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@ -260,6 +260,11 @@ def _polar_decomposition(T: _np.ndarray,
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Requested outputs: ‘R’ for the rotation tensor,
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‘V’ for left stretch tensor, and ‘U’ for right stretch tensor.
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Returns
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-------
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VRU : tuple of numpy.ndarray, shape (...,3,3)
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Requested components of the singular value decomposition.
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"""
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u, _, vh = _np.linalg.svd(T)
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R = _np.einsum('...ij,...jk',u,vh)
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@ -290,6 +295,11 @@ def _equivalent_Mises(T_sym: _np.ndarray,
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s : float
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Scaling factor (2/3 for strain, 3/2 for stress).
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Returns
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-------
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eq : numpy.ndarray, shape (...)
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Scaled second invariant of the deviatoric part of T_sym.
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"""
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d = _tensor.deviatoric(T_sym)
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return _np.sqrt(s*_np.sum(d**2.0,axis=(-1,-2)))
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