The equistress
module¶
Equivalent Stresses¶
Library to calculate the equivalent stress values of a FEM stress tensor.
By now the following calculation methods are implemented:
Principal stresses
Maximum principal stress
Minimum principal stress
Absolute maximum principal stress
Von Mises
Signed von Mises, sign from trace
Signed von Mises, sign from absolute maximum principal stress
Tresca
Signed Tresca, sign from trace
Signed Tresca, sign from absolute maximum principal stress
- pylife.stress.equistress.abs_max_principal(s11, s22, s33, s12, s13, s23)[source]¶
Calculate absolute maximum principal stress (maximum of absolute eigenvalues with corresponding sign).
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Absolute maximum principal stress. Shape is the same as the components.
- Return type
- pylife.stress.equistress.eigenval(s11, s22, s33, s12, s13, s23)[source]¶
Calculate eigenvalues of a symmetric 3D tensor.
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Array containing eigenvalues sorted in ascending order. Shape is (length of components, 3) or simply 3 if components are single values.
- Return type
- pylife.stress.equistress.max_principal(s11, s22, s33, s12, s13, s23)[source]¶
Calculate maximum principal stress (maximum of eigenvalues).
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Maximum principal stress. Shape is the same as the components.
- Return type
- pylife.stress.equistress.min_principal(s11, s22, s33, s12, s13, s23)[source]¶
Calculate minimum principal stress (minimum of eigenvalues).
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Minimum principal stress. Shape is the same as the components.
- Return type
- pylife.stress.equistress.mises(s11, s22, s33, s12, s13, s23)[source]¶
Calculate equivalent stress according to von Mises.
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Von Mises equivalent stress. Shape is the same as the components.
- Return type
- Raises
AssertionError – Components’ shape is not consistent.
- pylife.stress.equistress.principals(s11, s22, s33, s12, s13, s23)[source]¶
Calculate all principal stress components (eigenvalues).
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
All principal stresses. Shape (…, 3).
- Return type
- pylife.stress.equistress.signed_mises_abs_max_principal(s11, s22, s33, s12, s13, s23)[source]¶
Calculate equivalent stress according to von Mises, signed with the sign of the absolute maximum principal stress.
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Signed von Mises equivalent stress. Shape is the same as the components.
- Return type
- pylife.stress.equistress.signed_mises_trace(s11, s22, s33, s12, s13, s23)[source]¶
Calculate equivalent stress according to von Mises, signed with the sign of the trace (i.e s11 + s22 + s33).
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Signed von Mises equivalent stress. Shape is the same as the components.
- Return type
- pylife.stress.equistress.signed_tresca_abs_max_principal(s11, s22, s33, s12, s13, s23)[source]¶
Calculate equivalent stress according to Tresca, signed with the sign of the absolute maximum principal stress.
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Signed Tresca equivalent stress. Shape is the same as the components.
- Return type
- pylife.stress.equistress.signed_tresca_trace(s11, s22, s33, s12, s13, s23)[source]¶
Calculate equivalent stress according to Tresca, signed with the sign of the trace (i.e s11 + s22 + s33).
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Signed Tresca equivalent stress. Shape is the same as the components.
- Return type
- pylife.stress.equistress.tresca(s11, s22, s33, s12, s13, s23)[source]¶
Calculate equivalent stress according to Tresca.
- Parameters
s11 (array_like) – Component 11 of 3D tensor.
s22 (array_like) – Component 22 of 3D tensor.
s33 (array_like) – Component 33 of 3D tensor.
s12 (array_like) – Component 12 of 3D tensor.
s13 (array_like) – Component 13 of 3D tensor.
s23 (array_like) – Component 23 of 3D tensor.
- Returns
Equivalent Tresca stress. Shape is the same as the components.
- Return type