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shorter calculation of Seth–Hill strains

This commit is contained in:
Philip Eisenlohr 2023-02-20 14:42:31 -05:00
parent bcab153b94
commit 6aa566760f
1 changed files with 7 additions and 16 deletions
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23
python/damask/mechanics.py
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@ -177,9 +177,9 @@ def strain(F: _np.ndarray,
---------- ----------
F : numpy.ndarray, shape (...,3,3) F : numpy.ndarray, shape (...,3,3)
Deformation gradient. Deformation gradient.
t : {‘V’, ‘U’} t : {'V', 'U'}
Type of the polar decomposition, ‘V’ for left stretch tensor Type of the polar decomposition, 'V' for left stretch tensor
and ‘U’ for right stretch tensor. or 'U' for right stretch tensor.
m : float m : float
Order of the strain. Order of the strain.
@ -194,19 +194,10 @@ def strain(F: _np.ndarray,
https://de.wikipedia.org/wiki/Verzerrungstensor https://de.wikipedia.org/wiki/Verzerrungstensor
""" """
if t == 'V': if t not in ['V', 'U']: raise ValueError('polar decomposition type not in {V, U}')
w,n = _np.linalg.eigh(deformation_Cauchy_Green_left(F)) w,n = _np.linalg.eigh(deformation_Cauchy_Green_left(F) if t=='V' else deformation_Cauchy_Green_right(F))
elif t == 'U': return 0.5 * _np.einsum('...j,...kj,...lj',_np.log(w),n,n) if m == 0.0 \
w,n = _np.linalg.eigh(deformation_Cauchy_Green_right(F)) else 0.5/m * (_np.einsum('...j,...kj,...lj', w**m,n,n) - _np.eye(3))
if m > 0.0:
eps = 1.0/(2.0*abs(m)) * (+ _np.einsum('...j,...kj,...lj',w**m,n,n) - _np.eye(3))
elif m < 0.0:
eps = 1.0/(2.0*abs(m)) * (- _np.einsum('...j,...kj,...lj',w**m,n,n) + _np.eye(3))
else:
eps = _np.einsum('...j,...kj,...lj',0.5*_np.log(w),n,n)
return eps
def stress_Cauchy(P: _np.ndarray, def stress_Cauchy(P: _np.ndarray,