Class for elastic homogenization. More...

#include <homogenize.h>

Public Member Functions
	Homogenize ()
	Constructor. More...

	~Homogenize (void)
	Destructor. More...

void	voigt (FloatMatrix &PhaseMatrix)
	Parallel scheme of Voigt for any number of isotropic phases. More...

void	reuss (FloatMatrix &PhaseMatrix)
	Serial scheme of Reuss for any number of isotropic phases. More...

void	hashinShtrikmanWalpole (FloatMatrix &PhaseMatrix)
	Hashin-Shtrikman-Walpole lower and upper bounds for arbitrary number of isotropic phases. More...

void	moriTanaka (FloatMatrix &PhaseMatrix, int refRow)
	Mori-Tanaka homogenization method for spherical isotropic inclusions. More...

void	selfConsistent (FloatMatrix &PhaseMatrix)
	Self-consistent homogenization method of Hill and Budiansky for spherical isotropic inclusions. More...

void	herveZaoui (FloatMatrix &PhaseMatrix)
	Herve and Zaoui's homogenization scheme for n-spherical isotropic domains and arbitrary number of isotropic phases. More...

void	hirsch (FloatMatrix &PhaseMatrix, double chi)
	Hirsch's scheme combining Voigt and Reuss bounds. More...

void	hansen (FloatMatrix &PhaseMatrix)
	Hansen's model for a spherical inclusion in a spherical matrix, for Poisson's ratio 0.2 and two phases. More...

void	counto (FloatMatrix &PhaseMatrix)
	Counto's model for a prismatic inclusion in a prismatic matrix, two phases. More...

void	kusterToksoz (FloatMatrix &PhaseMatrix)
	Kuster-Toksoz model for two phases. More...

void	printYourself (int out=0)
	Print homogenized output. More...

void	ENuToKMu (const double E, const double nu, double &k, double &mu)
	Convert Young's modulus and Poisson's ratio to bulk and shear moduli, isotropic material. More...

void	kMuToENu (const double k, const double mu, double &E, double &nu)
	Convert bulk and shear moduli to Young's modulus and Poisson's ratio, isotropic material. More...

Public Attributes
double	E_hmg
	Effective Young's modulus or the lower bound. More...

double	E_hmg_2
	Upper bound of Young's modulus if applicable. More...

double	nu_hmg
	Effective Poisson's ratio. More...

double	nu_hmg_2
	Effective Poisson's ratio or the lower bound. More...

double	k_hmg
	Effective bulk modulus or the lower bound. More...

double	k_hmg_2
	Upper bound of bulk modulus if applicable. More...

double	mu_hmg
	Effective shear modulus or the lower bound. More...

double	mu_hmg_2
	Upper shear modulus if applicable. More...

Private Member Functions
double	lambda (double *PhaseMatrixKMu, int NumRows, double mu)
	Auxiliary function. More...

double	zeta (double k, double mu)
	Auxiliary function for Hashin-Shtrikman bounds. More...

double	gamma (FloatMatrix &SortedPhaseMatrix, double zeta)
	Auxiliary function. More...

void	checkVolFraction (FloatMatrix &PhaseMatrix)
	Check that the total volumetric fraction is the unity. More...

void	fillJ (FloatMatrix &J, double r, const FloatArray &mu, const FloatArray &k, int phase)
	Auxiliary function for Herve-Zaoui scheme. More...

void	fillL (FloatMatrix &L, double r, const FloatArray &mu, const FloatArray &k, int phase)
	Auxiliary function for Herve-Zaoui scheme. More...

Detailed Description

Class for elastic homogenization.

Following homogenization estimates and bounds are implemented : Voigt, Reuss, Hirsch, Counto, Mori-Tanaka, Self-consitent, Hashin-Shtrikman-Walpole, Kuster-Toksoz, and Herve-Zaoui's n-layered spherical assemblage. Only isotropic materials and spherical inclusions are considered for the homogenization. Many schemes work with unlimited number of elastic phases.

Definition at line 50 of file homogenize.h.

Constructor & Destructor Documentation

oofem::Homogenize::Homogenize ( )

Constructor.

Definition at line 39 of file homogenize.C.

oofem::Homogenize::~Homogenize ( void )

inline

Destructor.

Definition at line 58 of file homogenize.h.

References E.

Member Function Documentation

void oofem::Homogenize::checkVolFraction ( FloatMatrix & PhaseMatrix )

private

Check that the total volumetric fraction is the unity.

Parameters

PhaseMatrix matrix containing in each row the volume fraction, the Young modulus and the Poisson ratio for each phase

Definition at line 724 of file homogenize.C.

References oofem::FloatMatrix::giveNumberOfRows(), and OOFEM_ERROR.

Referenced by counto(), hansen(), hashinShtrikmanWalpole(), herveZaoui(), kusterToksoz(), moriTanaka(), reuss(), selfConsistent(), and voigt().

void oofem::Homogenize::counto ( FloatMatrix & PhaseMatrix )

Counto's model for a prismatic inclusion in a prismatic matrix, two phases.

Parameters

PhaseMatrix matrix containing in each row the volume fraction, the Young modulus and the Poisson ratio for each phase. The first row is an inclusion, the second row corresponds to the matrix.

Definition at line 626 of file homogenize.C.

References checkVolFraction(), E_hmg, ENuToKMu(), oofem::FloatMatrix::giveNumberOfRows(), k_hmg, mu_hmg, nu_hmg, and OOFEM_ERROR.

void oofem::Homogenize::ENuToKMu	(	const double	E,
		const double	nu,
		double &	k,
		double &	mu
	)

Convert Young's modulus and Poisson's ratio to bulk and shear moduli, isotropic material.

Definition at line 691 of file homogenize.C.

Referenced by counto(), hansen(), hashinShtrikmanWalpole(), herveZaoui(), kusterToksoz(), moriTanaka(), reuss(), selfConsistent(), and voigt().

void oofem::Homogenize::fillJ	(	FloatMatrix &	J,
		double	r,
		const FloatArray &	mu,
		const FloatArray &	k,
		int	phase
	)

private

Auxiliary function for Herve-Zaoui scheme.

Definition at line 739 of file homogenize.C.

Referenced by herveZaoui().

void oofem::Homogenize::fillL	(	FloatMatrix &	L,
		double	r,
		const FloatArray &	mu,
		const FloatArray &	k,
		int	phase
	)

private

Auxiliary function for Herve-Zaoui scheme.

Definition at line 748 of file homogenize.C.

Referenced by herveZaoui().

double oofem::Homogenize::gamma	(	FloatMatrix &	SortedPhaseMatrix,
		double	zeta
	)

private

Auxiliary function.

Definition at line 709 of file homogenize.C.

References oofem::FloatMatrix::giveNumberOfRows(), and zeta().

Referenced by hashinShtrikmanWalpole(), and herveZaoui().

void oofem::Homogenize::hansen ( FloatMatrix & PhaseMatrix )

Hansen's model for a spherical inclusion in a spherical matrix, for Poisson's ratio 0.2 and two phases.

Parameters

PhaseMatrix matrix containing in each row the volume fraction, the Young modulus and the Poisson ratio for each phase. The first row is an inclusion, the second row corresponds to the matrix.

Definition at line 605 of file homogenize.C.

References checkVolFraction(), E_hmg, ENuToKMu(), oofem::FloatMatrix::giveNumberOfRows(), k_hmg, mu_hmg, nu_hmg, and OOFEM_ERROR.

void oofem::Homogenize::hashinShtrikmanWalpole ( FloatMatrix & PhaseMatrix )

Hashin-Shtrikman-Walpole lower and upper bounds for arbitrary number of isotropic phases.

Parameters

PhaseMatrix matrix containing in each row the volume fraction, the Young modulus and the Poisson ratio for each phase implemented according to J.G. Berryman: Mixture Theories for Rock Properties, Physics and Phase Relations, A Handbook of Physical Constants, Am. Geophys, 1995

Definition at line 95 of file homogenize.C.

References checkVolFraction(), E_hmg, E_hmg_2, ENuToKMu(), gamma(), oofem::FloatMatrix::giveNumberOfRows(), k_hmg, k_hmg_2, kMuToENu(), mu_hmg, mu_hmg_2, nu_hmg, nu_hmg_2, and zeta().

void oofem::Homogenize::herveZaoui ( FloatMatrix & PhaseMatrix )

Herve and Zaoui's homogenization scheme for n-spherical isotropic domains and arbitrary number of isotropic phases.

Parameters

PhaseMatrix matrix containing in each row the volume fraction, the Young modulus and the Poisson ratio for each phase

Definition at line 344 of file homogenize.C.

References oofem::FloatArray::beProductOf(), oofem::FloatMatrix::beProductOf(), oofem::cbrt(), checkVolFraction(), E_hmg, ENuToKMu(), fillJ(), fillL(), gamma(), oofem::FloatMatrix::giveNumberOfColumns(), oofem::FloatMatrix::giveNumberOfRows(), k_hmg, kMuToENu(), mu_hmg, N, nu_hmg, OOFEM_ERROR, OOFEM_WARNING, oofem::sqr(), oofem::FloatArray::times(), and oofem::FloatArray::zero().

Referenced by oofem::CemhydMatStatus::AnalyticHomogenizationConcrete().

void oofem::Homogenize::hirsch	(	FloatMatrix &	PhaseMatrix,
		double	chi
	)

Hirsch's scheme combining Voigt and Reuss bounds.

Parameters

PhaseMatrix	matrix containing in each row the volume fraction, the Young modulus and the Poisson ratio for each phase.
chi	a weight parameter between Reuss (=0) and Voigt (=1) bounds

Definition at line 590 of file homogenize.C.

References E_hmg, k_hmg, kMuToENu(), mu_hmg, nu_hmg, reuss(), and voigt().

void oofem::Homogenize::kMuToENu	(	const double	k,
		const double	mu,
		double &	E,
		double &	nu
	)

Convert bulk and shear moduli to Young's modulus and Poisson's ratio, isotropic material.

Definition at line 697 of file homogenize.C.

Referenced by hashinShtrikmanWalpole(), herveZaoui(), hirsch(), kusterToksoz(), moriTanaka(), reuss(), selfConsistent(), and voigt().

void oofem::Homogenize::kusterToksoz ( FloatMatrix & PhaseMatrix )

Kuster-Toksoz model for two phases.

Parameters

PhaseMatrix matrix containing in each row the volume fraction, the Young modulus and the Poisson ratio for each phase. The first row is an inclusion, the second row corresponds to the matrix.

Definition at line 648 of file homogenize.C.

References checkVolFraction(), E_hmg, ENuToKMu(), oofem::FloatMatrix::giveNumberOfRows(), k_hmg, kMuToENu(), mu_hmg, nu_hmg, and OOFEM_ERROR.

double oofem::Homogenize::lambda	(	double *	PhaseMatrixKMu,
		int	NumRows,
		double	mu
	)

private

Auxiliary function.

void oofem::Homogenize::moriTanaka	(	FloatMatrix &	PhaseMatrix,
		int	refRow
	)

Mori-Tanaka homogenization method for spherical isotropic inclusions.

Parameters

PhaseMatrix	matrix containing in each row the volume fraction, the Young modulus and the Poisson ratio for each phase
refRow	row of the reference matrix phase (0 is the first)

Definition at line 176 of file homogenize.C.

References checkVolFraction(), E_hmg, ENuToKMu(), oofem::FloatMatrix::giveNumberOfRows(), k_hmg, kMuToENu(), mu_hmg, and nu_hmg.

Referenced by oofem::CemhydMatStatus::AnalyticHomogenizationConcrete(), and oofem::CemhydMatStatus::AnalyticHomogenizationPaste().

void oofem::Homogenize::printYourself ( int out = 0 )

Print homogenized output.

Parameters