Elasticipy 1.0.3

Collection of tools to work on strain, stress and stiffness tensors, with plotting features

Elasticipy

A python toolkit to manipulate elastic constants of materials. This package also provides a collection of easy-to-use and very fast tools to work on stress and strain tensors.

Basic examples

Working with stiffness tensor

First, create a stiffness tensor, taking into account the material symmetry:

 from Elasticipy.FourthOrderTensor import tensorFromCrystalSymmetry
 
 C = tensorFromCrystalSymmetry(symmetry='cubic', phase_name='ferrite'
                              C11=274, C12=175, C44=89)

Plot the directional Young moduli:

C.Young_modulus.plot()

Evaluate its mean value:

C.Young_modulus.mean()

Evaluate the shear modulus with respect to x and y:

C.shear_modulus.eval([1,0,0], [0,1,0])

Working with stress/strain tensors

import numpy as np
from Elasticipy.StressStrainTensors import StressTensor

First, let's create an array of stresses:

n_slices = 10
sigma = np.zeros((n_slices, 3, 3))
sigma[:, 1, 1] = np.linspace(0, 1, n_slices)
sigma = StressTensor(sigma)     # Convert it to stress

Now compute the strain:

eps = C.inv()*sigma

Check that the strain is of the same shape as the stress:

print(eps.shape)

Check out the von Mises equivalent stresses:

print(sigma.vonMises())

Let's apply a set of 1000 random rotations to the stiffness:

from scipy.spatial.transform import Rotation

orientations = Rotation.random(1000)
C_rotated = C*orientations

Now check the corresponding strains:

eps_rotated = C_rotated.inv()*sigma

See the shape of the results:

print(eps_rotated.shape)

Just to be sure, look at a particular value of eps_rotated:

print(eps_rotated[0,-1])

Evaluate the mean strain values over all orientations

eps_mean = eps_rotated.mean(axis=0)

Actually, a more direct method is to compute the Reuss average of stiffness tensor:

Creuss = C.Reuss_average(orientations=orientations)

Then compute the corresponding strain:

eps_reuss = Creuss.inv()*sigma

You can check that both the approaches are consistent:

np.all(np.isclose(eps_mean.matrix,eps_reuss.matrix))