cratepy.material.materialoperations.conjugate_spatial_log_strain

conjugate_spatial_log_strain(def_gradient, first_piola_stress)

Stress conjugate of spatial logarithmic strain tensor.

Spatial logarithmic strain tensor:

\[\boldsymbol{\varepsilon} = \frac{1}{2} \ln (\boldsymbol{F} \boldsymbol{F}^{T})\]

where \(\boldsymbol{\varepsilon}\) is the spatial logarithmic strain tensor and \(\boldsymbol{F}\) is the deformation gradient.

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Stress conjugate of spatial logarithmic strain tensor:

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

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

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Parameters:

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

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

Returns:

• spatial_log_strain (numpy.ndarray (2d)) – Spatial logarithmic strain.

• stress_conjugate (numpy.ndarray (2d)) – Stress conjugate to spatial logarithmic strain.