Vector and tensor components and invariants

Note:

In the documentation, invariant quantities are often referred to as derived results.

Vector components

X	For a rectangular coordinate system, the X-component of the vector quantity.
Y	For a rectangular coordinate system, the Y-component of the vector quantity.
Z	For a rectangular or cylindrical coordinate system, the Z-component of the vector quantity.
R	For a cylindrical or spherical coordinate system, the radial component of the vector quantity.
T	For a cylindrical and spherical coordinate system, the tangential component of the vector quantity.
P	For a spherical coordinate system, the Φ-component of the vector quantity.

Invariant quantity for vector results

Magnitude	The magnitude of the vector quantity.

Stress tensor components

XX	Normal stress on the +X-face in the +X-direction, σx.
YY	Normal stress on the +Y-face in the +Y-direction, σy.
ZZ	Normal stress on the +Z-face in the +Z-direction, σz.
XY	Shear stress on the +X-face in the +Y-direction, τxy.
YZ	Shear stress on the +Y-face in the +Z-direction, τyz.
ZX	Shear stress on the +Z-face in the +X-direction, τzx.

Invariant quantities for stress tensor results

Determinant	The determinant of the matrix of stress components.Also known as the 3rd stress invariant.
Mean	The arithmetic average of the three normal stresses, σave.Also known as the hydrostatic stress.
Max Shear	The maximum shear stress, τmax.
Min Principal	The minimum principal stress, σ3.
Mid Principal	The middle principal stress, σ2.
Max Principal	The maximum principal stress, σ1.
	Note: The principal stresses are ordered algebraically as follows:σ1 ≥ σ2 ≥ σ3
Worst Principal	The principal stress with the largest absolute value.
Octahedral	The shear stress on the octahedral plane, τoct.
Von-Mises	The von Mises stress, σvm.

Strain tensor components

XX	Normal strain in the X-direction, εx.
YY	Normal strain in the Y-direction, εy.
ZZ	Normal strain in the Z-direction, εz.
XY	Engineering shear strain, γxy.
YZ	Engineering shear strain, γyz.
ZX	Engineering shear strain, γzx.

Invariant quantities for strain tensor results

Note:

For the purpose of calculating invariant quantities for strain, if necessary, the post-processor converts the engineering shear strains to tensor shear strains.

Determinant	The determinant of the matrix of strain components.Also known as the 3rd strain invariant.
Mean	The arithmetic average of the three normal strains, εavg.
Max Shear	The maximum engineering shear strain, γmax.
Min Principal	The minimum principal normal strain, ε3.
Mid Principal	The middle principal normal strain, ε2.
Max Principal	The maximum principal normal strain, ε1.
	Note: The principal normal strains are ordered algebraically as follows:ε1 ≥ ε2 ≥ ε3
Worst Principal	The principal normal strain with the largest absolute value.
Octahedral	The octahedral engineering shear strain, γoct.
Von-Mises	The von Mises strain, εvm.

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Vector and tensor components and invariants, Simcenter 3D 2021.1 Series

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