Users:General FEM Analysis/Materials Reference/Tsai-Wu Failure Criterion

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General Description

It is a practically simple failure criterion which takes interaction of stresses in different directions into account by making use of strength tensors. It is considerably cheaper in computational effort compared to Puck criterion especially in 3D stress states. A drawback of this criterion is that it is based on von Mises criterion which is more suitable for ductile materials. 2D and 3D formulations are implemented into Carat++. As it can not distinguish between different fracture modes, Tsai-Wu Criterion returns one failure index for corresponding failure analysis.

Tsai-Wu in 2D

Strength Analysis

Fracture envelope for a 2D failure analysis [1]

Tsai-wu 2D.png

Parameter Description

Tsai-Wu Parameters (2D)
Compulsory Parameters
Parameter Values, Default(*) Description
T11 real Resistance to longitudinal tension (Direction 1)
C11 real Resistance to longitudinal compression (Direction 1)
T22 real Resistance to transverse tension (Direction 2)
C22 real Resistance to transverse compression (Direction 2)
S12 real Resistance to longitudinal shear
Optional Parameters
Parameter Values, Default(*) Description
STRESS TYPE 2D, 3D Indicates what kind of stress state should be used to calculate the failure condition. When not given, related element’s stress type is taken.
T33 real Resistance to tension in thickness direction (Direction 3) (De f ault = T22)
C33 real Resistance to compression in thickness direction (Direction 3) (De f ault = C22)
S13 real Resistance to longitudinal shear (De f ault = S 12)
FS12 real Coefficient, necessary for calculation of F12. (De f ault = -0.5)
F12 real F12 component of strength tensor; Fij. When not given, it is calculated using FS12.
P real Strength value, necessary for calculation of F12. See Section 3.2.3
U real Strength value, necessary for calculation of F12. See Section 3.2.3
V real Strength value, necessary for calculation of F12. See Section 3.2.3


Tsai-Wu in 3D

Strength Analysis

Fracture envelopes for a 3D failure analysis:

Tsai-wu 3D.png

Parameter Description

Tsai-Wu Parameters (3D)
Compulsory Parameters
Parameter Values, Default(*) Description
T11 real Resistance to longitudinal tension (Direction 1)
C11 real Resistance to longitudinal compression (Direction 1)
T22 real Resistance to transverse tension (Direction 2)
C22 real Resistance to transverse compression (Direction 2)
S12 real Resistance to longitudinal shear
S23 real Resistance to transverse shear
Optional Parameters
Parameter Values, Default(*) Description
STRESS TYPE 2D, 3D Indicates what kind of stress state should be used to calculate the failure condition. When not given, related element’s stress type is taken.
T33 real Resistance to tension in thickness direction (Direction 3) (De f ault = T22)
C33 real Resistance to compression in thickness direction (Direction 3) (De f ault = C22)
S13 real Resistance to longitudinal shear (De f ault = S 12)
FS12 real Coefficient, necessary for calculation of F12. (De f ault = -0.5)
F12 real F12 component of strength tensor; Fij. When not given, it is calculated using FS12.
P real Strength value, necessary for calculation of F12. See Section 3.2.3
U real Strength value, necessary for calculation of F12. See Section 3.2.3
V real Strength value, necessary for calculation of F12. See Section 3.2.3
FS13 real Coefficient, necessary for calculation of F13. (De f ault = -0.5)
F13 real F12 component of strength tensor; Fij. When not given, it is calculated using FS13.
FS23 real Coefficient, necessary for calculation of F23.(De f ault = -0.5)
F23 real F12 component of strength tensor; Fij. When not given, it is calculated using FS23.


Example of a Complete Input Block

Input tsai-wu.png

References

  1. H. Deuschle. 3D failure analysis of UD fibre reinforced composites: Puck’s theory within FEA. Phd thesis, Universität Stuttgart, 2010.




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