cratepy.material.materialoperations.first_piola_from_kirchhoff

first_piola_from_kirchhoff(def_gradient, kirchhoff_stress)[source]

First Piola-Kirchhoff stress tensor from Kirchhoff stress tensor.

\[\boldsymbol{P} = \boldsymbol{\tau} \boldsymbol{F}^{-T}\]

where \(\boldsymbol{P}\) is the first Piola-Kirchhoff stress tensor, \(\boldsymbol{\tau}\) is the Kirchhoff stress tensor, and \(\boldsymbol{F}\) is the deformation gradient.


Parameters:
Returns:

first_piola_stress – First Piola-Kirchhoff stress tensor.

Return type:

numpy.ndarray (2d)