cratepy.material.models.stvenant_kirchhoff.material_from_spatial_tangent_modulus

material_from_spatial_tangent_modulus(spatial_consistent_tangent, def_gradient)

Material consistent tangent modulus from spatial counterpart.

\[\mathsf{A}_{ijkl} = \det (\boldsymbol{F}) \, \mathsf{a}_{ipkq} \, F_{lq}^{-1} F_{jp}^{-1}\]

where \(\mathbf{\mathsf{A}}\) is the material consistent tangent modulus, \(\boldsymbol{F}\) is the deformation gradient, and \(\mathbf{\mathsf{a}}\) is the spatial consistent tangent modulus.

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Parameters:

• spatial_consistent_tangent (numpy.ndarray (4d)) – Spatial consistent tangent modulus.

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

Returns:

material_consistent_tangent – Material consistent tangent modulus.

Return type:

numpy.ndarray (4d)