diff --git a/python/damask/mechanics.py b/python/damask/mechanics.py
index 76c7ae13b..3c4a96d99 100644
--- a/python/damask/mechanics.py
+++ b/python/damask/mechanics.py
@@ -260,6 +260,11 @@ def _polar_decomposition(T: _np.ndarray,
         Requested outputs: ‘R’ for the rotation tensor,
         ‘V’ for left stretch tensor, and ‘U’ for right stretch tensor.
 
+    Returns
+    -------
+    VRU : tuple of numpy.ndarray, shape (...,3,3)
+       Requested components of the singular value decomposition.
+
     """
     u, _, vh = _np.linalg.svd(T)
     R = _np.einsum('...ij,...jk',u,vh)
@@ -290,6 +295,11 @@ def _equivalent_Mises(T_sym: _np.ndarray,
     s : float
         Scaling factor (2/3 for strain, 3/2 for stress).
 
+    Returns
+    -------
+    eq : numpy.ndarray, shape (...)
+        Scaled second invariant of the deviatoric part of T_sym.
+
     """
     d = _tensor.deviatoric(T_sym)
     return _np.sqrt(s*_np.sum(d**2.0,axis=(-1,-2)))