import numpy as np
from Elasticipy.SecondOrderTensor import SecondOrderTensor
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class StrainTensor(SecondOrderTensor):
"""
Class for manipulating symmetric strain tensors or arrays of symmetric strain tensors.
"""
name = 'Strain tensor'
voigt_map = [1, 1, 1, 2, 2, 2]
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def principalStrains(self):
"""
Values of the principals strains.
If the tensor array is of shape [m,n,...], the results will be of shape [m,n,...,3].
Returns
-------
np.ndarray
Principal strain values
"""
return self.eig()[0]
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def volumetricStrain(self):
"""
Volumetric change (1st invariant of the strain tensor)
Returns
-------
np.array or float
Volumetric change
"""
return self.I1
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class StressTensor(SecondOrderTensor):
"""
Class for manipulating stress tensors or arrays of stress tensors.
"""
name = 'Stress tensor'
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def principalStresses(self):
"""
Values of the principals stresses.
If the tensor array is of shape [m,n,...], the results will be of shape [m,n,...,3].
Returns
-------
np.ndarray
Principal stresses
"""
return np.real(self.eig()[0])
@property
def J1(self):
"""
First invariant of the deviatoric part of the stress tensor. It is always zeros, as the deviatoric part as null
trace.
Returns
-------
float or np.ndarray
zero(s)
"""
if self.shape:
return np.zeros(self.shape)
else:
return 0.0
@property
def J2(self):
"""
Second invariant of the deviatoric part of the stress tensor.
Returns
-------
float or np.ndarray
J2 invariant
"""
return -self.deviatoricPart().I2
@property
def J3(self):
"""
Third invariant of the deviatoric part of the stress tensor.
Returns
-------
float or np.ndarray
J3 invariant
"""
return self.deviatoricPart().I3
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def vonMises(self):
"""
von Mises equivalent stress.
Returns
-------
np.ndarray or float
von Mises equivalent stress
See Also
--------
Tresca : Tresca equivalent stress
"""
return np.sqrt(3 * self.J2)
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def Tresca(self):
"""
Tresca(-Guest) equivalent stress.
Returns
-------
np.ndarray or float
Tresca equivalent stress
See Also
--------
vonMises : von Mises equivalent stress
"""
ps = self.principalStresses()
return np.max(ps, axis=-1) - np.min(ps, axis=-1)
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def hydrostaticPressure(self):
"""
Hydrostatic pressure
Returns
-------
np.ndarray or float
See Also
--------
sphericalPart : spherical part of the stress
"""
return -self.I1/3