp_3term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary third nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference)

This function assembles the local third nonlinear isochoric Jacobian matrix for Second Order Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term:

Definition at line 2307 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_SecondOrderExp_4term()

void stiff_Jac_P1iso_SecondOrderExp_4term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const boost::multi_array< Real, 3 > &	Fk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		const std::vector< Real > &	Ic_k,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fourth nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference)

This function assembles the local fourth nonlinear isochoric Jacobian matrix for Second Order Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Fk	The deformation gradient that depends on the local displacement uk_loc
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
Ic_k	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term:

Definition at line 2351 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_SecondOrderExp_5term()

void stiff_Jac_P1iso_SecondOrderExp_5term	(	Real	coef,
		Real	coefExp,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary fifth nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference)

This function assembles the local fifth nonlinear isochoric Jacobian matrix for Second Order Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term :

copy of diagonal block

Definition at line 2394 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

◆ stiff_Jac_P1iso_SecondOrderExp_6term()

void stiff_Jac_P1iso_SecondOrderExp_6term	(	Real	coef,
		Real	coefExp,
		const boost::multi_array< Real, 3 > &	CofFk,
		const std::vector< Real > &	Jk,
		const std::vector< Real > &	Ic_isok,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Elementary sixth nonlinear isochoric Jacobian matrix for Second Order Exponential model (see the reference)

This function assembles the local sixth nonlinear isochoric Jacobian matrix for Second Order Exponential model.

Parameters

coef	The pre-exponential coefficient
coefExp	The expoenential coefficient
CofFk	The cofactor of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Jk	The determinant of the deformation gradient F that depends on the local displacement uk_loc (remark: the nonlinear vector depends on current displacement)
Ic_isok	The first invariant of the isochoric part of the right Cauchy-Green tensor C
elmat	The elementary matrix of the current volume
fe	The current finite element

Stiffness term : Int { 2.0/3.0 * coef * J^(-2) * Ic_iso * exp(coefExp( Ic_iso - 3)) * (CofF [ ]^t CofF ) : }

Definition at line 2430 of file fsi_blocks/solver/AssemblyElementalStructure.cpp.

Functions

Detailed Description

Function Documentation

◆ saveVectorAccordingToFunctor()

◆ saveBooleanVectorAccordingToFunctor()

◆ computeGradientLocalDisplacement()

◆ computeLocalDeformationGradient()

◆ computeLocalDeformationGradientWithoutIdentity()

◆ stiff_derdiv()

◆ stiff_dergradbis()

◆ stiff_divgrad()

◆ stiff_gradgrad()

◆ stiff_dergrad_gradbis()

◆ stiff_dergrad_gradbis_Tr()

◆ stiff_gradgradTr_gradbis()

◆ stiff_dergrad()

◆ stiff_divgrad_2()

◆ stiff_gradgrad_2()

◆ stiff_dergrad_gradbis_2()

◆ stiff_dergrad_gradbis_Tr_2()

◆ stiff_gradgradTr_gradbis_2()

◆ stiff_gradgradTr_gradbis_3()

◆ source_Pvol()

◆ stiff_Jac_Pvol_1term()

◆ stiff_Jac_Pvol_2term()

◆ source_P1iso_NH()

◆ computeInvariantsRightCauchyGreenTensor() [1/2]

◆ computeInvariantsRightCauchyGreenTensor() [2/2]

◆ computeCauchyStressTensor()

◆ computeEigenvalues()

◆ stiff_Jac_P1iso_NH_1term()

◆ stiff_Jac_P1iso_NH_2term()

◆ stiff_Jac_P1iso_NH_3term()

◆ stiff_Jac_P1iso_NH_4term()

◆ stiff_Jac_P1iso_NH_5term()

◆ source_P1iso_Exp()

◆ stiff_Jac_P1iso_Exp_1term()

◆ stiff_Jac_P1iso_Exp_2term()

◆ stiff_Jac_P1iso_Exp_3term()

◆ stiff_Jac_P1iso_Exp_4term()

◆ stiff_Jac_P1iso_Exp_5term()

◆ stiff_Jac_P1iso_Exp_6term()

◆ source_P1iso_VKPenalized()

◆ source_P2iso_VKPenalized()

◆ stiff_Jac_P1iso_VKPenalized_0term()

◆ stiff_Jac_P1iso_VKPenalized_1term()

◆ stiff_Jac_P1iso_VKPenalized_2term()

◆ stiff_Jac_P1iso_VKPenalized_3term()

◆ stiff_Jac_P1iso_VKPenalized_4term()

◆ stiff_Jac_P1iso_VKPenalized_5term()

◆ stiff_Jac_P1iso_VKPenalized_6term()

◆ stiff_Jac_P1iso_VKPenalized_7term()

◆ stiff_Jac_P1iso_VKPenalized_8term()

◆ stiff_Jac_P1iso_VKPenalized_9term()

◆ stiff_Jac_P1iso_VKPenalized_10term()

◆ stiff_Jac_P1iso_VKPenalized_11term()

◆ stiff_Jac_P1iso_VKPenalized_12term()

◆ stiff_Jac_P1iso_VKPenalized_13term()

◆ stiff_Jac_P1iso_VKPenalized_14term()

◆ source_P1iso_SecondOrderExponential()

◆ stiff_Jac_P1iso_SecondOrderExp_1term()

◆ stiff_Jac_P1iso_SecondOrderExp_2term()

◆ stiff_Jac_P1iso_SecondOrderExp_3term()

◆ stiff_Jac_P1iso_SecondOrderExp_4term()

◆ stiff_Jac_P1iso_SecondOrderExp_5term()

◆ stiff_Jac_P1iso_SecondOrderExp_6term()