A struct computing the value, first and second derivatives of the Green-Lagrange strain tensor (in Voigt notation), where the displacement gradient is enhanced. More...

#include <ikarus/finiteelements/mechanics/strainenhancements/easfunctions/displacementgradient.hh>

Static Public Member Functions
template<typename GEO , typename EAST >
static auto	value (const GEO &geo, const auto &uFunction, const Dune::FieldVector< double, GEO::mydimension > &gpPos, const EAST &easFunction, const auto &alpha)
	Compute the strain vector at a given integration point or its index. More...

template<int wrtCoeff, typename GEO , typename EAST >
static auto	firstDerivative (const GEO &geo, const auto &uFunction, const auto &localBasis, const auto &gpIndex, const Dune::FieldVector< double, GEO::mydimension > &gpPos, const EAST &easFunction, const auto &alpha, const int node=sNaN)
	Compute the first derivative of the Green-Lagrange strain w.r.t d or alpha for a given node and integration point. More...

template<int wrtCoeff, typename GEO , typename ST , typename EAST >
static auto	secondDerivative (const GEO &geo, const auto &uFunction, const auto &localBasis, const auto &gpIndex, const Dune::FieldVector< double, GEO::mydimension > &gpPos, const Eigen::Vector< ST, GEO::mydimension *(GEO::mydimension+1)/2 > &S, const EAST &easFunction, const auto &alpha, const int I=sNaN, const int J=sNaN)
	Compute the second derivative of the Green-Lagrange strain w.r.t d or alpha for a given node and integration point. More...

static constexpr auto	name ()
	The name of the strain measure enhanced w.r.t EAS method. More...

Detailed Description

See [10] for details.

Member Function Documentation

◆ firstDerivative()

template<int wrtCoeff, typename GEO , typename EAST >

static auto Ikarus::EAS::DisplacementGradient::firstDerivative	(	const GEO &	geo,
		const auto &	uFunction,
		const auto &	localBasis,
		const auto &	gpIndex,
		const Dune::FieldVector< double, GEO::mydimension > &	gpPos,
		const EAST &	easFunction,
		const auto &	alpha,
		const int	node = `sNaN`
	)

inlinestatic

Parameters

geo	The geometry object of the finite element.
uFunction	The function representing the displacement field.
localBasis	The local basis object.
gpPos	The position of the integration point.
gpIndex	The index of the integration point.
node	The FE node index (defaults to sNaN).
alpha	The coefficients of the EAS function.
easFunction	The EAS function.

Template Parameters

wrtCoeff	An integer indicating the coefficient w.r.t which the first derivative of Green-Lagrange strain is to be returned (0 = E,d; 1 = E,a).
GEO	The type of the geometry object.
EAST	The type of the EAS function.

Returns: The first derivative of the Green-Lagrange strain w.r.t d or alpha.

◆ name()

static constexpr auto Ikarus::EAS::DisplacementGradient::name ( )

inlinestaticconstexpr

◆ secondDerivative()

template<int wrtCoeff, typename GEO , typename ST , typename EAST >

static auto Ikarus::EAS::DisplacementGradient::secondDerivative	(	const GEO &	geo,
		const auto &	uFunction,
		const auto &	localBasis,
		const auto &	gpIndex,
		const Dune::FieldVector< double, GEO::mydimension > &	gpPos,
		const Eigen::Vector< ST, GEO::mydimension *(GEO::mydimension+1)/2 > &	S,
		const EAST &	easFunction,
		const auto &	alpha,
		const int	I = `sNaN`,
		const int	J = `sNaN`
	)

inlinestatic

Parameters

geo	The geometry object of the finite element.
uFunction	The function representing the displacement field.
localBasis	The local basis object.
gpPos	The position of the integration point.
gpIndex	The index of the integration point.
I	The FE node index I (defaults to sNaN).
J	The FE node index J (defaults to sNaN).
S	The PK2 stress (in Voigt notation).
easFunction	The EAS function.
alpha	The coefficients of the EAS function.

Template Parameters

wrtCoeff	An integer indicating the coefficient w.r.t which the second derivative of Green-Lagrange strain is to be returned (0 = E,dd; 1 = E,aa; 2 = E,ad = E,da).
GEO	The type of the geometry object.
ST	The underlying scalar type.
EAST	The type of the EAS function.

Returns: The second derivative of the Green-Lagrange strain w.r.t d, alpha or the mixed derivative (0 = E,dd; 1 = E,aa; 2 = E,ad = E,da).

◆ value()

template<typename GEO , typename EAST >

static auto Ikarus::EAS::DisplacementGradient::value	(	const GEO &	geo,
		const auto &	uFunction,
		const Dune::FieldVector< double, GEO::mydimension > &	gpPos,
		const EAST &	easFunction,
		const auto &	alpha
	)

inlinestatic

Parameters

geo	The geometry object providing the transposed Jacobian.
uFunction	The function representing the displacement field.
gpPos	The position of the integration point.
easFunction	The EAS function.
alpha	The coefficients of the EAS function.

Template Parameters

GEO	The type of the geometry object.
EAST	The type of the EAS function.

Returns: The Green-Lagrange strain vector at the given integration point.

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

easfunctions/displacementgradient.hh

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ firstDerivative()

◆ name()

◆ secondDerivative()

◆ value()