Detailed Description

template<short_t dim, class T, short_t matId, bool comp, enum Material mat = decodeMat_id<matId>::material, enum Implementation imp = decodeMat_id<matId>::implementation>
class gismo::gsMaterialMatrixNonlinear< dim, T, matId, comp, mat, imp >

This class defines hyperelastic material matrices.

Template Parameters

dim	The dimension of the problem (2 = planar, 3 = surface)
T	Real type
matId	Encoded ID for material (see encodeMat_id)
comp	Compressibility flag
mat	Material flag (see Material)
imp	Implementation flag (see Implementation)

Inheritance diagram for gsMaterialMatrixNonlinear< dim, T, matId, comp, mat, imp >:

Collaboration diagram for gsMaterialMatrixNonlinear< dim, T, matId, comp, mat, imp >:

Public Types
typedef memory::shared_ptr < gsMaterialMatrixNonlinear >	Ptr
	Shared pointer for gsMaterialMatrixNonlinear.

typedef memory::unique_ptr < gsMaterialMatrixNonlinear >	uPtr
	Unique pointer for gsMaterialMatrixNonlinear.

Public Member Functions
void	_computeMetricDeformed (const index_t patch, const gsMatrix< T > &u) const
	Computes metric quantities on the deformed geometry.

void	_computeMetricUndeformed (const index_t patch, const gsMatrix< T > &u) const
	Computes metric quantities on the undeformed geometry.

void	_computePStrain (const gsMatrix< T > &C) const
	Computes the stretch given deformation tensor C, into class members m_stretches and m_stretchDirs.

void	_computePStress (const gsMatrix< T > &C) const
	Computes the principal stresses of a given stress tensor S, into class members m_pstress and m_pstressvec.

void	_computeStretch (const gsMatrix< T > &C, const gsMatrix< T > &gcon_ori) const
	Computes the stretch given deformation tensor C, into class members m_stretches and m_stretchDirs.

std::pair< gsVector< T > , gsMatrix< T > >	_evalPStrain (const gsMatrix< T > &C) const
	Computes the principal strain given deformation tensor C, into a pair.

std::pair< gsVector< T > , gsMatrix< T > >	_evalPStress (const gsMatrix< T > &S) const
	Computes the principal stress given stress tensor S, into a pair.

std::pair< gsVector< T > , gsMatrix< T > >	_evalStretch (const gsMatrix< T > &C, const gsMatrix< T > &gcon_ori) const
	Computes the stretch given deformation tensor C, into a pair.

gsMatrix< T >	_getAcon_def (index_t k, T z) const
	Returns the contravariant a tensor on the deformed geometry.

gsMatrix< T >	_getacon_def (index_t k, T z) const
	Returns the contravariant basis vector a on the deformed geometry.

gsMatrix< T >	_getAcon_ori (index_t k, T z) const
	Returns the contravariant a tensor on the original geometry.

gsMatrix< T >	_getacon_ori (index_t k, T z) const
	Returns the contravariant basis vector a on the original geometry.

gsMatrix< T >	_getAcov_def (index_t k, T z) const
	Returns the covariant a tensor on the deformed geometry.

gsMatrix< T >	_getacov_def (index_t k, T z) const
	Returns the covariant basis vector a on the deformed geometry.

gsMatrix< T >	_getAcov_ori (index_t k, T z) const
	Returns the covariant a tensor on the original geometry.

gsMatrix< T >	_getacov_ori (index_t k, T z) const
	Returns the covariant basis vector a on the original geometry.

gsMatrix< T >	_getBcov_def (index_t k, T z) const
	Returns the covariant b tensor on the deformed geometry.

gsMatrix< T >	_getBcov_ori (index_t k, T z) const
	Returns the covariant b tensor on the original geometry.

gsMatrix< T >	_getGcon_def (index_t k, T z) const
	Returns the contravariant metric tensor on the deformed geometry.

gsMatrix< T >	_getgcon_def (index_t k, T z) const
	Returns the contravariant basis vector g on the deformed geometry.

gsMatrix< T >	_getGcon_ori (index_t k, T z) const
	Returns the contravariant metric tensor on the original geometry.

gsMatrix< T >	_getgcon_ori (index_t k, T z) const
	Returns the contravariant basis vector g on the original geometry.

gsMatrix< T >	_getGcov_def (index_t k, T z) const
	Returns the covariant metric tensor on the deformed geometry.

gsMatrix< T >	_getgcov_def (index_t k, T z) const
	Returns the covariant basis vector g on the deformed geometry.

gsMatrix< T >	_getGcov_ori (index_t k, T z) const
	Returns the covariant metric tensor on the original geometry.

gsMatrix< T >	_getgcov_ori (index_t k, T z) const
	Returns the covariant basis vector g on the original geometry.

void	_getMetric (const index_t k, const T z) const
	Gets metric quantities on the deformed and undeformed geometries.

void	_getMetric (index_t k, T z, const gsMatrix< T > &C) const
	Gets metric quantities on the deformed and undeformed geometries.

void	_getMetricDeformed (const index_t k, const T z) const
	Gets metric quantities on the deformed geometry.

void	_getMetricUndeformed (const index_t k, const T z) const
	Gets metric quantities on the undeformed geometry.

gsMatrix< T >	_getncov_def (index_t k, T z) const
	Returns the covariant n tensor on the deformed geometry.

gsMatrix< T >	_getncov_ori (index_t k, T z) const
	Returns the covariant n tensor on the original geometry.

gsMatrix< T >	_transformation (const gsMatrix< T > &basis1, const gsMatrix< T > &basis2) const
	Computes the stretch given deformation tensor C, into class members m_stretches and m_stretchDirs.

void	defaultOptions () override
	See gsMaterialMatrixBase for details.

virtual void	density_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_CauchyPStress (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_CauchyStress (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_CauchyVector (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_con2cart (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_cov2cart (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_deformation (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_detF (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_dmatrix (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_matrix (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_matrix_C (const gsMatrix< T > &Cmat, const index_t patch, const gsVector< T > &u, const T z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_pstrain (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_pstress (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_pstressDir (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_pstressTransform (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Provides the transformation of the principle stresses. More...

virtual gsMatrix< T >	eval3D_pstretch (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_pstretchDir (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_pstretchTransform (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Provides the transformation of the principle stretches. More...

virtual gsMatrix< T >	eval3D_spec2con (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_spec2cov (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_strain (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_stress (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_stress_C (const gsMatrix< T > &Cmat, const index_t patch, const gsVector< T > &u, const T z, enum MaterialOutput out=MaterialOutput::Generic) const
	See gsMaterialMatrixBase for details.

virtual gsMatrix< T >	eval3D_tensionfield (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_vector (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

gsMatrix< T >	eval3D_vector_C (const gsMatrix< T > &Cmat, const index_t patch, const gsVector< T > &u, const T z, enum MaterialOutput out=MaterialOutput::Generic) const override
	See gsMaterialMatrixBase for details.

const function_ptr	getAlpha (const index_t &i) const override
	Gets Alpha_i.

virtual const function_ptr	getDensity () const
	Gets the Density.

const function_ptr	getMu (const index_t &i) const override
	Gets Mu_i.

virtual const function_ptr	getParameter (const index_t i) const
	Gets parameter i. More...

const function_ptr	getPoissonsRatio () const override
	Gets the Poisson's Ratio.

const function_ptr	getRatio () const override
	Gets the Ratio for the MR material.

virtual const function_ptr	getThickness () const
	Gets the Density.

const function_ptr	getYoungsModulus () const override
	Gets the YoungsModulus.

	gsMaterialMatrixNonlinear (const gsFunctionSet< T > &mp, const gsFunctionSet< T > &thickness)
	Constructor without material parameters. More...

	gsMaterialMatrixNonlinear (const gsFunctionSet< T > &mp, const gsFunctionSet< T > &thickness, const std::vector< gsFunctionSet< T > * > &pars)
	General constructor without density. More...

	gsMaterialMatrixNonlinear (const gsFunctionSet< T > &thickness, const std::vector< gsFunctionSet< T > * > &pars)
	General constructor without density and multipatch. More...

	gsMaterialMatrixNonlinear (const gsFunctionSet< T > &thickness, const std::vector< gsFunctionSet< T > * > &pars, const gsFunctionSet< T > &Density)
	General constructor without multipatch. More...

	gsMaterialMatrixNonlinear (const gsFunctionSet< T > &mp, const gsFunctionSet< T > &thickness, const std::vector< gsFunctionSet< T > * > &pars, const gsFunctionSet< T > &Density)
	Full general constructor. More...

	gsMaterialMatrixNonlinear ()
	Destructor.

virtual bool	hasDensity () const
	Returns true if a density is assigned.

virtual bool	hasThickness () const
	Returns true if a thickness is assigned.

virtual void	info () const
	Prints info.

enum MatIntegration	isMatIntegrated () const override
	See gsMaterialMatrixBase for details.

enum MatIntegration	isVecIntegrated () const override
	See gsMaterialMatrixBase for details.

virtual const gsMaterialMatrixBase< T > *	material () const
	Returns this.

virtual gsMaterialMatrixBase< T > *	material ()
	Returns this.

virtual index_t	numParameters () const
	Gets the number of parameters.

virtual gsOptionList &	options ()
	Returns the options. More...

virtual void	parameters_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const override
	See gsMaterialMatrixBase for details.

std::ostream &	print (std::ostream &os) const override
	See gsMaterialMatrixBase for details.

virtual void	pstress_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluates the priciple stresses in the shell (3x1 vector) More...

virtual void	pstressDir_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Evaluates the directions of the priciple stresses in the shell (3x1 vector per direction) More...

void	pstretch_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const override
	See gsMaterialMatrixBase for details.

void	pstretchDir_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const override
	See gsMaterialMatrixBase for details.

virtual void	resetParameters ()
	See gsMaterialMatrixBase for details.

void	setAlpha (const index_t &i, const gsFunctionSet< T > &Alpha_i) override
	Sets Alpha_i.

virtual void	setDensity (function_ptr Density)
	Sets the density.

virtual void	setDensity (const gsFunctionSet< T > &Density)
	Sets the density.

void	setMu (const index_t &i, const gsFunctionSet< T > &Mu_i) override
	Sets Mu_i.

virtual void	setOptions (gsOptionList opt)
	Sets the options. More...

virtual void	setParameter (const index_t i, const function_ptr &par)
	Sets the material parameters. More...

virtual void	setParameter (const index_t i, const gsFunctionSet< T > &par)
	Sets the material parameters. More...

virtual void	setParameters (const std::vector< function_ptr > &pars)
	Sets the material parameters. More...

virtual void	setParameters (const std::vector< gsFunctionSet< T > * > &pars)
	Sets the material parameters. More...

void	setPoissonsRatio (const gsFunctionSet< T > &PoissonsRatio) override
	Sets the Poisson's Ratio.

void	setRatio (const gsFunctionSet< T > &Ratio) override
	Sets the Ratio for the MR material.

virtual void	setThickness (const function_ptr &thickness)
	Sets the thickness.

virtual void	setThickness (const gsFunctionSet< T > &thickness)
	Sets the thickness.

void	setYoungsModulus (const gsFunctionSet< T > &YoungsModulus) override
	Sets the YoungsModulus.

virtual void	thickness_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const override
	See gsMaterialMatrixBase for details.

virtual void	transform_into (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Constructs a transformation matrix that transforms a quantity (IN VOIGHT NOTATION) in the spectral basis to the (undeformed) convariant basis. More...

Protected Member Functions
constexpr T	_Cabcd (const index_t a, const index_t b, const index_t c, const index_t d) const
	The material matrix for stretch-based implementations. More...

constexpr T	_Cijkl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Returns an entry of the material tensor C for incompressible materials. More...

constexpr T	_Cijkl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Returns an entry of the material tensor C for compressible materials, with static condensation included. More...

constexpr T	_Cijkl3D (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Returns an entry of the material tensor C for compressible materials without static condensation. More...

constexpr T	_d2J_dab (const index_t a, const index_t b) const
	First derivative of the compressibilty function \(\J\) w.r.t. the stretches \(\lambda_a\) and \(\lambda_b\). More...

constexpr T	_d2Psi (const index_t i, const index_t j, const index_t k, const index_t l) const
	Provides the second (mixed) derivative of the incompressible strain energy density function w.r.t. components C_{ij} and C_{kl} of the deformation tensor. More...

constexpr T	_d2Psi (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Provides the second (mixed) derivative of the compressible strain energy density function w.r.t. components C_{ij} and C_{kl} of the deformation tensor. More...

constexpr T	_d2Psi_dab (const index_t a, const index_t b) const
	Second derivative of a strain energy density function \(\Psi\) w.r.t. the stretches \(\lambda_a\) and \(\lambda_b\). More...

constexpr T	_d2Psi_dab_vol (const index_t a, const index_t b) const
	Second derivative of the volumetric part of a strain energy density function \(\Psi_{vol}\) w.r.t. the stretches \(\lambda_a\) and \(\lambda_b\). More...

constexpr T	_d2Psi_vol (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Provides the second (mixed) derivative of the volumetric part of the compressible strain energy density function w.r.t. components C_{ij} and C_{kl} of the deformation tensor. More...

constexpr T	_dI_1 (const index_t i, const index_t j) const
	Provides the derivative of the first invariant compressible materials w.r.t. component C_{ij} of the deformation tensor. More...

constexpr T	_dI_2 (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Provides the derivative of the second invariant for compressible materials w.r.t. component C_{ij} of the deformation tensor. More...

constexpr T	_dJ_da (const index_t a) const
	First derivative of the compressibilty function \(\J\) w.r.t. the stretche \(\lambda_a\). More...

constexpr T	_dp_da (const index_t a) const
	First derivative of the Lagrange multiplier for incompressible materials w.r.t. the stretch \(\lambda_a\). More...

constexpr T	_dPsi (const index_t i, const index_t j) const
	Provides the derivative of the incompressible strain energy density function w.r.t. component C_{ij} of the deformation tensor. More...

constexpr T	_dPsi (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Provides the derivative of the compressible strain energy density function w.r.t. component C_{ij} of the deformation tensor. More...

constexpr T	_dPsi_da (const index_t a) const
	First derivative of a strain energy density function \(\Psi\) w.r.t. the stretch \(\lambda_a\). More...

constexpr T	_dPsi_da_vol (const index_t a) const
	First derivative of the volumetric part of a strain energy density function \(\Psi_{vol}\) w.r.t. the stretch \(\lambda_a\). More...

constexpr T	_dPsi_vol (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Provides the derivative of the volumetric part of the compressible strain energy density function w.r.t. component C_{ij} of the deformation tensor. More...

constexpr T	_dSa_db (const index_t a, const index_t b) const
	First derivative of the \(a^{\text{th}\) component of the stress w.r.t. the stretch \(\lambda_b\). More...

gsMatrix< T >	_eval3D_Compressible_C33 (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Evaluates the C33 (through thickness) component of the deformation tensor C for compressible materials. More...

gsMatrix< T >	_eval3D_Compressible_detF (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Evaluates the jacobian determinant for compressible materials. More...

gsMatrix< T >	_eval3D_Compressible_matrix (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Evalluates the compressible material matrix. More...

gsMatrix< T >	_eval3D_Compressible_stress (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Evalluates the compressible stress vector. More...

gsMatrix< T >	_eval3D_Incompressible_detF (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Evaluates the jacobian determinant for compressible materials. More...

gsMatrix< T >	_eval3D_Incompressible_matrix (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Evalluates the incompressible material matrix. More...

gsMatrix< T >	_eval3D_Incompressible_stress (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Evalluates the incompressible stress vector. More...

gsMatrix< T >	_eval_Compressible_CauchyVector (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Equivalent to _eval_Compressible_vector but for the Cauchy Vector.

gsMatrix< T >	_eval_Incompressible_CauchyVector (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Equivalent to _eval_Incompressible_vector but for the Cauchy Vector.

void	_initialize ()
	Initializes the object. More...

constexpr T	_p () const
	Lagrange multiplier for incompressible materials.

constexpr T	_Sa (const index_t a) const
	Component \(a\) of the stress. More...

constexpr T	_Sii (const index_t i) const
	Returns an entry of the diagonal of the stress tensor S for incompressible materials. More...

constexpr T	_Sii (const index_t i, const gsMatrix< T > &c) const
	Returns an entry of the diagonal of the stress tensor S for incompressible materials. More...

constexpr T	_Sij (const index_t i, const index_t j) const
	Returns an entry of the stress tensor S for incompressible materials. More...

constexpr T	_Sij (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Returns an entry of the stress tensor S for compressible materials. More...

	gsMaterialMatrixNonlinear (const gsFunctionSet< T > mp, const gsFunctionSet< T > thickness, const std::vector< gsFunctionSet< T > * > &pars, const gsFunctionSet< T > *Density)
	Full general constructor. More...

Private Member Functions
template<bool _com>
constexpr std::enable_if< _com, T >::type	_Cabcd_impl (const index_t a, const index_t b, const index_t c, const index_t d) const
	Specialization of _Cabcd(a,b,c,d) for compressible materials.

template<bool _com>
constexpr std::enable_if<!_com, T >::type	_Cabcd_impl (const index_t a, const index_t b, const index_t c, const index_t d) const
	Specialization of _Cabcd(a,b,c,d) for incompressible materials.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::SvK &&_imp==Implementation::Analytical, T >::type	_Cijkl3D_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl3D(i,j,k,l,c,cinv) for SvK materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::NH &&_imp==Implementation::Analytical, T >::type	_Cijkl3D_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl3D(i,j,k,l,c,cinv) for NH materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::MR &&_imp==Implementation::Analytical, T >::type	_Cijkl3D_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl3D(i,j,k,l,c,cinv) for MR materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::OG &&_imp==Implementation::Analytical, T >::type	_Cijkl3D_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl3D(i,j,k,l,c,cinv) for OG materials implemented analytically (not implemented)

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::NH_ext &&_imp==Implementation::Analytical, T >::type	_Cijkl3D_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl3D(i,j,k,l,c,cinv) for Extended NH materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Spectral, T >::type	_Cijkl3D_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl3D(i,j,k,l,c,cinv) for all materials implemented spectrally.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Generalized, T >::type	_Cijkl3D_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl3D(i,j,k,l,c,cinv) for all materials implemented generally.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::SvK &&_imp==Implementation::Analytical, T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Specialization for incompressible Cijkl(i,j,k,l) for SvK materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::NH &&_imp==Implementation::Analytical, T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Specialization for incompressible Cijkl(i,j,k,l) for NH materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::MR &&_imp==Implementation::Analytical, T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Specialization for incompressible Cijkl(i,j,k,l) for MR materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::OG &&_imp==Implementation::Analytical, T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Specialization for incompressible Cijkl(i,j,k,l) for OG materials implemented analytically (not implemented)

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::NH_ext &&_imp==Implementation::Analytical, T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Specialization for incompressible Cijkl(i,j,k,l) for Extended NH materials implemented analytically (not implemented)

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Spectral, T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Specialization for incompressible Cijkl(i,j,k,l) for all materials implemented spectrally.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Generalized, T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Specialization for incompressible Cijkl(i,j,k,l) for all materials implemented generally.

template<enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Spectral, T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl(i,j,k,l,c,cinv) for all materials implemented generally. More...

template<enum Implementation _imp>
constexpr std::enable_if <!(_imp==Implementation::Spectral), T >::type	_Cijkl_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Cijkl(i,j,k,l,c,cinv) for all materials implemented not spectrally.

template<enum Material _mat, bool _com>
constexpr std::enable_if< _com &&(_mat==Material::NH), T > ::type	_d2Psi_dab_impl (const index_t a, const index_t b) const
	Specialization of _d2Psi_dab(a,b) for compressible NH materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if<!_com &&(_mat==Material::NH), T > ::type	_d2Psi_dab_impl (const index_t a, const index_t b) const
	Specialization of _d2Psi_dab(a,b) for incompressible NH materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if< _com &&(_mat==Material::MR), T > ::type	_d2Psi_dab_impl (const index_t a, const index_t b) const
	Specialization of _d2Psi_dab(a,b) for compressible MR materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if<!_com &&(_mat==Material::MR), T > ::type	_d2Psi_dab_impl (const index_t a, const index_t b) const
	Specialization of _d2Psi_dab(a,b) for incompressible MR materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if< _com &&(_mat==Material::OG), T > ::type	_d2Psi_dab_impl (const index_t a, const index_t b) const
	Specialization of _d2Psi_dab(a,b) for compressible OG materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if<!_com &&(_mat==Material::OG), T > ::type	_d2Psi_dab_impl (const index_t a, const index_t b) const
	Specialization of _d2Psi_dab(a,b) for incompressible OG materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if< _com &&(_mat==Material::NH_ext), T > ::type	_d2Psi_dab_impl (const index_t a, const index_t b) const
	Specialization of _d2Psi_dab(a,b) for compressible Extended NH materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if<!_com &&(_mat==Material::NH_ext), T > ::type	_d2Psi_dab_impl (const index_t a, const index_t b) const
	Specialization of _d2Psi_dab(a,b) for incompressible Extended NH materials (not implemented)

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::NH, T >::type	_d2Psi_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Implementation of _d2Psi(i,j) for NH materials.

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::MR, T >::type	_d2Psi_impl (const index_t i, const index_t j, const index_t k, const index_t l) const
	Implementation of _d2Psi(i,j) for MR materials.

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::NH, T >::type	_d2Psi_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Implementation of _d2Psi(i,j,c,cinv) for NH materials.

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::MR, T >::type	_d2Psi_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Implementation of _d2Psi(i,j,c,cinv) for MR materials.

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::NH_ext, T >::type	_d2Psi_impl (const index_t i, const index_t j, const index_t k, const index_t l, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Implementation of _d2Psi(i,j,c,cinv) for Extended NH materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if< _com &&(_mat==Material::NH), T > ::type	_dPsi_da_impl (const index_t a) const
	Specialization of _dPsi_da(a) for compressible NH materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if<!_com &&(_mat==Material::NH), T > ::type	_dPsi_da_impl (const index_t a) const
	Specialization of _dPsi_da(a) for incompressible NH materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if< _com &&(_mat==Material::MR), T > ::type	_dPsi_da_impl (const index_t a) const
	Specialization of _dPsi_da(a) for compressible MR materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if<!_com &&(_mat==Material::MR), T > ::type	_dPsi_da_impl (const index_t a) const
	Specialization of _dPsi_da(a) for incompressible MR materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if< _com &&(_mat==Material::OG), T > ::type	_dPsi_da_impl (const index_t a) const
	Specialization of _dPsi_da(a) for compressible OG materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if<!_com &&(_mat==Material::OG), T > ::type	_dPsi_da_impl (const index_t a) const
	Specialization of _dPsi_da(a) for incompressible OG materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if< _com &&(_mat==Material::NH_ext), T > ::type	_dPsi_da_impl (const index_t a) const
	Specialization of _dPsi_da(a) for compressible Extended NH materials.

template<enum Material _mat, bool _com>
constexpr std::enable_if<!_com &&(_mat==Material::NH_ext), T > ::type	_dPsi_da_impl (const index_t a) const
	Specialization of _dPsi_da(a) for incompressible Extended NH materials (not implemented)

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::NH, T >::type	_dPsi_impl (const index_t i, const index_t j) const
	Implementation of _dPsi(i,j) for NH materials.

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::MR, T >::type	_dPsi_impl (const index_t i, const index_t j) const
	Implementation of _dPsi(i,j) for MR materials.

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::NH, T >::type	_dPsi_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Implementation of _dPsi(i,j,c,cinv) for NH materials.

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::MR, T >::type	_dPsi_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Implementation of _dPsi(i,j,c,cinv) for MR materials.

template<enum Material _mat>
constexpr std::enable_if< _mat==Material::NH_ext, T >::type	_dPsi_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Implementation of _dPsi(i,j,c,cinv) for Extended NH materials.

template<bool _com>
constexpr std::enable_if< _com, T >::type	_dSa_db_impl (const index_t a, const index_t b) const
	Specialization of _dSa_db(a,b) for compressible materials.

template<bool _com>
constexpr std::enable_if<!_com, T >::type	_dSa_db_impl (const index_t a, const index_t b) const
	Specialization of _dSa_db(a,b) for incompressible materials.

template<enum Material _mat, bool _com>
std::enable_if< _mat==Material::SvK, gsMatrix< T > >::type	_eval3D_CauchyVector_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Same as _eval3D_vector_impl for the Cauchy stress.

template<enum Material _mat, bool _com>
std::enable_if< _com &&!(_mat==Material::SvK), gsMatrix< T > >::type	_eval3D_CauchyVector_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Same as _eval3D_vector_impl for the Cauchy stress.

template<enum Material _mat, bool _com>
std::enable_if<!_com &&!(_mat==Material::SvK), gsMatrix< T > >::type	_eval3D_CauchyVector_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Same as _eval3D_vector_impl for the Cauchy stress.

template<enum Material _mat, bool _com>
std::enable_if< _mat==Material::SvK, gsMatrix< T > >::type	_eval3D_detF_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Implementation of jacobina determinant (detF) More...

template<enum Material _mat, bool _comp>
std::enable_if<!(!_comp &&_mat==Material::NH), gsMatrix< T > >::type	_eval3D_dmatrix_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z, enum MaterialOutput out) const
	{ function_description } More...

template<enum Material _mat, bool _com>
std::enable_if< _mat==Material::SvK, gsMatrix< T > >::type	_eval3D_matrix_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Implementation of the 3D (in-plane+thickness) evaluator of the material matrix, specialization for SvK material (incompressible) More...

template<enum Material _mat, bool _com>
std::enable_if< _com &&!(_mat==Material::SvK), gsMatrix< T > >::type	_eval3D_matrix_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Implementation of the 3D (in-plane+thickness) evaluator of the material matrix, specialization compressible models. More...

template<enum Material _mat, bool _com>
std::enable_if<!_com &&!(_mat==Material::SvK), gsMatrix< T > >::type	_eval3D_matrix_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Implementation of the 3D (in-plane+thickness) evaluator of the material matrix, specialization for incompressible models. More...

template<enum Material _mat, bool _com>
std::enable_if<!_com &&!(_mat==Material::SvK), gsMatrix< T > >::type	_eval3D_pstress_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Implementation of the 3D (in-plane+thickness) evaluator of the stress vector, specialization for compressible models. More...

template<enum Material _mat, bool _com>
std::enable_if< _mat==Material::SvK, gsMatrix< T > >::type	_eval3D_stress_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Implementation of the 3D (in-plane+thickness) evaluator of the stress vector, specialization for SvK material (incompressible) More...

template<enum Material _mat, bool _com>
std::enable_if< _com &&!(_mat==Material::SvK), gsMatrix< T > >::type	_eval3D_stress_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Implementation of the 3D (in-plane+thickness) evaluator of the stress vector, specialization for incompressible models. More...

template<enum Material _mat, bool _com>
std::enable_if<!_com &&!(_mat==Material::SvK), gsMatrix< T > >::type	_eval3D_stress_impl (const index_t patch, const gsMatrix< T > &u, const gsMatrix< T > &z) const
	Implementation of the 3D (in-plane+thickness) evaluator of the stress vector, specialization for compressible models. More...

template<bool _com>
std::enable_if< _com, void >::type	_pstretch_into_impl (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Implementation of pstretch_into, specialization for compressible materials. More...

template<bool _com>
std::enable_if<!_com, void >::type	_pstretch_into_impl (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Implementation of pstretch_into, specialization for incompressible materials. More...

template<bool _com>
std::enable_if< _com, void >::type	_pstretchDir_into_impl (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Implementation of stretchDir_into, specialization for compressible materials. More...

template<bool _com>
std::enable_if<!_com, void >::type	_pstretchDir_into_impl (const index_t patch, const gsMatrix< T > &u, gsMatrix< T > &result) const
	Implementation of stretchDir_into, specialization for incompressible materials. More...

template<bool _com>
constexpr std::enable_if< _com, T >::type	_Sa_impl (const index_t a) const
	Specialization of _Sa(a) for compressible materials.

template<bool _com>
constexpr std::enable_if<!_com, T >::type	_Sa_impl (const index_t a) const
	Specialization of _Sa(a) for incompressible materials.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::SvK &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j) const
	Specialization for incompressible Sij(i,j) for SvK materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::NH &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j) const
	Specialization for incompressible Sij(i,j) for NH materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::MR &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j) const
	Specialization for incompressible Sij(i,j) for MR materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::OG &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j) const
	Specialization for incompressible Sij(i,j) for OG materials implemented analytically (not implemented)

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::NH_ext &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j) const
	Specialization for incompressible Sij(i,j) for Extended NH materials implemented analytically (not implemented)

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Spectral, T >::type	_Sij_impl (const index_t i, const index_t j) const
	Specialization for incompressible Sij(i,j) for all materials implemented spectrally.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Generalized, T >::type	_Sij_impl (const index_t i, const index_t j) const
	Specialization for incompressible Sij(i,j) for all materials implemented generally.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::SvK &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Sij(i,j,c,cinv) for SvK materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::NH &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Sij(i,j,c,cinv) for NH materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::MR &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Sij(i,j,c,cinv) for MR materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::OG &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Sij(i,j,c,cinv) for OG materials implemented analytically (not implemented)

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _mat==Material::NH_ext &&_imp==Implementation::Analytical, T >::type	_Sij_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Sij(i,j,c,cinv) for Extended NH materials implemented analytically.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Spectral, T >::type	_Sij_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Sij(i,j,c,cinv) for all materials implemented spectrally.

template<enum Material _mat, enum Implementation _imp>
constexpr std::enable_if< _imp==Implementation::Generalized, T >::type	_Sij_impl (const index_t i, const index_t j, const gsMatrix< T > &c, const gsMatrix< T > &cinv) const
	Specialization for compressible Sij(i,j,c,cinv) for all materials implemented generally.

Constructor & Destructor Documentation

gsMaterialMatrixNonlinear	(	const gsFunctionSet< T > &	mp,
		const gsFunctionSet< T > &	thickness
	)

Constructor without material parameters.

Parameters

[in]	mp	Original geometry
[in]	thickness	Thickness function

gsMaterialMatrixNonlinear	(	const gsFunctionSet< T > &	mp,
		const gsFunctionSet< T > &	thickness,
		const std::vector< gsFunctionSet< T > * > &	pars
	)

General constructor without density.

Parameters

[in]	mp	Original geometry
[in]	thickness	Thickness function
[in]	pars	Vector with parameters (E, nu)

gsMaterialMatrixNonlinear	(	const gsFunctionSet< T > &	thickness,
		const std::vector< gsFunctionSet< T > * > &	pars
	)

General constructor without density and multipatch.

Parameters

[in]	thickness	Thickness function
[in]	pars	Vector with parameters (E, nu)

gsMaterialMatrixNonlinear	(	const gsFunctionSet< T > &	thickness,
		const std::vector< gsFunctionSet< T > * > &	pars,
		const gsFunctionSet< T > &	Density
	)

General constructor without multipatch.

Parameters

[in]	thickness	Thickness function
[in]	pars	Vector with parameters (E, nu)

gsMaterialMatrixNonlinear	(	const gsFunctionSet< T > &	mp,
		const gsFunctionSet< T > &	thickness,
		const std::vector< gsFunctionSet< T > * > &	pars,
		const gsFunctionSet< T > &	Density
	)

Full general constructor.

Parameters

[in]	mp	Original geometry
[in]	thickness	Thickness function
[in]	pars	Vector with parameters (E, nu)
[in]	Density	Density function

gsMaterialMatrixNonlinear	(	const gsFunctionSet< T > *	mp,
		const gsFunctionSet< T > *	thickness,
		const std::vector< gsFunctionSet< T > * > &	pars,
		const gsFunctionSet< T > *	Density
	)

protected

Full general constructor.

Parameters

[in]	mp	Original geometry
[in]	thickness	Thickness function
[in]	pars	Vector with parameters (E, nu)
[in]	Density	Density function

Member Function Documentation

constexpr T _Cabcd	(	const index_t	a,
		const index_t	b,
		const index_t	c,
		const index_t	d
	)		const

protected

The material matrix for stretch-based implementations.

Parameters

[in] a,b,c,d The indices a,b,c,d

constexpr T _Cijkl	(	const index_t	i,
		const index_t	j,
		const index_t	k,
		const index_t	l
	)		const

protected

Returns an entry of the material tensor C for incompressible materials.

Parameters

[in] i,j,k,l The indices

Returns: C^{ijkl}

constexpr T _Cijkl	(	const index_t	i,
		const index_t	j,
		const index_t	k,
		const index_t	l,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

protected

Returns an entry of the material tensor C for compressible materials, with static condensation included.

Parameters

[in]	i,j,k,l	The indices
[in]	c	The deformation tensor
[in]	cinv	The inverse of the deformation tensor

Returns: C^{ijkl}

constexpr T _Cijkl3D	(	const index_t	i,
		const index_t	j,
		const index_t	k,
		const index_t	l,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

protected

Returns an entry of the material tensor C for compressible materials without static condensation.

Parameters

[in]	i,j,k,l	The indices
[in]	c	The deformation tensor
[in]	cinv	The inverse of the deformation tensor

Returns: C^{ijkl}

constexpr std::enable_if< _imp==Implementation::Spectral, T >::type _Cijkl_impl	(	const index_t	i,
		const index_t	j,
		const index_t	k,
		const index_t	l,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

private

Specialization for compressible Cijkl(i,j,k,l,c,cinv) for all materials implemented generally.

Note: The specialization is required because static condensation for spectrally implemented material models is performed before the transformation. For all other implementation, static condensation is performed using the Cijkl3D function.

constexpr T _d2J_dab	(	const index_t	a,
		const index_t	b
	)		const

protected

First derivative of the compressibilty function \(\J\) w.r.t. the stretches \(\lambda_a\) and \(\lambda_b\).

Parameters

[in] a,b The indices a,b

constexpr T _d2Psi	(	const index_t	i,
		const index_t	j,
		const index_t	k,
		const index_t	l
	)		const

protected

Provides the second (mixed) derivative of the incompressible strain energy density function w.r.t. components C_{ij} and C_{kl} of the deformation tensor.

Parameters

[in]	i,j	The indices of C_{ij}
[in]	k,l	The indices of C_{kl}

Returns: The second (mixed) derivative of psi w.r.t. C_{ij} and C_{kl}

constexpr T _d2Psi	(	const index_t	i,
		const index_t	j,
		const index_t	k,
		const index_t	l,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

protected

Provides the second (mixed) derivative of the compressible strain energy density function w.r.t. components C_{ij} and C_{kl} of the deformation tensor.

Parameters

[in]	i,j	The indices of C_{ij}
[in]	k,l	The indices of C_{kl}
[in]	c	The deformation tensor
[in]	cinv	The inverse of the deformation tensor

Returns: The second (mixed) derivative of psi w.r.t. C_{ij} and C_{kl}

constexpr T _d2Psi_dab	(	const index_t	a,
		const index_t	b
	)		const

protected

Second derivative of a strain energy density function \(\Psi\) w.r.t. the stretches \(\lambda_a\) and \(\lambda_b\).

Parameters

[in] a,b The indices a,b

constexpr T _d2Psi_dab_vol	(	const index_t	a,
		const index_t	b
	)		const

protected

Second derivative of the volumetric part of a strain energy density function \(\Psi_{vol}\) w.r.t. the stretches \(\lambda_a\) and \(\lambda_b\).

Parameters

[in] a,b The indices a,b

constexpr T _d2Psi_vol	(	const index_t	i,
		const index_t	j,
		const index_t	k,
		const index_t	l,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

protected

Provides the second (mixed) derivative of the volumetric part of the compressible strain energy density function w.r.t. components C_{ij} and C_{kl} of the deformation tensor.

Parameters

[in]	i,j	The indices of C_{ij}
[in]	k,l	The indices of C_{kl}
[in]	c	The deformation tensor
[in]	cinv	The inverse of the deformation tensor

Returns: The second (mixed) derivative of psi w.r.t. C_{ij} and C_{kl}

constexpr T _dI_1	(	const index_t	i,
		const index_t	j
	)		const

protected

Provides the derivative of the first invariant compressible materials w.r.t. component C_{ij} of the deformation tensor.

Note: \(I_1=\trace{\mathbf{C}}\)

Parameters

[in] i,j The indices of C

Returns: The derivative the first invariant w.r.t. C_{ij}

constexpr T _dI_2	(	const index_t	i,
		const index_t	j,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

protected

Provides the derivative of the second invariant for compressible materials w.r.t. component C_{ij} of the deformation tensor.

Note: \(I_1=\frac{1}{2}\left( \trace{\mathbf{C}^2} + (\trace{\mathbf{C}})^2 \right)\)

Parameters

[in]	i,j	The indices of C
[in]	c	The deformation tensor
[in]	cinv	The inverse of the deformation tensor

Returns: The derivative the second invariant w.r.t. C_{ij}

constexpr T _dJ_da ( const index_t a ) const

protected

First derivative of the compressibilty function \(\J\) w.r.t. the stretche \(\lambda_a\).

Parameters

[in] a The index a

constexpr T _dp_da ( const index_t a ) const

protected

First derivative of the Lagrange multiplier for incompressible materials w.r.t. the stretch \(\lambda_a\).

Parameters

[in] a The index a

constexpr T _dPsi	(	const index_t	i,
		const index_t	j
	)		const

protected

Provides the derivative of the incompressible strain energy density function w.r.t. component C_{ij} of the deformation tensor.

Parameters

[in] i,j The indices of C

Returns: The derivative of psi w.r.t. C_{ij}

constexpr T _dPsi	(	const index_t	i,
		const index_t	j,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

protected

Provides the derivative of the compressible strain energy density function w.r.t. component C_{ij} of the deformation tensor.

Parameters

[in]	i,j	The indices of C
[in]	c	The deformation tensor
[in]	cinv	The inverse of the deformation tensor

Returns: The derivative of psi w.r.t. C_{ij}

constexpr T _dPsi_da ( const index_t a ) const

protected

First derivative of a strain energy density function \(\Psi\) w.r.t. the stretch \(\lambda_a\).

Parameters

[in] a The index a

constexpr T _dPsi_da_vol ( const index_t a ) const

protected

First derivative of the volumetric part of a strain energy density function \(\Psi_{vol}\) w.r.t. the stretch \(\lambda_a\).

Parameters

[in] a The index a

constexpr T _dPsi_vol	(	const index_t	i,
		const index_t	j,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

protected

Provides the derivative of the volumetric part of the compressible strain energy density function w.r.t. component C_{ij} of the deformation tensor.

Parameters

[in]	i,j	The indices of C
[in]	c	The deformation tensor
[in]	cinv	The inverse of the deformation tensor

Returns: The derivative of psi w.r.t. C_{ij}

constexpr T _dSa_db	(	const index_t	a,
		const index_t	b
	)		const

protected

First derivative of the \(a^{\text{th}\) component of the stress w.r.t. the stretch \(\lambda_b\).

Parameters

[in] a,b The indices a,b

gsMatrix< T > _eval3D_Compressible_C33	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

protected

Evaluates the C33 (through thickness) component of the deformation tensor C for compressible materials.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Returns: C33 values (every column for a point u*z)

gsMatrix< T > _eval3D_Compressible_detF	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

protected

Evaluates the jacobian determinant for compressible materials.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Returns: { description_of_the_return_value }

gsMatrix< T > _eval3D_Compressible_matrix	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

protected

Evalluates the compressible material matrix.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Returns: The matrices (9x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

gsMatrix< T > _eval3D_Compressible_stress	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

protected

Evalluates the compressible stress vector.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Returns: The vectors (3x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if< _mat==Material::SvK, gsMatrix< T > >::type _eval3D_detF_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

private

Implementation of jacobina determinant (detF)

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Template Parameters

_mat	The material model
_com	Compressibility parameter (true: compressible, false: incompressible)

Returns: The stress vector (3x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if<!(!_comp && _mat==Material::NH), gsMatrix<T> >::type _eval3D_dmatrix_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z,
		enum MaterialOutput	out
	)		const

private

{ function_description }

Parameters

[in]	patch	The patch
[in]	u	{ parameter_description }
[in]	z	{ parameter_description }
[in]	out	The out

Template Parameters

_mat	{ description }
_comp	{ description }

Returns: { description_of_the_return_value }

gsMatrix< T > _eval3D_Incompressible_detF	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

protected

Evaluates the jacobian determinant for compressible materials.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Returns: { description_of_the_return_value }

gsMatrix< T > _eval3D_Incompressible_matrix	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

protected

Evalluates the incompressible material matrix.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Returns: The matrices (9x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

gsMatrix< T > _eval3D_Incompressible_stress	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

protected

Evalluates the incompressible stress vector.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Returns: The vectors (3x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if< _mat==Material::SvK, gsMatrix< T > >::type _eval3D_matrix_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

private

Implementation of the 3D (in-plane+thickness) evaluator of the material matrix, specialization for SvK material (incompressible)

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Template Parameters

_mat	The material model
_com	Compressibility parameter (true: compressible, false: incompressible)

Returns: The material matrix (9x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if<_com && !(_mat==Material::SvK), gsMatrix<T> >::type _eval3D_matrix_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

private

Implementation of the 3D (in-plane+thickness) evaluator of the material matrix, specialization compressible models.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Template Parameters

_mat	The material model
_com	Compressibility parameter (true: compressible, false: incompressible)

Returns: The material matrix (9x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if<!_com && !(_mat==Material::SvK), gsMatrix<T> >::type _eval3D_matrix_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

private

Implementation of the 3D (in-plane+thickness) evaluator of the material matrix, specialization for incompressible models.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Template Parameters

_mat	The material model
_com	Compressibility parameter (true: compressible, false: incompressible)

Returns: The material matrix (9x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if<!_com && !(_mat==Material::SvK), gsMatrix<T> >::type _eval3D_pstress_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

private

Implementation of the 3D (in-plane+thickness) evaluator of the stress vector, specialization for compressible models.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Template Parameters

_mat	The material model
_com	Compressibility parameter (true: compressible, false: incompressible)

Returns: The principal stresses (3x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if< _mat==Material::SvK, gsMatrix< T > >::type _eval3D_stress_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

private

Implementation of the 3D (in-plane+thickness) evaluator of the stress vector, specialization for SvK material (incompressible)

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Template Parameters

_mat	The material model
_com	Compressibility parameter (true: compressible, false: incompressible)

Returns: The stress vector (3x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if<_com && !(_mat==Material::SvK), gsMatrix<T> >::type _eval3D_stress_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

private

Implementation of the 3D (in-plane+thickness) evaluator of the stress vector, specialization for incompressible models.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Template Parameters

_mat	The material model
_com	Compressibility parameter (true: compressible, false: incompressible)

Returns: The stress vector (3x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

std::enable_if<!_com && !(_mat==Material::SvK), gsMatrix<T> >::type _eval3D_stress_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

private

Implementation of the 3D (in-plane+thickness) evaluator of the stress vector, specialization for compressible models.

Parameters

[in]	patch	The patch index
[in]	u	The in-plane coordinates to be evaluated on
[in]	z	The through-thickness coordinate

Template Parameters

_mat	The material model
_com	Compressibility parameter (true: compressible, false: incompressible)

Returns: The stress vector (3x1 per column), stored per thickness per in-plane point [(u1,t1) (u2,t1),...,(u1,t2),(u2,t2)]

void _initialize ( )

protected

Initializes the object.

Initializes options, flags and defines the number of parameters

std::enable_if<_com, void>::type _pstretch_into_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

private

Implementation of pstretch_into, specialization for compressible materials.

Parameters

[in]	u	The in-plane coordinates to be evaluated on
	result	The result

Template Parameters

_com	Compressibility parameter (true: compressible, false: incompressible)

std::enable_if<!_com, void>::type _pstretch_into_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

private

Implementation of pstretch_into, specialization for incompressible materials.

Parameters

[in]	u	The in-plane coordinates to be evaluated on
	result	The result

Template Parameters

_com	Compressibility parameter (true: compressible, false: incompressible)

std::enable_if<_com, void>::type _pstretchDir_into_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

private

Implementation of stretchDir_into, specialization for compressible materials.

Parameters

[in]	u	The in-plane coordinates to be evaluated on
	result	The result

Template Parameters

_com	Compressibility parameter (true: compressible, false: incompressible)

std::enable_if<!_com, void>::type _pstretchDir_into_impl	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

private

Implementation of stretchDir_into, specialization for incompressible materials.

Parameters

[in]	u	The in-plane coordinates to be evaluated on
	result	The result

Template Parameters

_com	Compressibility parameter (true: compressible, false: incompressible)

constexpr T _Sa ( const index_t a ) const

protected

Component \(a\) of the stress.

Parameters

[in] a The index a

constexpr T _Sii ( const index_t i ) const

protected

Returns an entry of the diagonal of the stress tensor S for incompressible materials.

Parameters

[in] i The index

Returns: S^{ii}

constexpr T _Sii	(	const index_t	i,
		const gsMatrix< T > &	c
	)		const

protected

Returns an entry of the diagonal of the stress tensor S for incompressible materials.

Parameters

[in]	i	The index
[in]	c	The deformation tensor

Returns: S^{ii}

constexpr T _Sij	(	const index_t	i,
		const index_t	j
	)		const

protected

Returns an entry of the stress tensor S for incompressible materials.

Parameters

[in] i,j The indices

Returns: S^{ij}

constexpr T _Sij	(	const index_t	i,
		const index_t	j,
		const gsMatrix< T > &	c,
		const gsMatrix< T > &	cinv
	)		const

protected

Returns an entry of the stress tensor S for compressible materials.

Parameters

[in]	i,j	The indices
[in]	c	The deformation tensor
[in]	cinv	The inverse of the deformation tensor

Returns: S^{ij}

virtual gsMatrix<T> eval3D_pstressTransform	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

inlinevirtualinherited

Provides the transformation of the principle stresses.

Parameters

[in]	patch	The patch to be evaluated on
[in]	u	The in-plane shell coordinates to be eveluated on
[in]	z	The point through-thickness coorinate

Returns: Matrix with the result (deformation tensor) ordered per z coordinate per point [(u1,z1) (u2,z1) .. (un,z1), (u1,z2) .. (un,z2), .., (u1,zm) .. (un,zm)]

virtual gsMatrix<T> eval3D_pstretchTransform	(	const index_t	patch,
		const gsMatrix< T > &	u,
		const gsMatrix< T > &	z
	)		const

inlinevirtualinherited

Provides the transformation of the principle stretches.

Parameters

[in]	patch	The patch to be evaluated on
[in]	u	The in-plane shell coordinates to be eveluated on
[in]	z	The point through-thickness coorinate

Returns: Matrix with the result (deformation tensor) ordered per z coordinate per point [(u1,z1) (u2,z1) .. (un,z1), (u1,z2) .. (un,z2), .., (u1,zm) .. (un,zm)]

virtual const function_ptr getParameter ( const index_t i ) const

inlinevirtualinherited

Gets parameter i.

Parameters

[in] i The parameter index

Returns: The parameter.

virtual gsOptionList& options ( )

inlinevirtualinherited

Returns the options.

Returns: gsOptionList

Reimplemented in gsMaterialMatrixComposite< dim, T >.

virtual void pstress_into	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

inlinevirtualinherited

Evaluates the priciple stresses in the shell (3x1 vector)

Parameters

[in]	patch	The patch to be evaluated on
[in]	u	The in-plane shell coordinates to be eveluated on
	result	The result

Reimplemented in gsMaterialMatrixComposite< dim, T >.

virtual void pstressDir_into	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

inlinevirtualinherited

Evaluates the directions of the priciple stresses in the shell (3x1 vector per direction)

Parameters

[in]	patch	The patch to be evaluated on
[in]	u	The in-plane shell coordinates to be eveluated on
	result	The result

Reimplemented in gsMaterialMatrixComposite< dim, T >.

virtual void setOptions ( gsOptionList opt )

inlinevirtualinherited

Sets the options.

Parameters

[in] opt gsOptionList

Reimplemented in gsMaterialMatrixComposite< dim, T >.

virtual void setParameter	(	const index_t	i,
		const function_ptr &	par
	)

inlinevirtualinherited

Sets the material parameters.

Parameters

[in] pars Function pointers for the parameters in a container

virtual void setParameter	(	const index_t	i,
		const gsFunctionSet< T > &	par
	)

inlinevirtualinherited

Sets the material parameters.

Parameters

[in] pars Function pointers for the parameters in a container

virtual void setParameters ( const std::vector< function_ptr > & pars )

inlinevirtualinherited

Sets the material parameters.

Parameters

[in] pars Function pointers for the parameters in a container

virtual void setParameters ( const std::vector< gsFunctionSet< T > * > & pars )

inlinevirtualinherited

Sets the material parameters.

Parameters

[in] pars Function pointers for the parameters in a container

Reimplemented in gsMaterialMatrixTFT< dim, T, linear >, and gsMaterialMatrixTFT< 2, T >.

virtual void transform_into	(	const index_t	patch,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

inlinevirtualinherited

Constructs a transformation matrix that transforms a quantity (IN VOIGHT NOTATION) in the spectral basis to the (undeformed) convariant basis.

Parameters

[in]	patch	The patch to be evaluated on
[in]	u	The in-plane shell coordinates to be eveluated on
	result	The result

Reimplemented in gsMaterialMatrixComposite< dim, T >.

Detailed Description

template<short_t dim, class T, short_t matId, bool comp, enum Material mat = decodeMat_id<matId>::material, enum Implementation imp = decodeMat_id<matId>::implementation> class gismo::gsMaterialMatrixNonlinear< dim, T, matId, comp, mat, imp >

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Constructor & Destructor Documentation

Member Function Documentation

template<short_t dim, class T, short_t matId, bool comp, enum Material mat = decodeMat_id<matId>::material, enum Implementation imp = decodeMat_id<matId>::implementation>
class gismo::gsMaterialMatrixNonlinear< dim, T, matId, comp, mat, imp >