Marmot::ContinuumMechanics::VoigtNotation::Transformations Namespace Reference

Functions
Matrix6d	transformationMatrixStrainVoigt (const Matrix3d &transformedCoordinateSystem)
Matrix6d	transformationMatrixStressVoigt (const Matrix3d &transformedCoordinateSystem)
Matrix36d	projectVoigtStressToPlane (const Vector3d &normalVector)
Matrix36d	projectVoigtStrainToPlane (const Vector3d &normalVector)
Marmot::Vector6d	rotateVoigtStress (const Eigen::Matrix3d &Q, const Marmot::Vector6d &stress)

Function Documentation

transformationMatrixStrainVoigt()

Matrix6d Marmot::ContinuumMechanics::VoigtNotation::Transformations::transformationMatrixStrainVoigt

(

const Matrix3d &

transformedCoordinateSystem

)

Computes the transformation matrix \( R_{\varepsilon} \) to transform a voigt notated strain vector \( \boldsymbol{\varepsilon} \) to another cartesian coordinate system

transformationMatrixStressVoigt()

Matrix6d Marmot::ContinuumMechanics::VoigtNotation::Transformations::transformationMatrixStressVoigt

(

const Matrix3d &

transformedCoordinateSystem

)

Computes the transformation matrix \( R_{\sigma} \) to transform a voigt notated stress vector \( \boldsymbol{\sigma} \) to another cartesian coordinate system

projectVoigtStressToPlane()

Matrix36d Marmot::ContinuumMechanics::VoigtNotation::Transformations::projectVoigtStressToPlane

(

const Vector3d &

normalVector

)

Returns the projection matrix to calculate the stress vector \f$ \boldsymbol{t}^{(n)} \f$ effective on a plane

orientated with the normal vector \( \boldsymbol{n} \) from a voigt notated stress vector following cauchy's formula.

\[ \displaystyle t^{(n)}_i = \sigma_{ij}\,n_j \]

projectVoigtStrainToPlane()

Matrix36d Marmot::ContinuumMechanics::VoigtNotation::Transformations::projectVoigtStrainToPlane

(

const Vector3d &

normalVector

)

Returns the projection matrix to calculate the strain vector \( \boldsymbol{\varepsilon}^{(n)} \) effective on a plane orientated with the normal vector \( \boldsymbol{n} \) from a voigt notated strain vector (see projectVoigtStressToPlane())).

rotateVoigtStress()

Marmot::Vector6d Marmot::ContinuumMechanics::VoigtNotation::Transformations::rotateVoigtStress	(	const Eigen::Matrix3d &	Q,
		const Marmot::Vector6d &	stress
	)

Rotates a stress tensor \f$ \boldsymbol{\sigma} \f$ applying a rotation matrix \f$ \boldsymbol{Q} \f$ in voigt

notation.

\[ \displaystyle \boldsymbol{\sigma}^{\prime} = \boldsymbol{Q} \cdot \boldsymbol{\sigma} \cdot \boldsymbol{Q}^{T} \]