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

class pylife.stress.equistress.StressTensorEquistress(pandas_obj)[source]
abs_max_principal()[source]
max_principal()[source]
min_principal()[source]
mises()[source]
principals()[source]
signed_mises_abs_max_principal()[source]
signed_mises_trace()[source]
signed_tresca_abs_max_principal()[source]
signed_tresca_trace()[source]
tresca()[source]
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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray

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:

numpy.ndarray