cratepy.clustering.adaptivity.crve_adaptivity.cauchy_from_first_piola

cauchy_from_first_piola(def_gradient, first_piola_stress)

Cauchy stress tensor from first Piola-Kirchhoff stress tensor.

\[\boldsymbol{\sigma} = \frac{1}{\det (\boldsymbol{F})} \, \boldsymbol{P} \boldsymbol{F}^{T}\]

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

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Parameters:

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

• first_piola_stress (numpy.ndarray (2d)) – First Piola-Kirchhoff stress tensor.

Returns:

cauchy_stress – Cauchy stress tensor.

Return type:

numpy.ndarray (2d)