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.

$${\mathsf{A}}_{ijkl}=det(\mathit{F}){\mathsf{a}}_{ipkq}{F}_{lq}^{-1}{F}_{jp}^{-1}$$

where $\mathsf{A}$ is the material consistent tangent modulus, $\mathit{F}$ is the deformation gradient, and $\mathsf{a}$ 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)