cratepy.material.materialoperations.compute_rotation_tensor

compute_rotation_tensor(def_gradient)

Rotation tensor from polar decomposition of deformation gradient.

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

where \(\boldsymbol{R}\) is the rotation tensor and \(\boldsymbol{F}\) is the deformation gradient.

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Parameters:

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

Returns:

r – Rotation tensor.

Return type:

numpy.ndarray (2d)