Merge branch '284-more-friendly-output-name-of-add_strain-or-a-better…

…-presentation-in-documentation-webpage' into 'development'

Resolve "more friendly output name of `add_strain()` or a better presentation in documentation webpage"

Closes #284

See merge request damask/DAMASK!770

python/damask/_result.py

@@ -1201,7 +1201,7 @@ def _add_strain(F: Dict[str, Any], t: Literal['V', 'U'], m: float) -> Dict[str,
  'label': f"epsilon_{t}^{m}({F['label']})",
  'meta': {
  'unit': F['meta']['unit'],
- 'description': f'strain tensor of order {m} based on {side} stretch tensor '+\
+ 'description': f'Seth-Hill strain tensor of order {m} based on {side} stretch tensor '+\
  f"of {F['label']} ({F['meta']['description']})",
  'creator': 'add_strain'
  }
@@ -1210,10 +1210,11 @@ def add_strain(self,
  F: str = 'F',
  t: Literal['V', 'U'] = 'V',
  m: float = 0.0):
- """
- Add strain tensor of a deformation gradient.
+ r"""
+ Add strain tensor (Seth-Hill family) of a deformation gradient.
 
- For details, see damask.mechanics.strain.
+ By default, the logarithmic strain based on the
+ left stretch tensor is added.
 
  Parameters
  ----------
@@ -1247,6 +1248,23 @@ def add_strain(self,
  spatial/Eulerian strain measures (based on 'V') for elastic strains
  when calculating averages.
 
+ The strain is defined as:
+
+ .. math::
+
+ m = 0 \\\\
+ \vb*{\epsilon}_V^{(0)} = \ln (\vb{V}) \\\\
+ \vb*{\epsilon}_U^{(0)} = \ln (\vb{U}) \\\\
+
+ m \neq 0 \\\\
+ \vb*{\epsilon}_V^{(m)} = \frac{1}{2m} (\vb{V}^{2m} - \vb{I}) \\\\
+ \vb*{\epsilon}_U^{(m)} = \frac{1}{2m} (\vb{U}^{2m} - \vb{I})
+
+ References
+ ----------
+ | https://en.wikipedia.org/wiki/Finite_strain_theory
+ | https://de.wikipedia.org/wiki/Verzerrungstensor
+
  """
  self._add_generic_pointwise(self._add_strain,{'F':F},{'t':t,'m':m})