The equistress module#

Calculate 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]#

Accessor for equivalent stresses of a Voigt stress tensor.

Parameters:

pandas_obj (pandas.DataFrame) – The Voigt stress tensor with the columns S11, S22, S33, S12, S13, S23.

abs_max_principal()[source]#

Calculate the absolute maximum principal stress.

Returns:

The absolute maximum principal stress for each row.

Return type:

pandas.Series

max_principal()[source]#

Calculate the maximum principal stress.

Returns:

The maximum principal stress for each row.

Return type:

pandas.Series

min_principal()[source]#

Calculate the minimum principal stress.

Returns:

The minimum principal stress for each row.

Return type:

pandas.Series

mises()[source]#

Calculate the von Mises equivalent stress.

Returns:

The equivalent stress for each row.

Return type:

pandas.Series

principals()[source]#

Calculate the principal stresses.

Returns:

The principal stresses for each row.

Return type:

pandas.DataFrame

signed_mises_abs_max_principal()[source]#

Calculate the principal-signed von Mises equivalent stress.

Returns:

The equivalent stress for each row.

Return type:

pandas.Series

signed_mises_trace()[source]#

Calculate the trace-signed von Mises equivalent stress.

Returns:

The equivalent stress for each row.

Return type:

pandas.Series

signed_tresca_abs_max_principal()[source]#

Calculate the principal-signed Tresca equivalent stress.

Returns:

The equivalent stress for each row.

Return type:

pandas.Series

signed_tresca_trace()[source]#

Calculate the trace-signed Tresca equivalent stress.

Returns:

The equivalent stress for each row.

Return type:

pandas.Series

tresca()[source]#

Calculate the Tresca equivalent stress.

Returns:

The equivalent stress for each row.

Return type:

pandas.Series

pylife.stress.equistress.abs_max_principal(s11, s22, s33, s12, s13, s23)[source]#

Calculate absolute maximum principal stress.

This is the maximum of the 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:

ValueError – 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 von Mises equivalent stress signed by the principal stress.

The sign is that 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 von Mises equivalent stress signed by the trace.

The sign is that 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 Tresca equivalent stress signed by the principal stress.

The sign is that 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 Tresca equivalent stress signed by the trace.

The sign is that 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