Public Member Functions | Protected Member Functions | Static Private Attributes | List of all members
oomph::TimeHarmonicElasticityTensor Class Reference

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

#include <time_harmonic_elasticity_tensor.h>

+ Inheritance diagram for oomph::TimeHarmonicElasticityTensor:

Public Member Functions

virtual ~TimeHarmonicElasticityTensor ()
 Empty virtual Destructor. More...
 
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 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...
 
 TimeHarmonicElasticityTensor ()
 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 54 of file time_harmonic_elasticity_tensor.h.

Constructor & Destructor Documentation

◆ TimeHarmonicElasticityTensor()

oomph::TimeHarmonicElasticityTensor::TimeHarmonicElasticityTensor ( )
inlineprotected

Empty Constructor.

Definition at line 113 of file time_harmonic_elasticity_tensor.h.

◆ ~TimeHarmonicElasticityTensor()

virtual oomph::TimeHarmonicElasticityTensor::~TimeHarmonicElasticityTensor ( )
inlinevirtual

Empty virtual Destructor.

Definition at line 117 of file time_harmonic_elasticity_tensor.h.

Member Function Documentation

◆ independent_component()

virtual double oomph::TimeHarmonicElasticityTensor::independent_component ( const unsigned &  i) const
inlineprotectedvirtual

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

Reimplemented in oomph::TimeHarmonicIsotropicElasticityTensor.

Definition at line 63 of file time_harmonic_elasticity_tensor.h.

Referenced by operator()().

◆ operator()()

double oomph::TimeHarmonicElasticityTensor::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 122 of file time_harmonic_elasticity_tensor.h.

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

◆ range_check()

void oomph::TimeHarmonicElasticityTensor::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 73 of file time_harmonic_elasticity_tensor.h.

References i.

Referenced by operator()().

Member Data Documentation

◆ Index

const unsigned oomph::TimeHarmonicElasticityTensor::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 58 of file time_harmonic_elasticity_tensor.h.

Referenced by operator()().

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