A base class that represents the fourth-rank elasticity tensor $E_{ijkl}$ defined such that. More...

#include <pml_time_harmonic_elasticity_tensor.h>

Inheritance diagram for oomph::PMLTimeHarmonicElasticityTensor:

Public Member Functions
virtual	~PMLTimeHarmonicElasticityTensor ()
	Empty virtual Destructor. More...

std::complex< double >	operator() (const unsigned &i, const unsigned &j, const unsigned &k, const unsigned &l) const
	Return the appropriate independent component via the index translation scheme (const version). More...

Protected Member Functions
virtual std::complex< double >	independent_component (const unsigned &i) const
	Member function that returns the i-th independent component of the elasticity tensor. More...

void	range_check (const unsigned &i, const unsigned &j, const unsigned &k, const unsigned &l) const
	Helper range checking function (Note that this only captures over-runs in 3D but errors are likely to be caught in evaluation of the stress and strain tensors anyway...) More...

	PMLTimeHarmonicElasticityTensor ()
	Empty Constructor. More...

Static Private Attributes
static const unsigned	Index [3][3][3][3]
	Translation table from the four indices to the corresponding independent component. More...

Detailed Description

A base class that represents the fourth-rank elasticity tensor $E_{ijkl}$ defined such that.

$\tau_{ij} = E_{ijkl} e_{kl},$

where $e_{ij}$ is the infinitessimal (Cauchy) strain tensor and $\tau_{ij}$ is the stress tensor. The symmetries of the tensor are such that

$E_{ijkl} = E_{jikl} = E_{ijlk} = E_{klij}$

and thus there are relatively few independent components. These symmetries are included in the definition of the object so that non-physical symmetries cannot be accidentally imposed.

Definition at line 56 of file pml_time_harmonic_elasticity_tensor.h.

Constructor & Destructor Documentation

◆ PMLTimeHarmonicElasticityTensor()

oomph::PMLTimeHarmonicElasticityTensor::PMLTimeHarmonicElasticityTensor ( )

inlineprotected

Empty Constructor.

Definition at line 116 of file pml_time_harmonic_elasticity_tensor.h.

◆ ~PMLTimeHarmonicElasticityTensor()

virtual oomph::PMLTimeHarmonicElasticityTensor::~PMLTimeHarmonicElasticityTensor ( )

inlinevirtual

Empty virtual Destructor.

Definition at line 120 of file pml_time_harmonic_elasticity_tensor.h.

Member Function Documentation

◆ independent_component()

virtual std::complex<double> oomph::PMLTimeHarmonicElasticityTensor::independent_component ( const unsigned & i ) const

inlineprotectedvirtual

Member function that returns the i-th independent component of the elasticity tensor.

Reimplemented in oomph::PMLTimeHarmonicIsotropicElasticityTensor.

Definition at line 65 of file pml_time_harmonic_elasticity_tensor.h.

Referenced by operator()().

◆ operator()()

std::complex<double> oomph::PMLTimeHarmonicElasticityTensor::operator()	(	const unsigned &	i,
		const unsigned &	j,
		const unsigned &	k,
		const unsigned &	l
	)		const

inline

Return the appropriate independent component via the index translation scheme (const version).

Definition at line 125 of file pml_time_harmonic_elasticity_tensor.h.

References i, independent_component(), Index, and range_check().

◆ range_check()

void oomph::PMLTimeHarmonicElasticityTensor::range_check	(	const unsigned &	i,
		const unsigned &	j,
		const unsigned &	k,
		const unsigned &	l
	)		const

inlineprotected

Helper range checking function (Note that this only captures over-runs in 3D but errors are likely to be caught in evaluation of the stress and strain tensors anyway...)

Definition at line 76 of file pml_time_harmonic_elasticity_tensor.h.

References i.

Referenced by operator()().

Member Data Documentation

◆ Index

const unsigned oomph::PMLTimeHarmonicElasticityTensor::Index

staticprivate

Initial value:

= {
    {{{0, 1, 6}, {1, 2, 7}, {6, 7, 8}},
     {{1, 3, 9}, {3, 4, 10}, {9, 10, 11}},
     {{6, 9, 12}, {9, 13, 14}, {12, 14, 15}}},
 
    {{{1, 3, 9}, {3, 4, 10}, {9, 10, 11}},
     {{2, 4, 13}, {4, 5, 16}, {13, 16, 17}},
     {{7, 10, 14}, {10, 16, 18}, {14, 18, 19}}},
 
    {{{6, 9, 12}, {9, 13, 14}, {12, 14, 15}},
     {{7, 10, 14}, {10, 16, 18}, {14, 18, 19}},
     {{8, 11, 15}, {11, 17, 19}, {15, 19, 20}}}}

Translation table from the four indices to the corresponding independent component.

Translation scheme that takes account of the symmetries of the tensor. The independent coefficients are related to the coefficients of the elasticity tensor as follows:

/

$\begin{array}{cc} 0 & E_{1111} \\ 1 & E_{1112} \\ 2 & E_{1122} \\ 3 & E_{1212} \\ 4 & E_{1222} \\ 5 & E_{2222} \\ 6 & E_{1113} \\ 7 & E_{1123} \\ 8 & E_{1133} \\ 9 & E_{1213} \\ 10 & E_{1223} \\ 11 & E_{1233} \\ 12 & E_{1313} \\ 13 & E_{1322} \\ 14 & E_{1323} \\ 15 & E_{1333} \\ 16 & E_{2223} \\ 17 & E_{2233} \\ 18 & E_{2323} \\ 19 & E_{2333} \\ 20 & E_{3333} \end{array}$

/

Definition at line 60 of file pml_time_harmonic_elasticity_tensor.h.

Referenced by operator()().

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

Public Member Functions

Protected Member Functions

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PMLTimeHarmonicElasticityTensor()

◆ ~PMLTimeHarmonicElasticityTensor()

Member Function Documentation

◆ independent_component()

◆ operator()()

◆ range_check()

Member Data Documentation

◆ Index