Class for computation of properties based on an elasticity tensor. More...

#include <elastic_tensor.h>

Public Types
enum class	AveragingScheme { Voigt , Reuss , Hill , Numerical }

using	AngularDirection = Eigen::Ref< const Eigen::Vector< double, 2 > >

using	CartesianDirection = Eigen::Ref< const Eigen::Vector< double, 3 > >

Public Member Functions
	ElasticTensor (Eigen::Ref< const Mat6 > c_voigt)

double	youngs_modulus_angular (AngularDirection) const

double	youngs_modulus (CartesianDirection) const

double	linear_compressibility_angular (AngularDirection) const

double	linear_compressibility (CartesianDirection) const

double	shear_modulus_angular (AngularDirection, double angle) const

double	shear_modulus (CartesianDirection, double angle) const

double	shear_modulus (CartesianDirection, CartesianDirection) const

std::pair< double, double >	shear_modulus_minmax (CartesianDirection) const

double	poisson_ratio_angular (AngularDirection, double angle) const

double	poisson_ratio (CartesianDirection, double angle) const

double	poisson_ratio (CartesianDirection, CartesianDirection) const

std::pair< double, double >	poisson_ratio_minmax (CartesianDirection) const

double	average_poisson_ratio_direction (CartesianDirection, int num_samples=360) const

double	reduced_youngs_modulus (CartesianDirection, int num_samples=360) const

double	average_bulk_modulus (AveragingScheme avg=AveragingScheme::Hill) const

double	average_shear_modulus (AveragingScheme avg=AveragingScheme::Hill) const

double	average_youngs_modulus (AveragingScheme avg=AveragingScheme::Hill) const

double	average_poisson_ratio (AveragingScheme avg=AveragingScheme::Hill) const

double	transverse_acoustic_velocity (double bulk_modulus_gpa, double shear_modulus_gpa, double density_g_cm3) const
	Calculate the transverse (shear) acoustic velocity.

double	longitudinal_acoustic_velocity (double bulk_modulus_gpa, double shear_modulus_gpa, double density_g_cm3) const
	Calculate the longitudinal (compressional) acoustic velocity.

const Mat6 &	voigt_s () const

const Mat6 &	voigt_c () const

Mat6	voigt_rotation_matrix (const Mat3 &rotation) const
	Get the 6x6 rotation matrix in order to rotate the Voigt representations of the tensors.

Mat6	rotate_voigt_stiffness (const Mat3 &rotation) const
	Rotate the elastic tensor using a 3x3 rotation matrix.

Mat6	rotate_voigt_compliance (const Mat3 &rotation) const
	Rotate the compliance tensor using a 3x3 rotation matrix.

double	component (int i, int j, int k, int l) const

double &	component (int i, int j, int k, int l)

Vec6	eigenvalues () const

double *	data ()

double const *	data () const

Detailed Description

Class for computation of properties based on an elasticity tensor.

This implementation would not have been possible without the ELATE[1] software, https://progs.coudert.name/elate which heavily inspired it and was wonderful as a refereence implementation for the various properties.

[1] Gaillac et al. https://doi.org/10.1088/0953-8984/28/27/275201

Member Typedef Documentation

◆ AngularDirection

using occ::core::ElasticTensor::AngularDirection = Eigen::Ref<const Eigen::Vector<double, 2> >

◆ CartesianDirection

using occ::core::ElasticTensor::CartesianDirection = Eigen::Ref<const Eigen::Vector<double, 3> >

Member Enumeration Documentation

◆ AveragingScheme

enum class occ::core::ElasticTensor::AveragingScheme

strong

Enumerator
Voigt
Reuss
Hill
Numerical

Constructor & Destructor Documentation

◆ ElasticTensor()

occ::core::ElasticTensor::ElasticTensor ( Eigen::Ref< const Mat6 > c_voigt )

explicit

Member Function Documentation

◆ average_bulk_modulus()

double occ::core::ElasticTensor::average_bulk_modulus ( AveragingScheme avg = AveragingScheme::Hill ) const

◆ average_poisson_ratio()

double occ::core::ElasticTensor::average_poisson_ratio ( AveragingScheme avg = AveragingScheme::Hill ) const

◆ average_poisson_ratio_direction()

double occ::core::ElasticTensor::average_poisson_ratio_direction	(	CartesianDirection	,
		int	num_samples = `360`
	)		const

◆ average_shear_modulus()

double occ::core::ElasticTensor::average_shear_modulus ( AveragingScheme avg = AveragingScheme::Hill ) const

◆ average_youngs_modulus()

double occ::core::ElasticTensor::average_youngs_modulus ( AveragingScheme avg = AveragingScheme::Hill ) const

◆ component() [1/2]

double & occ::core::ElasticTensor::component	(	int	i,
		int	j,
		int	k,
		int	l
	)

◆ component() [2/2]

double occ::core::ElasticTensor::component	(	int	i,
		int	j,
		int	k,
		int	l
	)		const

◆ data() [1/2]

double * occ::core::ElasticTensor::data ( )

inline

◆ data() [2/2]

double const * occ::core::ElasticTensor::data ( ) const

inline

◆ eigenvalues()

Vec6 occ::core::ElasticTensor::eigenvalues ( ) const

◆ linear_compressibility()

double occ::core::ElasticTensor::linear_compressibility ( CartesianDirection ) const

◆ linear_compressibility_angular()

double occ::core::ElasticTensor::linear_compressibility_angular ( AngularDirection ) const

◆ longitudinal_acoustic_velocity()

double occ::core::ElasticTensor::longitudinal_acoustic_velocity	(	double	bulk_modulus_gpa,
		double	shear_modulus_gpa,
		double	density_g_cm3
	)		const

Calculate the longitudinal (compressional) acoustic velocity.

Parameters

bulk_modulus_gpa	Bulk modulus in GPa
shear_modulus_gpa	Shear modulus in GPa
density_g_cm3	Density in g/cm³

Returns: Longitudinal acoustic velocity in m/s

Calculates V_p = sqrt((4G + 3K)/(3ρ)) where G is the shear modulus, K is the bulk modulus, and ρ is the density. This represents the velocity of compressional waves propagating through the material.

◆ poisson_ratio() [1/2]

double occ::core::ElasticTensor::poisson_ratio	(	CartesianDirection	,
		CartesianDirection
	)		const

◆ poisson_ratio() [2/2]

double occ::core::ElasticTensor::poisson_ratio	(	CartesianDirection	,
		double	angle
	)		const

◆ poisson_ratio_angular()

double occ::core::ElasticTensor::poisson_ratio_angular	(	AngularDirection	,
		double	angle
	)		const

◆ poisson_ratio_minmax()

std::pair< double, double > occ::core::ElasticTensor::poisson_ratio_minmax ( CartesianDirection ) const

◆ reduced_youngs_modulus()

double occ::core::ElasticTensor::reduced_youngs_modulus	(	CartesianDirection	,
		int	num_samples = `360`
	)		const

◆ rotate_voigt_compliance()

Mat6 occ::core::ElasticTensor::rotate_voigt_compliance ( const Mat3 & rotation ) const

Rotate the compliance tensor using a 3x3 rotation matrix.

Parameters

rotation 3x3 rotation matrix R

Returns: Rotated 6x6 compliance tensor in Voigt notation (S' = T @ S @ T^T)

◆ rotate_voigt_stiffness()

Mat6 occ::core::ElasticTensor::rotate_voigt_stiffness ( const Mat3 & rotation ) const

Rotate the elastic tensor using a 3x3 rotation matrix.

Parameters

rotation 3x3 rotation matrix R

Returns: Rotated 6x6 stiffness tensor in Voigt notation (C' = T @ C @ T^T)

◆ shear_modulus() [1/2]

double occ::core::ElasticTensor::shear_modulus	(	CartesianDirection	,
		CartesianDirection
	)		const

◆ shear_modulus() [2/2]

double occ::core::ElasticTensor::shear_modulus	(	CartesianDirection	,
		double	angle
	)		const

◆ shear_modulus_angular()

double occ::core::ElasticTensor::shear_modulus_angular	(	AngularDirection	,
		double	angle
	)		const

◆ shear_modulus_minmax()

std::pair< double, double > occ::core::ElasticTensor::shear_modulus_minmax ( CartesianDirection ) const

◆ transverse_acoustic_velocity()

double occ::core::ElasticTensor::transverse_acoustic_velocity	(	double	bulk_modulus_gpa,
		double	shear_modulus_gpa,
		double	density_g_cm3
	)		const

Calculate the transverse (shear) acoustic velocity.

Parameters

bulk_modulus_gpa	Bulk modulus in GPa (not used in calculation, included for API consistency)
shear_modulus_gpa	Shear modulus in GPa
density_g_cm3	Density in g/cm³

Returns: Transverse acoustic velocity in m/s

Calculates V_s = sqrt(G/ρ) where G is the shear modulus and ρ is the density. This represents the velocity of shear waves propagating through the material.

◆ voigt_c()

const Mat6 & occ::core::ElasticTensor::voigt_c ( ) const

◆ voigt_rotation_matrix()

Mat6 occ::core::ElasticTensor::voigt_rotation_matrix ( const Mat3 & rotation ) const

Get the 6x6 rotation matrix in order to rotate the Voigt representations of the tensors.

Parameters

rotation 3x3 rotation matrix R

Returns: 6x6 rotation matrix Tto be used as (C' = T @ C @ T^T)

◆ voigt_s()

const Mat6 & occ::core::ElasticTensor::voigt_s ( ) const

◆ youngs_modulus()

double occ::core::ElasticTensor::youngs_modulus ( CartesianDirection ) const

◆ youngs_modulus_angular()

double occ::core::ElasticTensor::youngs_modulus_angular ( AngularDirection ) const

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

/home/runner/work/occ/occ/include/occ/core/elastic_tensor.h

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ AngularDirection

◆ CartesianDirection

Member Enumeration Documentation

◆ AveragingScheme

Constructor & Destructor Documentation

◆ ElasticTensor()

Member Function Documentation

◆ average_bulk_modulus()

◆ average_poisson_ratio()

◆ average_poisson_ratio_direction()

◆ average_shear_modulus()

◆ average_youngs_modulus()

◆ component() [1/2]

◆ component() [2/2]

◆ data() [1/2]

◆ data() [2/2]

◆ eigenvalues()

◆ linear_compressibility()

◆ linear_compressibility_angular()

◆ longitudinal_acoustic_velocity()

◆ poisson_ratio() [1/2]

◆ poisson_ratio() [2/2]

◆ poisson_ratio_angular()

◆ poisson_ratio_minmax()

◆ reduced_youngs_modulus()

◆ rotate_voigt_compliance()

◆ rotate_voigt_stiffness()

◆ shear_modulus() [1/2]

◆ shear_modulus() [2/2]

◆ shear_modulus_angular()

◆ shear_modulus_minmax()

◆ transverse_acoustic_velocity()

◆ voigt_c()

◆ voigt_rotation_matrix()

◆ voigt_s()

◆ youngs_modulus()

◆ youngs_modulus_angular()