Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue > Class Template Reference

Full (right) Green-Lagrange strain tensor, the workhorse of hyperelasticity. More...

#include <elasto.hh>

Detailed Description

template<class Scalar, int dim, bool byValue = true>
class Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >

Full (right) Green-Lagrange strain tensor, the workhorse of hyperelasticity.

The right Green Lagrange strain tensor for a displacement \( u \) is defined as

\[ E = \frac{1}{2}(u_x + u_x^T + u_x^T u_x) = \frac{1}{2}(F^TF - I) = \frac{1}{2}(C-I). \]

Template Parameters

Scalar	the scalar field type, usually double
dim	the spatial dimension, usually 2 or 3
byValue	if true (default), the displacement derivative \( u_x \) is stored by value, otherwise by reference

Definition at line 340 of file elasto.hh.

Public Types
typedef Dune::FieldMatrix< Scalar, dim, dim >	Tensor

Public Member Functions
	GreenLagrangeTensor (Tensor const &du_)
	Constructor. More...
	GreenLagrangeTensor ()
	Default constructor. This initializes the displacement derivative to 0, i.e. to the reference configuration. More...
void	setDisplacementDerivative (Tensor const &du_)
Tensor	d0 () const
	The linearized Green-Lagrange strain tensor \( E = \frac{1}{2} (u_x + u_x^T + u_x^T u_x) \). More...
Tensor	d1 (Tensor const &dv) const
	The first derivative of the linearized Green-Lagrange strain tensor in direction dv. More...
Tensor	d2 (Tensor const &dv, Tensor const &dw) const
	The second derivative of the linearized Green-Lagrange strain tensor in direction dv,dw. More...

Member Typedef Documentation

Tensor

template<class Scalar , int dim, bool byValue = true>

typedef Dune::FieldMatrix<Scalar,dim,dim> Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::Tensor

Definition at line 343 of file elasto.hh.

Constructor & Destructor Documentation

GreenLagrangeTensor() [1/2]

template<class Scalar , int dim, bool byValue = true>

Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::GreenLagrangeTensor ( Tensor const &  du_ )

inline

Constructor.

Parameters

du	The spatial derivative of the displacement.

Definition at line 349 of file elasto.hh.

GreenLagrangeTensor() [2/2]

template<class Scalar , int dim, bool byValue = true>

Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::GreenLagrangeTensor ( )

inline

Default constructor. This initializes the displacement derivative to 0, i.e. to the reference configuration.

Definition at line 355 of file elasto.hh.

Member Function Documentation

d0()

template<class Scalar , int dim, bool byValue = true>

Tensor Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::d0 ( ) const

inline

The linearized Green-Lagrange strain tensor \( E = \frac{1}{2} (u_x + u_x^T + u_x^T u_x) \).

Definition at line 366 of file elasto.hh.

d1()

template<class Scalar , int dim, bool byValue = true>

Tensor Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::d1 ( Tensor const &  dv ) const

inline

The first derivative of the linearized Green-Lagrange strain tensor in direction dv.

This is \( \E_{u_x}(u_x) v_x = \frac{1}{2}(v_x + v_x^T + v_x^T u_x + u_x^T v_x). \)

Definition at line 373 of file elasto.hh.

d2()

template<class Scalar , int dim, bool byValue = true>

Tensor Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::d2 ( Tensor const &  dv, Tensor const &  dw  ) const

inline

The second derivative of the linearized Green-Lagrange strain tensor in direction dv,dw.

This is \( E_{u_x,u_x}(u_x) [v_x,w_x] = \frac{1}{2}(v_x^T w_x + w_x^T v_x). \)

Definition at line 380 of file elasto.hh.

setDisplacementDerivative()

template<class Scalar , int dim, bool byValue = true>

void Kaskade::Elastomechanics::GreenLagrangeTensor< Scalar, dim, byValue >::setDisplacementDerivative ( Tensor const &  du_ )

inline

Definition at line 358 of file elasto.hh.

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

• elasto.hh