cratepy.material.materialoperations.first_piola_from_cauchy

first_piola_from_cauchy(def_gradient, cauchy_stress)

First Piola-Kirchhoff stress tensor from Cauchy stress tensor.

\[\boldsymbol{P} = \det (\boldsymbol{F}) \, \boldsymbol{\sigma} \boldsymbol{F}^{-T}\]

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

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Parameters:

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

• cauchy_stress (numpy.ndarray (2d)) – Cauchy stress tensor.

Returns:

first_piola_stress – First Piola-Kirchhoff stress tensor.

Return type:

numpy.ndarray (2d)