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DAMASK_EICMD
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clearer names

This commit is contained in:
Martin Diehl 2020-03-02 23:11:05 +01:00
parent 4970f22e13
commit 15c3cab549
1 changed files with 49 additions and 48 deletions
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97
python/damask/mechanics.py
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@ -21,21 +21,21 @@ def Cauchy(P,F):
return symmetric(sigma) return symmetric(sigma)
def deviatoric_part(x): def deviatoric_part(T):
""" """
Return deviatoric part of a tensor. Return deviatoric part of a tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the deviatoric part is computed. Tensor of which the deviatoric part is computed.
""" """
return x - np.eye(3)*spherical_part(x) if np.shape(x) == (3,3) else \ return T - np.eye(3)*spherical_part(T) if np.shape(T) == (3,3) else \
x - np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),[x.shape[0],3,3]),spherical_part(x)) T - np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),[T.shape[0],3,3]),spherical_part(T))
def eigenvalues(x): def eigenvalues(T_sym):
""" """
Return the eigenvalues, i.e. principal components, of a symmetric tensor. Return the eigenvalues, i.e. principal components, of a symmetric tensor.
@ -44,14 +44,14 @@ def eigenvalues(x):
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T_sym : numpy.array of shape (:,3,3) or (3,3)
Symmetric tensor of which the eigenvalues are computed. Symmetric tensor of which the eigenvalues are computed.
""" """
return np.linalg.eigvalsh(symmetric(x)) return np.linalg.eigvalsh(symmetric(T_sym))
def eigenvectors(x,RHS=False): def eigenvectors(T_sym,RHS=False):
""" """
Return eigenvectors of a symmetric tensor. Return eigenvectors of a symmetric tensor.
@ -59,47 +59,47 @@ def eigenvectors(x,RHS=False):
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T_sym : numpy.array of shape (:,3,3) or (3,3)
Symmetric tensor of which the eigenvectors are computed. Symmetric tensor of which the eigenvectors are computed.
RHS: bool, optional RHS: bool, optional
Enforce right-handed coordinate system. Default is False. Enforce right-handed coordinate system. Default is False.
""" """
(u,v) = np.linalg.eigh(symmetric(x)) (u,v) = np.linalg.eigh(symmetric(T_sym))
if RHS: if RHS:
if np.shape(x) == (3,3): if np.shape(T_sym) == (3,3):
if np.linalg.det(v) < 0.0: v[:,2] *= -1.0 if np.linalg.det(v) < 0.0: v[:,2] *= -1.0
else: else:
v[np.linalg.det(v) < 0.0,:,2] *= -1.0 v[np.linalg.det(v) < 0.0,:,2] *= -1.0
return v return v
def left_stretch(x): def left_stretch(T):
""" """
Return the left stretch of a tensor. Return the left stretch of a tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the left stretch is computed. Tensor of which the left stretch is computed.
""" """
return __polar_decomposition(x,'V')[0] return __polar_decomposition(T,'V')[0]
def maximum_shear(x): def maximum_shear(T_sym):
""" """
Return the maximum shear component of a symmetric tensor. Return the maximum shear component of a symmetric tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T_sym : numpy.array of shape (:,3,3) or (3,3)
Symmetric tensor of which the maximum shear is computed. Symmetric tensor of which the maximum shear is computed.
""" """
w = eigenvalues(x) w = eigenvalues(T_sym)
return (w[0] - w[2])*0.5 if np.shape(x) == (3,3) else \ return (w[0] - w[2])*0.5 if np.shape(T_sym) == (3,3) else \
(w[:,0] - w[:,2])*0.5 (w[:,0] - w[:,2])*0.5
@ -147,53 +147,54 @@ def PK2(P,F):
S = np.einsum('ijk,ikl->ijl',np.linalg.inv(F),P) S = np.einsum('ijk,ikl->ijl',np.linalg.inv(F),P)
return symmetric(S) return symmetric(S)
def right_stretch(x):
def right_stretch(T):
""" """
Return the right stretch of a tensor. Return the right stretch of a tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the right stretch is computed. Tensor of which the right stretch is computed.
""" """
return __polar_decomposition(x,'U')[0] return __polar_decomposition(T,'U')[0]
def rotational_part(x): def rotational_part(T):
""" """
Return the rotational part of a tensor. Return the rotational part of a tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the rotational part is computed. Tensor of which the rotational part is computed.
""" """
return __polar_decomposition(x,'R')[0] return __polar_decomposition(T,'R')[0]
def spherical_part(x,tensor=False): def spherical_part(T,tensor=False):
""" """
Return spherical (hydrostatic) part of a tensor. Return spherical (hydrostatic) part of a tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the hydrostatic part is computed. Tensor of which the hydrostatic part is computed.
tensor : bool, optional tensor : bool, optional
Map spherical part onto identity tensor. Default is false Map spherical part onto identity tensor. Default is false
""" """
if x.shape == (3,3): if T.shape == (3,3):
sph = np.trace(x)/3.0 sph = np.trace(T)/3.0
return sph if not tensor else np.eye(3)*sph return sph if not tensor else np.eye(3)*sph
else: else:
sph = np.trace(x,axis1=1,axis2=2)/3.0 sph = np.trace(T,axis1=1,axis2=2)/3.0
if not tensor: if not tensor:
return sph return sph
else: else:
return np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),(x.shape[0],3,3)),sph) return np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),(T.shape[0],3,3)),sph)
def strain_tensor(F,t,m): def strain_tensor(F,t,m):
@ -234,73 +235,73 @@ def strain_tensor(F,t,m):
eps eps
def symmetric(x): def symmetric(T):
""" """
Return the symmetrized tensor. Return the symmetrized tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the symmetrized values are computed. Tensor of which the symmetrized values are computed.
""" """
return (x+transpose(x))*0.5 return (T+transpose(T))*0.5
def transpose(x): def transpose(T):
""" """
Return the transpose of a tensor. Return the transpose of a tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the transpose is computed. Tensor of which the transpose is computed.
""" """
return x.T if np.shape(x) == (3,3) else \ return T.T if np.shape(T) == (3,3) else \
np.transpose(x,(0,2,1)) np.transpose(T,(0,2,1))
def __polar_decomposition(x,requested): def __polar_decomposition(T,requested):
""" """
Singular value decomposition. Singular value decomposition.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T : numpy.array of shape (:,3,3) or (3,3)
Tensor of which the singular values are computed. Tensor of which the singular values are computed.
requested : iterable of str requested : iterable of str
Requested outputs: ‘R’ for the rotation tensor, Requested outputs: ‘R’ for the rotation tensor,
‘V’ for left stretch tensor and ‘U’ for right stretch tensor. ‘V’ for left stretch tensor and ‘U’ for right stretch tensor.
""" """
u, s, vh = np.linalg.svd(x) u, s, vh = np.linalg.svd(T)
R = np.dot(u,vh) if np.shape(x) == (3,3) else \ R = np.dot(u,vh) if np.shape(T) == (3,3) else \
np.einsum('ijk,ikl->ijl',u,vh) np.einsum('ijk,ikl->ijl',u,vh)
output = [] output = []
if 'R' in requested: if 'R' in requested:
output.append(R) output.append(R)
if 'V' in requested: if 'V' in requested:
output.append(np.dot(x,R.T) if np.shape(x) == (3,3) else np.einsum('ijk,ilk->ijl',x,R)) output.append(np.dot(T,R.T) if np.shape(T) == (3,3) else np.einsum('ijk,ilk->ijl',T,R))
if 'U' in requested: if 'U' in requested:
output.append(np.dot(R.T,x) if np.shape(x) == (3,3) else np.einsum('ikj,ikl->ijl',R,x)) output.append(np.dot(R.T,T) if np.shape(T) == (3,3) else np.einsum('ikj,ikl->ijl',R,T))
return tuple(output) return tuple(output)
def __Mises(x,s): def __Mises(T_sym,s):
""" """
Base equation for Mises equivalent of a stres or strain tensor. Base equation for Mises equivalent of a stres or strain tensor.
Parameters Parameters
---------- ----------
x : numpy.array of shape (:,3,3) or (3,3) T_sym : numpy.array of shape (:,3,3) or (3,3)
Symmetric tensor of which the von Mises equivalent is computed. Symmetric tensor of which the von Mises equivalent is computed.
s : float s : float
Scaling factor (2/3 for strain, 3/2 for stress). Scaling factor (2/3 for strain, 3/2 for stress).
""" """
d = deviatoric_part(x) d = deviatoric_part(T_sym)
return np.sqrt(s*(np.sum(d**2.0))) if np.shape(x) == (3,3) else \ return np.sqrt(s*(np.sum(d**2.0))) if np.shape(T_sym) == (3,3) else \
np.sqrt(s*np.einsum('ijk->i',d**2.0)) np.sqrt(s*np.einsum('ijk->i',d**2.0))