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switch to physics macros

This commit is contained in:
Philip Eisenlohr 2023-02-16 11:59:19 -05:00
parent 66b0b2e9dc
commit 61f2ae295b
1 changed files with 10 additions and 10 deletions
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20
python/damask/mechanics.py
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@ -65,11 +65,11 @@ def equivalent_strain_Mises(epsilon: _np.ndarray) -> _np.ndarray:
Notes
-----
The von Mises equivalent of a strain tensor is defined as:
The von Mises equivalent of a deviatoric strain tensor is defined as:
.. math::
\epsilon_{\mathrm{vM}} = \sqrt{2/3 \epsilon_{ij}' \epsilon_{ij}'}
\epsilon_\text{vM} = \sqrt{2/3 \epsilon^\prime_{ij} \epsilon^\prime_{ij}}
"""
return _equivalent_Mises(epsilon,2.0/3.0)
@ -91,11 +91,11 @@ def equivalent_stress_Mises(sigma: _np.ndarray) -> _np.ndarray:
Notes
-----
The von Mises equivalent of a stress tensor is defined as:
The von Mises equivalent of a deviatoric stress tensor is defined as:
.. math::
\sigma_{\mathrm{vM}} = \sqrt{3/2 \sigma_{ij}' \sigma_{ij}'}
\sigma_\text{vM} = \sqrt{3/2 \sigma^\prime_{ij} \sigma^\prime_{ij}}
"""
return _equivalent_Mises(sigma,3.0/2.0)
@ -140,9 +140,9 @@ def rotation(T: _np.ndarray) -> _rotation.Rotation:
.. math::
\mathbf{R} = \mathbf{T} \mathbf{U}^{-1} = \mathbf{V}^{-1} \mathbf{T}
\vb{R} = \vb{T} \vb{U}^{-1} = \vb{V}^{-1} \vb{T}
where :math:`\mathbf{V}` and :math:`\mathbf{U}` are left
where :math:`\vb{V}` and :math:`\vb{U}` are left
and right stretch tensor, respectively.
"""
@ -259,9 +259,9 @@ def stretch_left(T: _np.ndarray) -> _np.ndarray:
.. math::
\mathbf{V} = \mathbf{T} \mathbf{R}^\mathrm{T}
\vb{V} = \vb{T} \vb{R}^\text{T}
where :math:`\mathbf{R}` is a rotation.
where :math:`\vb{R}` is a rotation.
"""
return _polar_decomposition(T,'V')[0]
@ -288,9 +288,9 @@ def stretch_right(T: _np.ndarray) -> _np.ndarray:
.. math::
\mathbf{U} = \mathbf{R}^\mathrm{T} \mathbf{T}
\vb{U} = \vb{R}^\text{T} \vb{T}
where :math:`\mathbf{R}` is a rotation.
where :math:`\vb{R}` is a rotation.
"""
return _polar_decomposition(T,'U')[0]