Ikarus::Materials::DeviatoricInvariants< PS > Struct Template Reference

Implementation of the deviatoric invariants and its derivatives. More...

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

Public Types
using	PrincipalStretches = PS
using	ScalarType = PrincipalStretches::value_type
using	Invariants = PrincipalStretches
using	FirstDerivative = Eigen::Vector< ScalarType, dim >
using	SecondDerivative = Eigen::Matrix< ScalarType, dim, dim >

Public Member Functions
	DeviatoricInvariants (const PrincipalStretches &lambda)
	Constructor for DeviatoricInvariants. More...
auto	value () const
	Computation of value of the deviatoric invariants. More...
auto	firstDerivative () const
	Computation of the first derivatives of the deviatoric invariants w.r.t the total principal stretches. More...
auto	secondDerivative () const
	Computation of the second derivatives of the deviatoric invariants w.r.t the total principal stretches. More...

Static Public Attributes
static constexpr int	dim = PrincipalStretches::RowsAtCompileTime

Detailed Description

template<typename PS>
struct Ikarus::Materials::DeviatoricInvariants< PS >

The three invariants are

\[ I_1 = \la_1^2 + \la_2^2 + \la_3^2, \]

\[ I_2 = \la_1^2 \la_2^2 + \la_2^2 \la_3^2 + \la_1^2 \la_3^2, \]

\[ I_3 = \la_1^2 \la_2^2 \la_3^2. \]

The deviatoric invariants are then defined as

\[ W_1 = I_1 I_3^{-1/3}, \]

\[ W_2 = I_2 I_3^{-2/3}, \]

Template Parameters

PS	Type of the principal stretches.

Member Typedef Documentation

FirstDerivative

template<typename PS >

using Ikarus::Materials::DeviatoricInvariants< PS >::FirstDerivative = Eigen::Vector<ScalarType, dim>

Invariants

template<typename PS >

using Ikarus::Materials::DeviatoricInvariants< PS >::Invariants = PrincipalStretches

PrincipalStretches

template<typename PS >

using Ikarus::Materials::DeviatoricInvariants< PS >::PrincipalStretches = PS

ScalarType

template<typename PS >

using Ikarus::Materials::DeviatoricInvariants< PS >::ScalarType = PrincipalStretches::value_type

SecondDerivative

template<typename PS >

using Ikarus::Materials::DeviatoricInvariants< PS >::SecondDerivative = Eigen::Matrix<ScalarType, dim, dim>

Constructor & Destructor Documentation

DeviatoricInvariants()

template<typename PS >

Ikarus::Materials::DeviatoricInvariants< PS >::DeviatoricInvariants ( const PrincipalStretches &  lambda )

inlineexplicit

Parameters

lambda

The principal stretches.

Member Function Documentation

firstDerivative()

template<typename PS >

auto Ikarus::Materials::DeviatoricInvariants< PS >::firstDerivative ( ) const

inline

secondDerivative()

template<typename PS >

auto Ikarus::Materials::DeviatoricInvariants< PS >::secondDerivative ( ) const

inline

value()

template<typename PS >

auto Ikarus::Materials::DeviatoricInvariants< PS >::value ( ) const

inline

Member Data Documentation

dim

template<typename PS >

constexpr int Ikarus::Materials::DeviatoricInvariants< PS >::dim = PrincipalStretches::RowsAtCompileTime

staticconstexpr

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

• deviatoricinvariants.hh