NuTo::EngineeringStrainInvariants Namespace Reference

Typedefs
using	Tensor = Eigen::Matrix3d

Functions
Tensor	ToTensor (EngineeringStrain< 3 > &v)
double	I1 (const EngineeringStrain< 3 > &v)
	returns I1 - the first strain invariant of the characteristic equation \[ \lambda^3 - I_1 \lambda^2 + I_2 \lambda - I_3 \] More...
double	I2 (const EngineeringStrain< 3 > &v)
	returns I2 - the first strain invariant of the characteristic equation \[ \lambda^3 - I_1 \lambda^2 + I_2 \lambda - I_3 \] More...
double	I3 (const EngineeringStrain< 3 > &v)
	returns I3 - the first strain invariant of the characteristic equation \[ \lambda^3 - I_1 \lambda^2 + I_2 \lambda - I_3 \] More...
double	J2 (const EngineeringStrain< 3 > &v)
	returns J2 - the second deviatoric strain invariant of the characteristic equation \[ \lambda^3 - J_1 \lambda^2 - J_2 \lambda - J_3 \] Note the minus sign in front of J2. More...
EngineeringStrain< 3 >	Deviatoric (EngineeringStrain< 3 > v)
	returns the deviatoric part More...

Typedef Documentation

using NuTo::EngineeringStrainInvariants::Tensor = typedef Eigen::Matrix3d

Function Documentation

EngineeringStrain<3> NuTo::EngineeringStrainInvariants::Deviatoric ( EngineeringStrain< 3 >  v )

inline

returns the deviatoric part

double NuTo::EngineeringStrainInvariants::I1 ( const EngineeringStrain< 3 > &  v )

inline

returns I1 - the first strain invariant of the characteristic equation

\[ \lambda^3 - I_1 \lambda^2 + I_2 \lambda - I_3 \]

double NuTo::EngineeringStrainInvariants::I2 ( const EngineeringStrain< 3 > &  v )

inline

returns I2 - the first strain invariant of the characteristic equation

\[ \lambda^3 - I_1 \lambda^2 + I_2 \lambda - I_3 \]

double NuTo::EngineeringStrainInvariants::I3 ( const EngineeringStrain< 3 > &  v )

inline

returns I3 - the first strain invariant of the characteristic equation

\[ \lambda^3 - I_1 \lambda^2 + I_2 \lambda - I_3 \]

double NuTo::EngineeringStrainInvariants::J2 ( const EngineeringStrain< 3 > &  v )

inline

returns J2 - the second deviatoric strain invariant of the characteristic equation

\[ \lambda^3 - J_1 \lambda^2 - J_2 \lambda - J_3 \]

Note the minus sign in front of J2.

This is not consistent with the I2 invariant but apparently common practice.

Tensor NuTo::EngineeringStrainInvariants::ToTensor ( EngineeringStrain< 3 > &  v )

inline