Marmot::ContinuumMechanics::HaighWestergaard Namespace Reference

Classes
struct	HaighWestergaardCoordinates

Functions
template<typename T = double>
HaighWestergaardCoordinates< T >	haighWestergaard (const Eigen::Matrix< T, 6, 1 > &stress)
HaighWestergaardCoordinates< double >	haighWestergaardFromStrain (const Marmot::Vector6d &strain)

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Class Documentation

Marmot::ContinuumMechanics::HaighWestergaard::HaighWestergaardCoordinates

struct Marmot::ContinuumMechanics::HaighWestergaard::HaighWestergaardCoordinates

template<typename T = double>
struct Marmot::ContinuumMechanics::HaighWestergaard::HaighWestergaardCoordinates< T >

Aggregate of the Haigh-Westergaard coordinates (invariants) \(\xi\), \(\rho\), \(\theta\).

Class Members
T	xi	Hydrostatic component \(\xi\).
T	rho	Deviatoric radius \(\rho\).
T	theta	Lode angle \(\theta\) specified in radian.

Function Documentation

haighWestergaard()

template<typename T = double>

HaighWestergaardCoordinates< T > Marmot::ContinuumMechanics::HaighWestergaard::haighWestergaard

(

const Eigen::Matrix< T, 6, 1 > &

stress

)

Computes the stress coordinates in the Haigh-Westergaard space.

Note

The stress coordinates are computed from the invariants \(I_1,\,J_2,\,J_3\) of the stress tensor as follows:

\[\xi=I_1/\sqrt{3}\]

\[\rho=\sqrt{2\,J_2}\]

\[\theta=\frac{1}{3}\,\arccos{\left(\frac{3\,\sqrt{3}}{2}\,\frac{J_3}{\sqrt{J_2^3}}\right)}\]

Parameters

stress

Stress tensor \(\sig\) given in Voigt notation.

haighWestergaardFromStrain()

HaighWestergaardCoordinates< double > Marmot::ContinuumMechanics::HaighWestergaard::haighWestergaardFromStrain

(

const Marmot::Vector6d &

strain

)

Computes the strain coordinates in the Haigh-Westergaard space.

Note

The computation is equal to haighWestergaard by replacing the stress invariants with the strain invariants.

Parameters

strain

Strain tensor \(\eps\) given in Voigt notation.