Ikarus::Materials::BlatzKoT< ST_ > Struct Template Reference

Implementation of the Blatz-Ko material model. More...

#include <ikarus/finiteelements/mechanics/materials/hyperelastic/deviatoric/blatzko.hh>

Public Types
using	ScalarType = ST_
template<typename ST = ScalarType>
using	PrincipalStretches = Eigen::Vector< ST, 3 >
template<typename ST = ScalarType>
using	FirstDerivative = Eigen::Vector< ST, dim >
template<typename ST = ScalarType>
using	SecondDerivative = Eigen::Matrix< ST, dim, dim >
using	MaterialParameters = double

Public Member Functions
	BlatzKoT (MaterialParameters mu)
	Constructor for BlatzKoT. More...
MaterialParameters	materialParametersImpl () const
	Returns the material parameters stored in the material. More...
template<typename ST >
ST	storedEnergyImpl (const PrincipalStretches< ST > &lambda) const
	Computes the stored energy in the BlatzKo material model. More...
template<typename ST >
FirstDerivative< ST >	firstDerivativeImpl (const PrincipalStretches< ST > &lambda) const
	Computes the first derivative of the stored energy function w.r.t. the total principal stretches. More...
template<typename ST >
SecondDerivative< ST >	secondDerivativeImpl (const PrincipalStretches< ST > &lambda) const
	Computes the second derivatives of the stored energy function w.r.t. the total principal stretches. More...
template<typename STO >
auto	rebind () const
	Rebinds the material to a different scalar type. More...

Static Public Member Functions
static constexpr std::string	name () noexcept

Static Public Attributes
static constexpr int	dim = 3
static constexpr auto	stretchTag = PrincipalStretchTags::total

Detailed Description

template<typename ST_>
struct Ikarus::Materials::BlatzKoT< ST_ >

The energy is computed as

\[ \hat{\Psi}(\la_1, \la_2, \la_3) = \frac{\mu}{2}( \frac{1}{\la_1^2} + \frac{1}{\la_2^2} + \frac{1}{\la_3^2} + 2\la_1 \la_2 \la_3 - 5). \]

Remarks

A special Blatz-Ko material model is implemented here. It assumes material parameters which corresponds to a Poisson's ratio of 0.25.

Template Parameters

ST_	The underlying scalar type.

Member Typedef Documentation

FirstDerivative

template<typename ST_ >

template<typename ST = ScalarType>

using Ikarus::Materials::BlatzKoT< ST_ >::FirstDerivative = Eigen::Vector<ST, dim>

MaterialParameters

template<typename ST_ >

using Ikarus::Materials::BlatzKoT< ST_ >::MaterialParameters = double

PrincipalStretches

template<typename ST_ >

template<typename ST = ScalarType>

using Ikarus::Materials::BlatzKoT< ST_ >::PrincipalStretches = Eigen::Vector<ST, 3>

ScalarType

template<typename ST_ >

using Ikarus::Materials::BlatzKoT< ST_ >::ScalarType = ST_

SecondDerivative

template<typename ST_ >

template<typename ST = ScalarType>

using Ikarus::Materials::BlatzKoT< ST_ >::SecondDerivative = Eigen::Matrix<ST, dim, dim>

Constructor & Destructor Documentation

BlatzKoT()

template<typename ST_ >

Ikarus::Materials::BlatzKoT< ST_ >::BlatzKoT ( MaterialParameters  mu )

inlineexplicit

Parameters

mu	The shear modulus.

Member Function Documentation

firstDerivativeImpl()

template<typename ST_ >

template<typename ST >

FirstDerivative< ST > Ikarus::Materials::BlatzKoT< ST_ >::firstDerivativeImpl ( const PrincipalStretches< ST > &  lambda ) const

inline

Parameters

lambda

principal stretches

Returns

ScalarType

materialParametersImpl()

template<typename ST_ >

MaterialParameters Ikarus::Materials::BlatzKoT< ST_ >::materialParametersImpl ( ) const

inline

name()

template<typename ST_ >

static constexpr std::string Ikarus::Materials::BlatzKoT< ST_ >::name ( )

inlinestaticconstexprnoexcept

rebind()

template<typename ST_ >

template<typename STO >

auto Ikarus::Materials::BlatzKoT< ST_ >::rebind ( ) const

inline

Template Parameters

STO	The target scalar type.

Returns

BlatzKoT<ScalarTypeOther> The rebound BlatzKo material.

secondDerivativeImpl()

template<typename ST_ >

template<typename ST >

SecondDerivative< ST > Ikarus::Materials::BlatzKoT< ST_ >::secondDerivativeImpl ( const PrincipalStretches< ST > &  lambda ) const

inline

Parameters

lambda

principal stretches

Template Parameters

ST	the scalartype of the principal stretches

Returns

ScalarType

storedEnergyImpl()

template<typename ST_ >

template<typename ST >

ST Ikarus::Materials::BlatzKoT< ST_ >::storedEnergyImpl ( const PrincipalStretches< ST > &  lambda ) const

inline

Parameters

lambda

principal stretches

Template Parameters

ST	the scalartype of the principal stretches

Returns

ScalarType

Member Data Documentation

dim

template<typename ST_ >

constexpr int Ikarus::Materials::BlatzKoT< ST_ >::dim = 3

staticconstexpr

stretchTag

template<typename ST_ >

constexpr auto Ikarus::Materials::BlatzKoT< ST_ >::stretchTag = PrincipalStretchTags::total

staticconstexpr

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

• blatzko.hh