cratepy.material.materialmodeling.first_piola_from_kirchhoff

first_piola_from_kirchhoff(def_gradient, kirchhoff_stress)

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.

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Parameters:

• def_gradient (numpy.ndarray (2d)) – Deformation gradient.

• kirchhoff_stress (numpy.ndarray (2d)) – Kirchhoff stress tensor.

Returns:

first_piola_stress – First Piola-Kirchhoff stress tensor.

Return type:

numpy.ndarray (2d)